Cryo Explorer Ethereum Mainnet

// SPDX-License-Identifier: BUSL-1.1
pragma solidity ^0.8.28;

import { UUPSUpgradeable } from "@openzeppelin/contracts-upgradeable/proxy/utils/UUPSUpgradeable.sol";
import { ERC1155Upgradeable } from "@openzeppelin/contracts-upgradeable/token/ERC1155/ERC1155Upgradeable.sol";
import { PausableUpgradeable } from "@openzeppelin/contracts-upgradeable/utils/PausableUpgradeable.sol";
import { MerkleProof } from "@openzeppelin/contracts/utils/cryptography/MerkleProof.sol";

import { Access } from "../access/Access.sol";
import { ISoulboundERC1155Merkle } from "../interfaces/ISoulboundERC1155Merkle.sol";
import { SoulboundERC1155MerkleStorageUtils } from "../storage/SoulboundERC1155MerkleStorageUtils.sol";

/// @title SoulboundERC1155Merkle
/// @author kexley, Cap Labs
/// @notice Soulbound ERC1155 with Merkle proofs for minting
/// @dev Admin must set the Merkle root and unpause to enable public minting. Hashed user addresses are used as leaves in the Merkle tree.
/// Once an address owns a token, it is soulbound and cannot be transferred. Only one token per address can be minted.
contract SoulboundERC1155Merkle is
    ISoulboundERC1155Merkle,
    UUPSUpgradeable,
    ERC1155Upgradeable,
    PausableUpgradeable,
    Access,
    SoulboundERC1155MerkleStorageUtils
{
    /// @custom:oz-upgrades-unsafe-allow constructor
    constructor() {
        _disableInitializers();
    }

    /// @inheritdoc ISoulboundERC1155Merkle
    function initialize(address _accessControl, string calldata _uri) external initializer {
        if (_accessControl == address(0)) revert ZeroAddressNotValid();
        __Access_init(_accessControl);
        __ERC1155_init(_uri);
        __Pausable_init();
        __UUPSUpgradeable_init();
        _pause(); // pause public minting by default
    }

    /// @inheritdoc ISoulboundERC1155Merkle
    function mint(address _to, bytes32[] calldata _proofs) external whenNotPaused {
        if (balanceOf(_to, 0) > 0) revert AlreadyMinted();
        bytes32 leaf = keccak256(bytes.concat(keccak256(abi.encode(_to))));
        if (!MerkleProof.verifyCalldata(_proofs, getSoulboundERC1155MerkleStorage().root, leaf)) revert InvalidProof();
        _mint(_to, 0, 1, "");
    }

    /// @inheritdoc ISoulboundERC1155Merkle
    function ownerMint(address[] calldata _to) external checkAccess(this.ownerMint.selector) {
        for (uint256 i = 0; i < _to.length; i++) {
            if (balanceOf(_to[i], 0) > 0) revert AlreadyMinted();
            _mint(_to[i], 0, 1, "");
        }
    }

    /// @inheritdoc ISoulboundERC1155Merkle
    function setRoot(bytes32 _root) external checkAccess(this.setRoot.selector) {
        getSoulboundERC1155MerkleStorage().root = _root;
        emit SetRoot(_root);
    }

    /// @inheritdoc ISoulboundERC1155Merkle
    function setURI(string calldata _uri) external checkAccess(this.setURI.selector) {
        _setURI(_uri);
        emit SetURI(_uri);
    }

    /// @inheritdoc ISoulboundERC1155Merkle
    function pause() external checkAccess(this.pause.selector) {
        _pause();
    }

    /// @inheritdoc ISoulboundERC1155Merkle
    function unpause() external checkAccess(this.unpause.selector) {
        _unpause();
    }

    /// @inheritdoc ISoulboundERC1155Merkle
    function root() external view returns (bytes32) {
        return getSoulboundERC1155MerkleStorage().root;
    }

    /// @dev Override to prevent transfers after minting
    /// @param _from Sender address
    /// @param _to Receiver address
    /// @param _ids Token IDs to transfer
    /// @param _values Amounts of tokens to transfer
    function _update(address _from, address _to, uint256[] memory _ids, uint256[] memory _values) internal override {
        if (_from != address(0)) revert Soulbound(); // only minting is allowed
        super._update(_from, _to, _ids, _values);
    }

    /// @inheritdoc UUPSUpgradeable
    function _authorizeUpgrade(address) internal view override checkAccess(bytes4(0)) { }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.3.0) (proxy/utils/UUPSUpgradeable.sol)

pragma solidity ^0.8.22;

import {IERC1822Proxiable} from "@openzeppelin/contracts/interfaces/draft-IERC1822.sol";
import {ERC1967Utils} from "@openzeppelin/contracts/proxy/ERC1967/ERC1967Utils.sol";
import {Initializable} from "./Initializable.sol";

/**
 * @dev An upgradeability mechanism designed for UUPS proxies. The functions included here can perform an upgrade of an
 * {ERC1967Proxy}, when this contract is set as the implementation behind such a proxy.
 *
 * A security mechanism ensures that an upgrade does not turn off upgradeability accidentally, although this risk is
 * reinstated if the upgrade retains upgradeability but removes the security mechanism, e.g. by replacing
 * `UUPSUpgradeable` with a custom implementation of upgrades.
 *
 * The {_authorizeUpgrade} function must be overridden to include access restriction to the upgrade mechanism.
 */
abstract contract UUPSUpgradeable is Initializable, IERC1822Proxiable {
    /// @custom:oz-upgrades-unsafe-allow state-variable-immutable
    address private immutable __self = address(this);

    /**
     * @dev The version of the upgrade interface of the contract. If this getter is missing, both `upgradeTo(address)`
     * and `upgradeToAndCall(address,bytes)` are present, and `upgradeTo` must be used if no function should be called,
     * while `upgradeToAndCall` will invoke the `receive` function if the second argument is the empty byte string.
     * If the getter returns `"5.0.0"`, only `upgradeToAndCall(address,bytes)` is present, and the second argument must
     * be the empty byte string if no function should be called, making it impossible to invoke the `receive` function
     * during an upgrade.
     */
    string public constant UPGRADE_INTERFACE_VERSION = "5.0.0";

    /**
     * @dev The call is from an unauthorized context.
     */
    error UUPSUnauthorizedCallContext();

    /**
     * @dev The storage `slot` is unsupported as a UUID.
     */
    error UUPSUnsupportedProxiableUUID(bytes32 slot);

    /**
     * @dev Check that the execution is being performed through a delegatecall call and that the execution context is
     * a proxy contract with an implementation (as defined in ERC-1967) pointing to self. This should only be the case
     * for UUPS and transparent proxies that are using the current contract as their implementation. Execution of a
     * function through ERC-1167 minimal proxies (clones) would not normally pass this test, but is not guaranteed to
     * fail.
     */
    modifier onlyProxy() {
        _checkProxy();
        _;
    }

    /**
     * @dev Check that the execution is not being performed through a delegate call. This allows a function to be
     * callable on the implementing contract but not through proxies.
     */
    modifier notDelegated() {
        _checkNotDelegated();
        _;
    }

    function __UUPSUpgradeable_init() internal onlyInitializing {
    }

    function __UUPSUpgradeable_init_unchained() internal onlyInitializing {
    }
    /**
     * @dev Implementation of the ERC-1822 {proxiableUUID} function. This returns the storage slot used by the
     * implementation. It is used to validate the implementation's compatibility when performing an upgrade.
     *
     * IMPORTANT: A proxy pointing at a proxiable contract should not be considered proxiable itself, because this risks
     * bricking a proxy that upgrades to it, by delegating to itself until out of gas. Thus it is critical that this
     * function revert if invoked through a proxy. This is guaranteed by the `notDelegated` modifier.
     */
    function proxiableUUID() external view virtual notDelegated returns (bytes32) {
        return ERC1967Utils.IMPLEMENTATION_SLOT;
    }

    /**
     * @dev Upgrade the implementation of the proxy to `newImplementation`, and subsequently execute the function call
     * encoded in `data`.
     *
     * Calls {_authorizeUpgrade}.
     *
     * Emits an {Upgraded} event.
     *
     * @custom:oz-upgrades-unsafe-allow-reachable delegatecall
     */
    function upgradeToAndCall(address newImplementation, bytes memory data) public payable virtual onlyProxy {
        _authorizeUpgrade(newImplementation);
        _upgradeToAndCallUUPS(newImplementation, data);
    }

    /**
     * @dev Reverts if the execution is not performed via delegatecall or the execution
     * context is not of a proxy with an ERC-1967 compliant implementation pointing to self.
     */
    function _checkProxy() internal view virtual {
        if (
            address(this) == __self || // Must be called through delegatecall
            ERC1967Utils.getImplementation() != __self // Must be called through an active proxy
        ) {
            revert UUPSUnauthorizedCallContext();
        }
    }

    /**
     * @dev Reverts if the execution is performed via delegatecall.
     * See {notDelegated}.
     */
    function _checkNotDelegated() internal view virtual {
        if (address(this) != __self) {
            // Must not be called through delegatecall
            revert UUPSUnauthorizedCallContext();
        }
    }

    /**
     * @dev Function that should revert when `msg.sender` is not authorized to upgrade the contract. Called by
     * {upgradeToAndCall}.
     *
     * Normally, this function will use an xref:access.adoc[access control] modifier such as {Ownable-onlyOwner}.
     *
     * ```solidity
     * function _authorizeUpgrade(address) internal onlyOwner {}
     * ```
     */
    function _authorizeUpgrade(address newImplementation) internal virtual;

    /**
     * @dev Performs an implementation upgrade with a security check for UUPS proxies, and additional setup call.
     *
     * As a security check, {proxiableUUID} is invoked in the new implementation, and the return value
     * is expected to be the implementation slot in ERC-1967.
     *
     * Emits an {IERC1967-Upgraded} event.
     */
    function _upgradeToAndCallUUPS(address newImplementation, bytes memory data) private {
        try IERC1822Proxiable(newImplementation).proxiableUUID() returns (bytes32 slot) {
            if (slot != ERC1967Utils.IMPLEMENTATION_SLOT) {
                revert UUPSUnsupportedProxiableUUID(slot);
            }
            ERC1967Utils.upgradeToAndCall(newImplementation, data);
        } catch {
            // The implementation is not UUPS
            revert ERC1967Utils.ERC1967InvalidImplementation(newImplementation);
        }
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.1.0) (token/ERC1155/ERC1155.sol)

pragma solidity ^0.8.20;

import {IERC1155} from "@openzeppelin/contracts/token/ERC1155/IERC1155.sol";
import {IERC1155MetadataURI} from "@openzeppelin/contracts/token/ERC1155/extensions/IERC1155MetadataURI.sol";
import {ERC1155Utils} from "@openzeppelin/contracts/token/ERC1155/utils/ERC1155Utils.sol";
import {ContextUpgradeable} from "../../utils/ContextUpgradeable.sol";
import {IERC165} from "@openzeppelin/contracts/utils/introspection/IERC165.sol";
import {ERC165Upgradeable} from "../../utils/introspection/ERC165Upgradeable.sol";
import {Arrays} from "@openzeppelin/contracts/utils/Arrays.sol";
import {IERC1155Errors} from "@openzeppelin/contracts/interfaces/draft-IERC6093.sol";
import {Initializable} from "../../proxy/utils/Initializable.sol";

/**
 * @dev Implementation of the basic standard multi-token.
 * See https://eips.ethereum.org/EIPS/eip-1155
 * Originally based on code by Enjin: https://github.com/enjin/erc-1155
 */
abstract contract ERC1155Upgradeable is Initializable, ContextUpgradeable, ERC165Upgradeable, IERC1155, IERC1155MetadataURI, IERC1155Errors {
    using Arrays for uint256[];
    using Arrays for address[];

    /// @custom:storage-location erc7201:openzeppelin.storage.ERC1155
    struct ERC1155Storage {
        mapping(uint256 id => mapping(address account => uint256)) _balances;

        mapping(address account => mapping(address operator => bool)) _operatorApprovals;

        // Used as the URI for all token types by relying on ID substitution, e.g. https://token-cdn-domain/{id}.json
        string _uri;
    }

    // keccak256(abi.encode(uint256(keccak256("openzeppelin.storage.ERC1155")) - 1)) & ~bytes32(uint256(0xff))
    bytes32 private constant ERC1155StorageLocation = 0x88be536d5240c274a3b1d3a1be54482fd9caa294f08c62a7cde569f49a3c4500;

    function _getERC1155Storage() private pure returns (ERC1155Storage storage $) {
        assembly {
            $.slot := ERC1155StorageLocation
        }
    }

    /**
     * @dev See {_setURI}.
     */
    function __ERC1155_init(string memory uri_) internal onlyInitializing {
        __ERC1155_init_unchained(uri_);
    }

    function __ERC1155_init_unchained(string memory uri_) internal onlyInitializing {
        _setURI(uri_);
    }

    /**
     * @dev See {IERC165-supportsInterface}.
     */
    function supportsInterface(bytes4 interfaceId) public view virtual override(ERC165Upgradeable, IERC165) returns (bool) {
        return
            interfaceId == type(IERC1155).interfaceId ||
            interfaceId == type(IERC1155MetadataURI).interfaceId ||
            super.supportsInterface(interfaceId);
    }

    /**
     * @dev See {IERC1155MetadataURI-uri}.
     *
     * This implementation returns the same URI for *all* token types. It relies
     * on the token type ID substitution mechanism
     * https://eips.ethereum.org/EIPS/eip-1155#metadata[defined in the ERC].
     *
     * Clients calling this function must replace the `\{id\}` substring with the
     * actual token type ID.
     */
    function uri(uint256 /* id */) public view virtual returns (string memory) {
        ERC1155Storage storage $ = _getERC1155Storage();
        return $._uri;
    }

    /**
     * @dev See {IERC1155-balanceOf}.
     */
    function balanceOf(address account, uint256 id) public view virtual returns (uint256) {
        ERC1155Storage storage $ = _getERC1155Storage();
        return $._balances[id][account];
    }

    /**
     * @dev See {IERC1155-balanceOfBatch}.
     *
     * Requirements:
     *
     * - `accounts` and `ids` must have the same length.
     */
    function balanceOfBatch(
        address[] memory accounts,
        uint256[] memory ids
    ) public view virtual returns (uint256[] memory) {
        if (accounts.length != ids.length) {
            revert ERC1155InvalidArrayLength(ids.length, accounts.length);
        }

        uint256[] memory batchBalances = new uint256[](accounts.length);

        for (uint256 i = 0; i < accounts.length; ++i) {
            batchBalances[i] = balanceOf(accounts.unsafeMemoryAccess(i), ids.unsafeMemoryAccess(i));
        }

        return batchBalances;
    }

    /**
     * @dev See {IERC1155-setApprovalForAll}.
     */
    function setApprovalForAll(address operator, bool approved) public virtual {
        _setApprovalForAll(_msgSender(), operator, approved);
    }

    /**
     * @dev See {IERC1155-isApprovedForAll}.
     */
    function isApprovedForAll(address account, address operator) public view virtual returns (bool) {
        ERC1155Storage storage $ = _getERC1155Storage();
        return $._operatorApprovals[account][operator];
    }

    /**
     * @dev See {IERC1155-safeTransferFrom}.
     */
    function safeTransferFrom(address from, address to, uint256 id, uint256 value, bytes memory data) public virtual {
        address sender = _msgSender();
        if (from != sender && !isApprovedForAll(from, sender)) {
            revert ERC1155MissingApprovalForAll(sender, from);
        }
        _safeTransferFrom(from, to, id, value, data);
    }

    /**
     * @dev See {IERC1155-safeBatchTransferFrom}.
     */
    function safeBatchTransferFrom(
        address from,
        address to,
        uint256[] memory ids,
        uint256[] memory values,
        bytes memory data
    ) public virtual {
        address sender = _msgSender();
        if (from != sender && !isApprovedForAll(from, sender)) {
            revert ERC1155MissingApprovalForAll(sender, from);
        }
        _safeBatchTransferFrom(from, to, ids, values, data);
    }

    /**
     * @dev Transfers a `value` amount of tokens of type `id` from `from` to `to`. Will mint (or burn) if `from`
     * (or `to`) is the zero address.
     *
     * Emits a {TransferSingle} event if the arrays contain one element, and {TransferBatch} otherwise.
     *
     * Requirements:
     *
     * - If `to` refers to a smart contract, it must implement either {IERC1155Receiver-onERC1155Received}
     *   or {IERC1155Receiver-onERC1155BatchReceived} and return the acceptance magic value.
     * - `ids` and `values` must have the same length.
     *
     * NOTE: The ERC-1155 acceptance check is not performed in this function. See {_updateWithAcceptanceCheck} instead.
     */
    function _update(address from, address to, uint256[] memory ids, uint256[] memory values) internal virtual {
        ERC1155Storage storage $ = _getERC1155Storage();
        if (ids.length != values.length) {
            revert ERC1155InvalidArrayLength(ids.length, values.length);
        }

        address operator = _msgSender();

        for (uint256 i = 0; i < ids.length; ++i) {
            uint256 id = ids.unsafeMemoryAccess(i);
            uint256 value = values.unsafeMemoryAccess(i);

            if (from != address(0)) {
                uint256 fromBalance = $._balances[id][from];
                if (fromBalance < value) {
                    revert ERC1155InsufficientBalance(from, fromBalance, value, id);
                }
                unchecked {
                    // Overflow not possible: value <= fromBalance
                    $._balances[id][from] = fromBalance - value;
                }
            }

            if (to != address(0)) {
                $._balances[id][to] += value;
            }
        }

        if (ids.length == 1) {
            uint256 id = ids.unsafeMemoryAccess(0);
            uint256 value = values.unsafeMemoryAccess(0);
            emit TransferSingle(operator, from, to, id, value);
        } else {
            emit TransferBatch(operator, from, to, ids, values);
        }
    }

    /**
     * @dev Version of {_update} that performs the token acceptance check by calling
     * {IERC1155Receiver-onERC1155Received} or {IERC1155Receiver-onERC1155BatchReceived} on the receiver address if it
     * contains code (eg. is a smart contract at the moment of execution).
     *
     * IMPORTANT: Overriding this function is discouraged because it poses a reentrancy risk from the receiver. So any
     * update to the contract state after this function would break the check-effect-interaction pattern. Consider
     * overriding {_update} instead.
     */
    function _updateWithAcceptanceCheck(
        address from,
        address to,
        uint256[] memory ids,
        uint256[] memory values,
        bytes memory data
    ) internal virtual {
        _update(from, to, ids, values);
        if (to != address(0)) {
            address operator = _msgSender();
            if (ids.length == 1) {
                uint256 id = ids.unsafeMemoryAccess(0);
                uint256 value = values.unsafeMemoryAccess(0);
                ERC1155Utils.checkOnERC1155Received(operator, from, to, id, value, data);
            } else {
                ERC1155Utils.checkOnERC1155BatchReceived(operator, from, to, ids, values, data);
            }
        }
    }

    /**
     * @dev Transfers a `value` tokens of token type `id` from `from` to `to`.
     *
     * Emits a {TransferSingle} event.
     *
     * Requirements:
     *
     * - `to` cannot be the zero address.
     * - `from` must have a balance of tokens of type `id` of at least `value` amount.
     * - If `to` refers to a smart contract, it must implement {IERC1155Receiver-onERC1155Received} and return the
     * acceptance magic value.
     */
    function _safeTransferFrom(address from, address to, uint256 id, uint256 value, bytes memory data) internal {
        if (to == address(0)) {
            revert ERC1155InvalidReceiver(address(0));
        }
        if (from == address(0)) {
            revert ERC1155InvalidSender(address(0));
        }
        (uint256[] memory ids, uint256[] memory values) = _asSingletonArrays(id, value);
        _updateWithAcceptanceCheck(from, to, ids, values, data);
    }

    /**
     * @dev xref:ROOT:erc1155.adoc#batch-operations[Batched] version of {_safeTransferFrom}.
     *
     * Emits a {TransferBatch} event.
     *
     * Requirements:
     *
     * - If `to` refers to a smart contract, it must implement {IERC1155Receiver-onERC1155BatchReceived} and return the
     * acceptance magic value.
     * - `ids` and `values` must have the same length.
     */
    function _safeBatchTransferFrom(
        address from,
        address to,
        uint256[] memory ids,
        uint256[] memory values,
        bytes memory data
    ) internal {
        if (to == address(0)) {
            revert ERC1155InvalidReceiver(address(0));
        }
        if (from == address(0)) {
            revert ERC1155InvalidSender(address(0));
        }
        _updateWithAcceptanceCheck(from, to, ids, values, data);
    }

    /**
     * @dev Sets a new URI for all token types, by relying on the token type ID
     * substitution mechanism
     * https://eips.ethereum.org/EIPS/eip-1155#metadata[defined in the ERC].
     *
     * By this mechanism, any occurrence of the `\{id\}` substring in either the
     * URI or any of the values in the JSON file at said URI will be replaced by
     * clients with the token type ID.
     *
     * For example, the `https://token-cdn-domain/\{id\}.json` URI would be
     * interpreted by clients as
     * `https://token-cdn-domain/000000000000000000000000000000000000000000000000000000000004cce0.json`
     * for token type ID 0x4cce0.
     *
     * See {uri}.
     *
     * Because these URIs cannot be meaningfully represented by the {URI} event,
     * this function emits no events.
     */
    function _setURI(string memory newuri) internal virtual {
        ERC1155Storage storage $ = _getERC1155Storage();
        $._uri = newuri;
    }

    /**
     * @dev Creates a `value` amount of tokens of type `id`, and assigns them to `to`.
     *
     * Emits a {TransferSingle} event.
     *
     * Requirements:
     *
     * - `to` cannot be the zero address.
     * - If `to` refers to a smart contract, it must implement {IERC1155Receiver-onERC1155Received} and return the
     * acceptance magic value.
     */
    function _mint(address to, uint256 id, uint256 value, bytes memory data) internal {
        if (to == address(0)) {
            revert ERC1155InvalidReceiver(address(0));
        }
        (uint256[] memory ids, uint256[] memory values) = _asSingletonArrays(id, value);
        _updateWithAcceptanceCheck(address(0), to, ids, values, data);
    }

    /**
     * @dev xref:ROOT:erc1155.adoc#batch-operations[Batched] version of {_mint}.
     *
     * Emits a {TransferBatch} event.
     *
     * Requirements:
     *
     * - `ids` and `values` must have the same length.
     * - `to` cannot be the zero address.
     * - If `to` refers to a smart contract, it must implement {IERC1155Receiver-onERC1155BatchReceived} and return the
     * acceptance magic value.
     */
    function _mintBatch(address to, uint256[] memory ids, uint256[] memory values, bytes memory data) internal {
        if (to == address(0)) {
            revert ERC1155InvalidReceiver(address(0));
        }
        _updateWithAcceptanceCheck(address(0), to, ids, values, data);
    }

    /**
     * @dev Destroys a `value` amount of tokens of type `id` from `from`
     *
     * Emits a {TransferSingle} event.
     *
     * Requirements:
     *
     * - `from` cannot be the zero address.
     * - `from` must have at least `value` amount of tokens of type `id`.
     */
    function _burn(address from, uint256 id, uint256 value) internal {
        if (from == address(0)) {
            revert ERC1155InvalidSender(address(0));
        }
        (uint256[] memory ids, uint256[] memory values) = _asSingletonArrays(id, value);
        _updateWithAcceptanceCheck(from, address(0), ids, values, "");
    }

    /**
     * @dev xref:ROOT:erc1155.adoc#batch-operations[Batched] version of {_burn}.
     *
     * Emits a {TransferBatch} event.
     *
     * Requirements:
     *
     * - `from` cannot be the zero address.
     * - `from` must have at least `value` amount of tokens of type `id`.
     * - `ids` and `values` must have the same length.
     */
    function _burnBatch(address from, uint256[] memory ids, uint256[] memory values) internal {
        if (from == address(0)) {
            revert ERC1155InvalidSender(address(0));
        }
        _updateWithAcceptanceCheck(from, address(0), ids, values, "");
    }

    /**
     * @dev Approve `operator` to operate on all of `owner` tokens
     *
     * Emits an {ApprovalForAll} event.
     *
     * Requirements:
     *
     * - `operator` cannot be the zero address.
     */
    function _setApprovalForAll(address owner, address operator, bool approved) internal virtual {
        ERC1155Storage storage $ = _getERC1155Storage();
        if (operator == address(0)) {
            revert ERC1155InvalidOperator(address(0));
        }
        $._operatorApprovals[owner][operator] = approved;
        emit ApprovalForAll(owner, operator, approved);
    }

    /**
     * @dev Creates an array in memory with only one value for each of the elements provided.
     */
    function _asSingletonArrays(
        uint256 element1,
        uint256 element2
    ) private pure returns (uint256[] memory array1, uint256[] memory array2) {
        assembly ("memory-safe") {
            // Load the free memory pointer
            array1 := mload(0x40)
            // Set array length to 1
            mstore(array1, 1)
            // Store the single element at the next word after the length (where content starts)
            mstore(add(array1, 0x20), element1)

            // Repeat for next array locating it right after the first array
            array2 := add(array1, 0x40)
            mstore(array2, 1)
            mstore(add(array2, 0x20), element2)

            // Update the free memory pointer by pointing after the second array
            mstore(0x40, add(array2, 0x40))
        }
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.3.0) (utils/Pausable.sol)

pragma solidity ^0.8.20;

import {ContextUpgradeable} from "../utils/ContextUpgradeable.sol";
import {Initializable} from "../proxy/utils/Initializable.sol";

/**
 * @dev Contract module which allows children to implement an emergency stop
 * mechanism that can be triggered by an authorized account.
 *
 * This module is used through inheritance. It will make available the
 * modifiers `whenNotPaused` and `whenPaused`, which can be applied to
 * the functions of your contract. Note that they will not be pausable by
 * simply including this module, only once the modifiers are put in place.
 */
abstract contract PausableUpgradeable is Initializable, ContextUpgradeable {
    /// @custom:storage-location erc7201:openzeppelin.storage.Pausable
    struct PausableStorage {
        bool _paused;
    }

    // keccak256(abi.encode(uint256(keccak256("openzeppelin.storage.Pausable")) - 1)) & ~bytes32(uint256(0xff))
    bytes32 private constant PausableStorageLocation = 0xcd5ed15c6e187e77e9aee88184c21f4f2182ab5827cb3b7e07fbedcd63f03300;

    function _getPausableStorage() private pure returns (PausableStorage storage $) {
        assembly {
            $.slot := PausableStorageLocation
        }
    }

    /**
     * @dev Emitted when the pause is triggered by `account`.
     */
    event Paused(address account);

    /**
     * @dev Emitted when the pause is lifted by `account`.
     */
    event Unpaused(address account);

    /**
     * @dev The operation failed because the contract is paused.
     */
    error EnforcedPause();

    /**
     * @dev The operation failed because the contract is not paused.
     */
    error ExpectedPause();

    /**
     * @dev Modifier to make a function callable only when the contract is not paused.
     *
     * Requirements:
     *
     * - The contract must not be paused.
     */
    modifier whenNotPaused() {
        _requireNotPaused();
        _;
    }

    /**
     * @dev Modifier to make a function callable only when the contract is paused.
     *
     * Requirements:
     *
     * - The contract must be paused.
     */
    modifier whenPaused() {
        _requirePaused();
        _;
    }

    function __Pausable_init() internal onlyInitializing {
    }

    function __Pausable_init_unchained() internal onlyInitializing {
    }
    /**
     * @dev Returns true if the contract is paused, and false otherwise.
     */
    function paused() public view virtual returns (bool) {
        PausableStorage storage $ = _getPausableStorage();
        return $._paused;
    }

    /**
     * @dev Throws if the contract is paused.
     */
    function _requireNotPaused() internal view virtual {
        if (paused()) {
            revert EnforcedPause();
        }
    }

    /**
     * @dev Throws if the contract is not paused.
     */
    function _requirePaused() internal view virtual {
        if (!paused()) {
            revert ExpectedPause();
        }
    }

    /**
     * @dev Triggers stopped state.
     *
     * Requirements:
     *
     * - The contract must not be paused.
     */
    function _pause() internal virtual whenNotPaused {
        PausableStorage storage $ = _getPausableStorage();
        $._paused = true;
        emit Paused(_msgSender());
    }

    /**
     * @dev Returns to normal state.
     *
     * Requirements:
     *
     * - The contract must be paused.
     */
    function _unpause() internal virtual whenPaused {
        PausableStorage storage $ = _getPausableStorage();
        $._paused = false;
        emit Unpaused(_msgSender());
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.1.0) (utils/cryptography/MerkleProof.sol)
// This file was procedurally generated from scripts/generate/templates/MerkleProof.js.

pragma solidity ^0.8.20;

import {Hashes} from "./Hashes.sol";

/**
 * @dev These functions deal with verification of Merkle Tree proofs.
 *
 * The tree and the proofs can be generated using our
 * https://github.com/OpenZeppelin/merkle-tree[JavaScript library].
 * You will find a quickstart guide in the readme.
 *
 * WARNING: You should avoid using leaf values that are 64 bytes long prior to
 * hashing, or use a hash function other than keccak256 for hashing leaves.
 * This is because the concatenation of a sorted pair of internal nodes in
 * the Merkle tree could be reinterpreted as a leaf value.
 * OpenZeppelin's JavaScript library generates Merkle trees that are safe
 * against this attack out of the box.
 *
 * IMPORTANT: Consider memory side-effects when using custom hashing functions
 * that access memory in an unsafe way.
 *
 * NOTE: This library supports proof verification for merkle trees built using
 * custom _commutative_ hashing functions (i.e. `H(a, b) == H(b, a)`). Proving
 * leaf inclusion in trees built using non-commutative hashing functions requires
 * additional logic that is not supported by this library.
 */
library MerkleProof {
    /**
     *@dev The multiproof provided is not valid.
     */
    error MerkleProofInvalidMultiproof();

    /**
     * @dev Returns true if a `leaf` can be proved to be a part of a Merkle tree
     * defined by `root`. For this, a `proof` must be provided, containing
     * sibling hashes on the branch from the leaf to the root of the tree. Each
     * pair of leaves and each pair of pre-images are assumed to be sorted.
     *
     * This version handles proofs in memory with the default hashing function.
     */
    function verify(bytes32[] memory proof, bytes32 root, bytes32 leaf) internal pure returns (bool) {
        return processProof(proof, leaf) == root;
    }

    /**
     * @dev Returns the rebuilt hash obtained by traversing a Merkle tree up
     * from `leaf` using `proof`. A `proof` is valid if and only if the rebuilt
     * hash matches the root of the tree. When processing the proof, the pairs
     * of leaves & pre-images are assumed to be sorted.
     *
     * This version handles proofs in memory with the default hashing function.
     */
    function processProof(bytes32[] memory proof, bytes32 leaf) internal pure returns (bytes32) {
        bytes32 computedHash = leaf;
        for (uint256 i = 0; i < proof.length; i++) {
            computedHash = Hashes.commutativeKeccak256(computedHash, proof[i]);
        }
        return computedHash;
    }

    /**
     * @dev Returns true if a `leaf` can be proved to be a part of a Merkle tree
     * defined by `root`. For this, a `proof` must be provided, containing
     * sibling hashes on the branch from the leaf to the root of the tree. Each
     * pair of leaves and each pair of pre-images are assumed to be sorted.
     *
     * This version handles proofs in memory with a custom hashing function.
     */
    function verify(
        bytes32[] memory proof,
        bytes32 root,
        bytes32 leaf,
        function(bytes32, bytes32) view returns (bytes32) hasher
    ) internal view returns (bool) {
        return processProof(proof, leaf, hasher) == root;
    }

    /**
     * @dev Returns the rebuilt hash obtained by traversing a Merkle tree up
     * from `leaf` using `proof`. A `proof` is valid if and only if the rebuilt
     * hash matches the root of the tree. When processing the proof, the pairs
     * of leaves & pre-images are assumed to be sorted.
     *
     * This version handles proofs in memory with a custom hashing function.
     */
    function processProof(
        bytes32[] memory proof,
        bytes32 leaf,
        function(bytes32, bytes32) view returns (bytes32) hasher
    ) internal view returns (bytes32) {
        bytes32 computedHash = leaf;
        for (uint256 i = 0; i < proof.length; i++) {
            computedHash = hasher(computedHash, proof[i]);
        }
        return computedHash;
    }

    /**
     * @dev Returns true if a `leaf` can be proved to be a part of a Merkle tree
     * defined by `root`. For this, a `proof` must be provided, containing
     * sibling hashes on the branch from the leaf to the root of the tree. Each
     * pair of leaves and each pair of pre-images are assumed to be sorted.
     *
     * This version handles proofs in calldata with the default hashing function.
     */
    function verifyCalldata(bytes32[] calldata proof, bytes32 root, bytes32 leaf) internal pure returns (bool) {
        return processProofCalldata(proof, leaf) == root;
    }

    /**
     * @dev Returns the rebuilt hash obtained by traversing a Merkle tree up
     * from `leaf` using `proof`. A `proof` is valid if and only if the rebuilt
     * hash matches the root of the tree. When processing the proof, the pairs
     * of leaves & pre-images are assumed to be sorted.
     *
     * This version handles proofs in calldata with the default hashing function.
     */
    function processProofCalldata(bytes32[] calldata proof, bytes32 leaf) internal pure returns (bytes32) {
        bytes32 computedHash = leaf;
        for (uint256 i = 0; i < proof.length; i++) {
            computedHash = Hashes.commutativeKeccak256(computedHash, proof[i]);
        }
        return computedHash;
    }

    /**
     * @dev Returns true if a `leaf` can be proved to be a part of a Merkle tree
     * defined by `root`. For this, a `proof` must be provided, containing
     * sibling hashes on the branch from the leaf to the root of the tree. Each
     * pair of leaves and each pair of pre-images are assumed to be sorted.
     *
     * This version handles proofs in calldata with a custom hashing function.
     */
    function verifyCalldata(
        bytes32[] calldata proof,
        bytes32 root,
        bytes32 leaf,
        function(bytes32, bytes32) view returns (bytes32) hasher
    ) internal view returns (bool) {
        return processProofCalldata(proof, leaf, hasher) == root;
    }

    /**
     * @dev Returns the rebuilt hash obtained by traversing a Merkle tree up
     * from `leaf` using `proof`. A `proof` is valid if and only if the rebuilt
     * hash matches the root of the tree. When processing the proof, the pairs
     * of leaves & pre-images are assumed to be sorted.
     *
     * This version handles proofs in calldata with a custom hashing function.
     */
    function processProofCalldata(
        bytes32[] calldata proof,
        bytes32 leaf,
        function(bytes32, bytes32) view returns (bytes32) hasher
    ) internal view returns (bytes32) {
        bytes32 computedHash = leaf;
        for (uint256 i = 0; i < proof.length; i++) {
            computedHash = hasher(computedHash, proof[i]);
        }
        return computedHash;
    }

    /**
     * @dev Returns true if the `leaves` can be simultaneously proven to be a part of a Merkle tree defined by
     * `root`, according to `proof` and `proofFlags` as described in {processMultiProof}.
     *
     * This version handles multiproofs in memory with the default hashing function.
     *
     * CAUTION: Not all Merkle trees admit multiproofs. See {processMultiProof} for details.
     *
     * NOTE: Consider the case where `root == proof[0] && leaves.length == 0` as it will return `true`.
     * The `leaves` must be validated independently. See {processMultiProof}.
     */
    function multiProofVerify(
        bytes32[] memory proof,
        bool[] memory proofFlags,
        bytes32 root,
        bytes32[] memory leaves
    ) internal pure returns (bool) {
        return processMultiProof(proof, proofFlags, leaves) == root;
    }

    /**
     * @dev Returns the root of a tree reconstructed from `leaves` and sibling nodes in `proof`. The reconstruction
     * proceeds by incrementally reconstructing all inner nodes by combining a leaf/inner node with either another
     * leaf/inner node or a proof sibling node, depending on whether each `proofFlags` item is true or false
     * respectively.
     *
     * This version handles multiproofs in memory with the default hashing function.
     *
     * CAUTION: Not all Merkle trees admit multiproofs. To use multiproofs, it is sufficient to ensure that: 1) the tree
     * is complete (but not necessarily perfect), 2) the leaves to be proven are in the opposite order they are in the
     * tree (i.e., as seen from right to left starting at the deepest layer and continuing at the next layer).
     *
     * NOTE: The _empty set_ (i.e. the case where `proof.length == 1 && leaves.length == 0`) is considered a no-op,
     * and therefore a valid multiproof (i.e. it returns `proof[0]`). Consider disallowing this case if you're not
     * validating the leaves elsewhere.
     */
    function processMultiProof(
        bytes32[] memory proof,
        bool[] memory proofFlags,
        bytes32[] memory leaves
    ) internal pure returns (bytes32 merkleRoot) {
        // This function rebuilds the root hash by traversing the tree up from the leaves. The root is rebuilt by
        // consuming and producing values on a queue. The queue starts with the `leaves` array, then goes onto the
        // `hashes` array. At the end of the process, the last hash in the `hashes` array should contain the root of
        // the Merkle tree.
        uint256 leavesLen = leaves.length;
        uint256 proofFlagsLen = proofFlags.length;

        // Check proof validity.
        if (leavesLen + proof.length != proofFlagsLen + 1) {
            revert MerkleProofInvalidMultiproof();
        }

        // The xxxPos values are "pointers" to the next value to consume in each array. All accesses are done using
        // `xxx[xxxPos++]`, which return the current value and increment the pointer, thus mimicking a queue's "pop".
        bytes32[] memory hashes = new bytes32[](proofFlagsLen);
        uint256 leafPos = 0;
        uint256 hashPos = 0;
        uint256 proofPos = 0;
        // At each step, we compute the next hash using two values:
        // - a value from the "main queue". If not all leaves have been consumed, we get the next leaf, otherwise we
        //   get the next hash.
        // - depending on the flag, either another value from the "main queue" (merging branches) or an element from the
        //   `proof` array.
        for (uint256 i = 0; i < proofFlagsLen; i++) {
            bytes32 a = leafPos < leavesLen ? leaves[leafPos++] : hashes[hashPos++];
            bytes32 b = proofFlags[i]
                ? (leafPos < leavesLen ? leaves[leafPos++] : hashes[hashPos++])
                : proof[proofPos++];
            hashes[i] = Hashes.commutativeKeccak256(a, b);
        }

        if (proofFlagsLen > 0) {
            if (proofPos != proof.length) {
                revert MerkleProofInvalidMultiproof();
            }
            unchecked {
                return hashes[proofFlagsLen - 1];
            }
        } else if (leavesLen > 0) {
            return leaves[0];
        } else {
            return proof[0];
        }
    }

    /**
     * @dev Returns true if the `leaves` can be simultaneously proven to be a part of a Merkle tree defined by
     * `root`, according to `proof` and `proofFlags` as described in {processMultiProof}.
     *
     * This version handles multiproofs in memory with a custom hashing function.
     *
     * CAUTION: Not all Merkle trees admit multiproofs. See {processMultiProof} for details.
     *
     * NOTE: Consider the case where `root == proof[0] && leaves.length == 0` as it will return `true`.
     * The `leaves` must be validated independently. See {processMultiProof}.
     */
    function multiProofVerify(
        bytes32[] memory proof,
        bool[] memory proofFlags,
        bytes32 root,
        bytes32[] memory leaves,
        function(bytes32, bytes32) view returns (bytes32) hasher
    ) internal view returns (bool) {
        return processMultiProof(proof, proofFlags, leaves, hasher) == root;
    }

    /**
     * @dev Returns the root of a tree reconstructed from `leaves` and sibling nodes in `proof`. The reconstruction
     * proceeds by incrementally reconstructing all inner nodes by combining a leaf/inner node with either another
     * leaf/inner node or a proof sibling node, depending on whether each `proofFlags` item is true or false
     * respectively.
     *
     * This version handles multiproofs in memory with a custom hashing function.
     *
     * CAUTION: Not all Merkle trees admit multiproofs. To use multiproofs, it is sufficient to ensure that: 1) the tree
     * is complete (but not necessarily perfect), 2) the leaves to be proven are in the opposite order they are in the
     * tree (i.e., as seen from right to left starting at the deepest layer and continuing at the next layer).
     *
     * NOTE: The _empty set_ (i.e. the case where `proof.length == 1 && leaves.length == 0`) is considered a no-op,
     * and therefore a valid multiproof (i.e. it returns `proof[0]`). Consider disallowing this case if you're not
     * validating the leaves elsewhere.
     */
    function processMultiProof(
        bytes32[] memory proof,
        bool[] memory proofFlags,
        bytes32[] memory leaves,
        function(bytes32, bytes32) view returns (bytes32) hasher
    ) internal view returns (bytes32 merkleRoot) {
        // This function rebuilds the root hash by traversing the tree up from the leaves. The root is rebuilt by
        // consuming and producing values on a queue. The queue starts with the `leaves` array, then goes onto the
        // `hashes` array. At the end of the process, the last hash in the `hashes` array should contain the root of
        // the Merkle tree.
        uint256 leavesLen = leaves.length;
        uint256 proofFlagsLen = proofFlags.length;

        // Check proof validity.
        if (leavesLen + proof.length != proofFlagsLen + 1) {
            revert MerkleProofInvalidMultiproof();
        }

        // The xxxPos values are "pointers" to the next value to consume in each array. All accesses are done using
        // `xxx[xxxPos++]`, which return the current value and increment the pointer, thus mimicking a queue's "pop".
        bytes32[] memory hashes = new bytes32[](proofFlagsLen);
        uint256 leafPos = 0;
        uint256 hashPos = 0;
        uint256 proofPos = 0;
        // At each step, we compute the next hash using two values:
        // - a value from the "main queue". If not all leaves have been consumed, we get the next leaf, otherwise we
        //   get the next hash.
        // - depending on the flag, either another value from the "main queue" (merging branches) or an element from the
        //   `proof` array.
        for (uint256 i = 0; i < proofFlagsLen; i++) {
            bytes32 a = leafPos < leavesLen ? leaves[leafPos++] : hashes[hashPos++];
            bytes32 b = proofFlags[i]
                ? (leafPos < leavesLen ? leaves[leafPos++] : hashes[hashPos++])
                : proof[proofPos++];
            hashes[i] = hasher(a, b);
        }

        if (proofFlagsLen > 0) {
            if (proofPos != proof.length) {
                revert MerkleProofInvalidMultiproof();
            }
            unchecked {
                return hashes[proofFlagsLen - 1];
            }
        } else if (leavesLen > 0) {
            return leaves[0];
        } else {
            return proof[0];
        }
    }

    /**
     * @dev Returns true if the `leaves` can be simultaneously proven to be a part of a Merkle tree defined by
     * `root`, according to `proof` and `proofFlags` as described in {processMultiProof}.
     *
     * This version handles multiproofs in calldata with the default hashing function.
     *
     * CAUTION: Not all Merkle trees admit multiproofs. See {processMultiProof} for details.
     *
     * NOTE: Consider the case where `root == proof[0] && leaves.length == 0` as it will return `true`.
     * The `leaves` must be validated independently. See {processMultiProofCalldata}.
     */
    function multiProofVerifyCalldata(
        bytes32[] calldata proof,
        bool[] calldata proofFlags,
        bytes32 root,
        bytes32[] memory leaves
    ) internal pure returns (bool) {
        return processMultiProofCalldata(proof, proofFlags, leaves) == root;
    }

    /**
     * @dev Returns the root of a tree reconstructed from `leaves` and sibling nodes in `proof`. The reconstruction
     * proceeds by incrementally reconstructing all inner nodes by combining a leaf/inner node with either another
     * leaf/inner node or a proof sibling node, depending on whether each `proofFlags` item is true or false
     * respectively.
     *
     * This version handles multiproofs in calldata with the default hashing function.
     *
     * CAUTION: Not all Merkle trees admit multiproofs. To use multiproofs, it is sufficient to ensure that: 1) the tree
     * is complete (but not necessarily perfect), 2) the leaves to be proven are in the opposite order they are in the
     * tree (i.e., as seen from right to left starting at the deepest layer and continuing at the next layer).
     *
     * NOTE: The _empty set_ (i.e. the case where `proof.length == 1 && leaves.length == 0`) is considered a no-op,
     * and therefore a valid multiproof (i.e. it returns `proof[0]`). Consider disallowing this case if you're not
     * validating the leaves elsewhere.
     */
    function processMultiProofCalldata(
        bytes32[] calldata proof,
        bool[] calldata proofFlags,
        bytes32[] memory leaves
    ) internal pure returns (bytes32 merkleRoot) {
        // This function rebuilds the root hash by traversing the tree up from the leaves. The root is rebuilt by
        // consuming and producing values on a queue. The queue starts with the `leaves` array, then goes onto the
        // `hashes` array. At the end of the process, the last hash in the `hashes` array should contain the root of
        // the Merkle tree.
        uint256 leavesLen = leaves.length;
        uint256 proofFlagsLen = proofFlags.length;

        // Check proof validity.
        if (leavesLen + proof.length != proofFlagsLen + 1) {
            revert MerkleProofInvalidMultiproof();
        }

        // The xxxPos values are "pointers" to the next value to consume in each array. All accesses are done using
        // `xxx[xxxPos++]`, which return the current value and increment the pointer, thus mimicking a queue's "pop".
        bytes32[] memory hashes = new bytes32[](proofFlagsLen);
        uint256 leafPos = 0;
        uint256 hashPos = 0;
        uint256 proofPos = 0;
        // At each step, we compute the next hash using two values:
        // - a value from the "main queue". If not all leaves have been consumed, we get the next leaf, otherwise we
        //   get the next hash.
        // - depending on the flag, either another value from the "main queue" (merging branches) or an element from the
        //   `proof` array.
        for (uint256 i = 0; i < proofFlagsLen; i++) {
            bytes32 a = leafPos < leavesLen ? leaves[leafPos++] : hashes[hashPos++];
            bytes32 b = proofFlags[i]
                ? (leafPos < leavesLen ? leaves[leafPos++] : hashes[hashPos++])
                : proof[proofPos++];
            hashes[i] = Hashes.commutativeKeccak256(a, b);
        }

        if (proofFlagsLen > 0) {
            if (proofPos != proof.length) {
                revert MerkleProofInvalidMultiproof();
            }
            unchecked {
                return hashes[proofFlagsLen - 1];
            }
        } else if (leavesLen > 0) {
            return leaves[0];
        } else {
            return proof[0];
        }
    }

    /**
     * @dev Returns true if the `leaves` can be simultaneously proven to be a part of a Merkle tree defined by
     * `root`, according to `proof` and `proofFlags` as described in {processMultiProof}.
     *
     * This version handles multiproofs in calldata with a custom hashing function.
     *
     * CAUTION: Not all Merkle trees admit multiproofs. See {processMultiProof} for details.
     *
     * NOTE: Consider the case where `root == proof[0] && leaves.length == 0` as it will return `true`.
     * The `leaves` must be validated independently. See {processMultiProofCalldata}.
     */
    function multiProofVerifyCalldata(
        bytes32[] calldata proof,
        bool[] calldata proofFlags,
        bytes32 root,
        bytes32[] memory leaves,
        function(bytes32, bytes32) view returns (bytes32) hasher
    ) internal view returns (bool) {
        return processMultiProofCalldata(proof, proofFlags, leaves, hasher) == root;
    }

    /**
     * @dev Returns the root of a tree reconstructed from `leaves` and sibling nodes in `proof`. The reconstruction
     * proceeds by incrementally reconstructing all inner nodes by combining a leaf/inner node with either another
     * leaf/inner node or a proof sibling node, depending on whether each `proofFlags` item is true or false
     * respectively.
     *
     * This version handles multiproofs in calldata with a custom hashing function.
     *
     * CAUTION: Not all Merkle trees admit multiproofs. To use multiproofs, it is sufficient to ensure that: 1) the tree
     * is complete (but not necessarily perfect), 2) the leaves to be proven are in the opposite order they are in the
     * tree (i.e., as seen from right to left starting at the deepest layer and continuing at the next layer).
     *
     * NOTE: The _empty set_ (i.e. the case where `proof.length == 1 && leaves.length == 0`) is considered a no-op,
     * and therefore a valid multiproof (i.e. it returns `proof[0]`). Consider disallowing this case if you're not
     * validating the leaves elsewhere.
     */
    function processMultiProofCalldata(
        bytes32[] calldata proof,
        bool[] calldata proofFlags,
        bytes32[] memory leaves,
        function(bytes32, bytes32) view returns (bytes32) hasher
    ) internal view returns (bytes32 merkleRoot) {
        // This function rebuilds the root hash by traversing the tree up from the leaves. The root is rebuilt by
        // consuming and producing values on a queue. The queue starts with the `leaves` array, then goes onto the
        // `hashes` array. At the end of the process, the last hash in the `hashes` array should contain the root of
        // the Merkle tree.
        uint256 leavesLen = leaves.length;
        uint256 proofFlagsLen = proofFlags.length;

        // Check proof validity.
        if (leavesLen + proof.length != proofFlagsLen + 1) {
            revert MerkleProofInvalidMultiproof();
        }

        // The xxxPos values are "pointers" to the next value to consume in each array. All accesses are done using
        // `xxx[xxxPos++]`, which return the current value and increment the pointer, thus mimicking a queue's "pop".
        bytes32[] memory hashes = new bytes32[](proofFlagsLen);
        uint256 leafPos = 0;
        uint256 hashPos = 0;
        uint256 proofPos = 0;
        // At each step, we compute the next hash using two values:
        // - a value from the "main queue". If not all leaves have been consumed, we get the next leaf, otherwise we
        //   get the next hash.
        // - depending on the flag, either another value from the "main queue" (merging branches) or an element from the
        //   `proof` array.
        for (uint256 i = 0; i < proofFlagsLen; i++) {
            bytes32 a = leafPos < leavesLen ? leaves[leafPos++] : hashes[hashPos++];
            bytes32 b = proofFlags[i]
                ? (leafPos < leavesLen ? leaves[leafPos++] : hashes[hashPos++])
                : proof[proofPos++];
            hashes[i] = hasher(a, b);
        }

        if (proofFlagsLen > 0) {
            if (proofPos != proof.length) {
                revert MerkleProofInvalidMultiproof();
            }
            unchecked {
                return hashes[proofFlagsLen - 1];
            }
        } else if (leavesLen > 0) {
            return leaves[0];
        } else {
            return proof[0];
        }
    }
}

// SPDX-License-Identifier: BUSL-1.1
pragma solidity ^0.8.28;

import { IAccess } from "../interfaces/IAccess.sol";
import { IAccessControl } from "../interfaces/IAccessControl.sol";

import { AccessStorageUtils } from "../storage/AccessStorageUtils.sol";
import { Initializable } from "@openzeppelin/contracts-upgradeable/proxy/utils/Initializable.sol";

/// @title Access
/// @author kexley, Cap Labs
/// @notice Inheritable access
abstract contract Access is IAccess, Initializable, AccessStorageUtils {
    /// @dev Check caller has permissions for a function, revert if call is not allowed
    /// @param _selector Function selector
    modifier checkAccess(bytes4 _selector) {
        _checkAccess(_selector);
        _;
    }

    /// @dev Initialize the access control address
    /// @param _accessControl Access control address
    function __Access_init(address _accessControl) internal onlyInitializing {
        __Access_init_unchained(_accessControl);
    }

    /// @dev Initialize unchained
    /// @param _accessControl Access control address
    function __Access_init_unchained(address _accessControl) internal onlyInitializing {
        getAccessStorage().accessControl = _accessControl;
    }

    /// @dev Check caller has access to a function, revert overwise
    /// @param _selector Function selector
    function _checkAccess(bytes4 _selector) internal view {
        bool hasAccess =
            IAccessControl(getAccessStorage().accessControl).checkAccess(_selector, address(this), msg.sender);
        if (!hasAccess) revert AccessDenied();
    }
}

// SPDX-License-Identifier: BUSL-1.1
pragma solidity ^0.8.28;

import { IERC1155 } from "@openzeppelin/contracts/token/ERC1155/IERC1155.sol";

/// @title ISoulboundERC1155Merkle
/// @author kexley, Cap Labs
/// @notice Interface for Soulbound ERC1155 with Merkle proofs for minting
interface ISoulboundERC1155Merkle is IERC1155 {
    /// @custom:storage-location erc7201:cap.storage.SoulboundERC1155Merkle
    /// @dev SoulboundERC1155Merkle storage
    /// @param root Merkle root
    struct SoulboundERC1155MerkleStorage {
        bytes32 root;
    }

    /// @dev Address already owns a token
    error AlreadyMinted();

    /// @dev Invalid Merkle proof
    error InvalidProof();

    /// @dev Token is soulbound
    error Soulbound();

    /// @dev Zero address not valid
    error ZeroAddressNotValid();

    /// @dev Emitted when the Merkle root is set
    event SetRoot(bytes32 root);

    /// @dev Emitted when the URI is set
    event SetURI(string uri);

    /// @notice Initialize the SoulboundERC1155Merkle token
    /// @dev Minting using Merkle proofs is paused by default
    /// @param _accessControl Access control address
    /// @param _uri URI for token metadata
    function initialize(address _accessControl, string calldata _uri) external;

    /// @notice Mint a token to an address using Merkle proofs
    /// @dev Anyone can mint a token to an approved address using Merkle proofs on behalf of that address
    /// @param _to Address to mint the token to
    /// @param _proofs Merkle proofs for the address
    function mint(address _to, bytes32[] calldata _proofs) external;

    /// @notice Mint a token to multiple addresses using owner privileges without Merkle proofs
    /// @param _to Addresses to mint the token to
    function ownerMint(address[] calldata _to) external;

    /// @notice Set the Merkle root
    /// @param _root Merkle root
    function setRoot(bytes32 _root) external;

    /// @notice Set the URI for token metadata
    /// @param _uri Base URI
    function setURI(string calldata _uri) external;

    /// @notice Pause minting
    function pause() external;

    /// @notice Unpause minting
    function unpause() external;

    /// @notice Get the Merkle root
    /// @return root Merkle root
    function root() external view returns (bytes32);
}

// SPDX-License-Identifier: BUSL-1.1
pragma solidity ^0.8.28;

import { ISoulboundERC1155Merkle } from "../interfaces/ISoulboundERC1155Merkle.sol";

/// @title SoulboundERC1155Merkle Storage Utils
/// @author kexley, Cap Labs
/// @notice Storage utilities for SoulboundERC1155Merkle
abstract contract SoulboundERC1155MerkleStorageUtils {
    /// @dev keccak256(abi.encode(uint256(keccak256("cap.storage.SoulboundERC1155Merkle")) - 1)) & ~bytes32(uint256(0xff))
    bytes32 private constant SoulboundERC1155MerkleStorageLocation =
        0x6d5a367baf12d23a28fe5a1303a7e187165117fd327ccfa867169347edcde600;

    /// @dev Get SoulboundERC1155Merkle storage
    /// @return $ Storage pointer
    function getSoulboundERC1155MerkleStorage()
        internal
        pure
        returns (ISoulboundERC1155Merkle.SoulboundERC1155MerkleStorage storage $)
    {
        assembly {
            $.slot := SoulboundERC1155MerkleStorageLocation
        }
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.1.0) (interfaces/draft-IERC1822.sol)

pragma solidity ^0.8.20;

/**
 * @dev ERC-1822: Universal Upgradeable Proxy Standard (UUPS) documents a method for upgradeability through a simplified
 * proxy whose upgrades are fully controlled by the current implementation.
 */
interface IERC1822Proxiable {
    /**
     * @dev Returns the storage slot that the proxiable contract assumes is being used to store the implementation
     * address.
     *
     * IMPORTANT: A proxy pointing at a proxiable contract should not be considered proxiable itself, because this risks
     * bricking a proxy that upgrades to it, by delegating to itself until out of gas. Thus it is critical that this
     * function revert if invoked through a proxy.
     */
    function proxiableUUID() external view returns (bytes32);
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.2.0) (proxy/ERC1967/ERC1967Utils.sol)

pragma solidity ^0.8.22;

import {IBeacon} from "../beacon/IBeacon.sol";
import {IERC1967} from "../../interfaces/IERC1967.sol";
import {Address} from "../../utils/Address.sol";
import {StorageSlot} from "../../utils/StorageSlot.sol";

/**
 * @dev This library provides getters and event emitting update functions for
 * https://eips.ethereum.org/EIPS/eip-1967[ERC-1967] slots.
 */
library ERC1967Utils {
    /**
     * @dev Storage slot with the address of the current implementation.
     * This is the keccak-256 hash of "eip1967.proxy.implementation" subtracted by 1.
     */
    // solhint-disable-next-line private-vars-leading-underscore
    bytes32 internal constant IMPLEMENTATION_SLOT = 0x360894a13ba1a3210667c828492db98dca3e2076cc3735a920a3ca505d382bbc;

    /**
     * @dev The `implementation` of the proxy is invalid.
     */
    error ERC1967InvalidImplementation(address implementation);

    /**
     * @dev The `admin` of the proxy is invalid.
     */
    error ERC1967InvalidAdmin(address admin);

    /**
     * @dev The `beacon` of the proxy is invalid.
     */
    error ERC1967InvalidBeacon(address beacon);

    /**
     * @dev An upgrade function sees `msg.value > 0` that may be lost.
     */
    error ERC1967NonPayable();

    /**
     * @dev Returns the current implementation address.
     */
    function getImplementation() internal view returns (address) {
        return StorageSlot.getAddressSlot(IMPLEMENTATION_SLOT).value;
    }

    /**
     * @dev Stores a new address in the ERC-1967 implementation slot.
     */
    function _setImplementation(address newImplementation) private {
        if (newImplementation.code.length == 0) {
            revert ERC1967InvalidImplementation(newImplementation);
        }
        StorageSlot.getAddressSlot(IMPLEMENTATION_SLOT).value = newImplementation;
    }

    /**
     * @dev Performs implementation upgrade with additional setup call if data is nonempty.
     * This function is payable only if the setup call is performed, otherwise `msg.value` is rejected
     * to avoid stuck value in the contract.
     *
     * Emits an {IERC1967-Upgraded} event.
     */
    function upgradeToAndCall(address newImplementation, bytes memory data) internal {
        _setImplementation(newImplementation);
        emit IERC1967.Upgraded(newImplementation);

        if (data.length > 0) {
            Address.functionDelegateCall(newImplementation, data);
        } else {
            _checkNonPayable();
        }
    }

    /**
     * @dev Storage slot with the admin of the contract.
     * This is the keccak-256 hash of "eip1967.proxy.admin" subtracted by 1.
     */
    // solhint-disable-next-line private-vars-leading-underscore
    bytes32 internal constant ADMIN_SLOT = 0xb53127684a568b3173ae13b9f8a6016e243e63b6e8ee1178d6a717850b5d6103;

    /**
     * @dev Returns the current admin.
     *
     * TIP: To get this value clients can read directly from the storage slot shown below (specified by ERC-1967) using
     * the https://eth.wiki/json-rpc/API#eth_getstorageat[`eth_getStorageAt`] RPC call.
     * `0xb53127684a568b3173ae13b9f8a6016e243e63b6e8ee1178d6a717850b5d6103`
     */
    function getAdmin() internal view returns (address) {
        return StorageSlot.getAddressSlot(ADMIN_SLOT).value;
    }

    /**
     * @dev Stores a new address in the ERC-1967 admin slot.
     */
    function _setAdmin(address newAdmin) private {
        if (newAdmin == address(0)) {
            revert ERC1967InvalidAdmin(address(0));
        }
        StorageSlot.getAddressSlot(ADMIN_SLOT).value = newAdmin;
    }

    /**
     * @dev Changes the admin of the proxy.
     *
     * Emits an {IERC1967-AdminChanged} event.
     */
    function changeAdmin(address newAdmin) internal {
        emit IERC1967.AdminChanged(getAdmin(), newAdmin);
        _setAdmin(newAdmin);
    }

    /**
     * @dev The storage slot of the UpgradeableBeacon contract which defines the implementation for this proxy.
     * This is the keccak-256 hash of "eip1967.proxy.beacon" subtracted by 1.
     */
    // solhint-disable-next-line private-vars-leading-underscore
    bytes32 internal constant BEACON_SLOT = 0xa3f0ad74e5423aebfd80d3ef4346578335a9a72aeaee59ff6cb3582b35133d50;

    /**
     * @dev Returns the current beacon.
     */
    function getBeacon() internal view returns (address) {
        return StorageSlot.getAddressSlot(BEACON_SLOT).value;
    }

    /**
     * @dev Stores a new beacon in the ERC-1967 beacon slot.
     */
    function _setBeacon(address newBeacon) private {
        if (newBeacon.code.length == 0) {
            revert ERC1967InvalidBeacon(newBeacon);
        }

        StorageSlot.getAddressSlot(BEACON_SLOT).value = newBeacon;

        address beaconImplementation = IBeacon(newBeacon).implementation();
        if (beaconImplementation.code.length == 0) {
            revert ERC1967InvalidImplementation(beaconImplementation);
        }
    }

    /**
     * @dev Change the beacon and trigger a setup call if data is nonempty.
     * This function is payable only if the setup call is performed, otherwise `msg.value` is rejected
     * to avoid stuck value in the contract.
     *
     * Emits an {IERC1967-BeaconUpgraded} event.
     *
     * CAUTION: Invoking this function has no effect on an instance of {BeaconProxy} since v5, since
     * it uses an immutable beacon without looking at the value of the ERC-1967 beacon slot for
     * efficiency.
     */
    function upgradeBeaconToAndCall(address newBeacon, bytes memory data) internal {
        _setBeacon(newBeacon);
        emit IERC1967.BeaconUpgraded(newBeacon);

        if (data.length > 0) {
            Address.functionDelegateCall(IBeacon(newBeacon).implementation(), data);
        } else {
            _checkNonPayable();
        }
    }

    /**
     * @dev Reverts if `msg.value` is not zero. It can be used to avoid `msg.value` stuck in the contract
     * if an upgrade doesn't perform an initialization call.
     */
    function _checkNonPayable() private {
        if (msg.value > 0) {
            revert ERC1967NonPayable();
        }
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.3.0) (proxy/utils/Initializable.sol)

pragma solidity ^0.8.20;

/**
 * @dev This is a base contract to aid in writing upgradeable contracts, or any kind of contract that will be deployed
 * behind a proxy. Since proxied contracts do not make use of a constructor, it's common to move constructor logic to an
 * external initializer function, usually called `initialize`. It then becomes necessary to protect this initializer
 * function so it can only be called once. The {initializer} modifier provided by this contract will have this effect.
 *
 * The initialization functions use a version number. Once a version number is used, it is consumed and cannot be
 * reused. This mechanism prevents re-execution of each "step" but allows the creation of new initialization steps in
 * case an upgrade adds a module that needs to be initialized.
 *
 * For example:
 *
 * [.hljs-theme-light.nopadding]
 * ```solidity
 * contract MyToken is ERC20Upgradeable {
 *     function initialize() initializer public {
 *         __ERC20_init("MyToken", "MTK");
 *     }
 * }
 *
 * contract MyTokenV2 is MyToken, ERC20PermitUpgradeable {
 *     function initializeV2() reinitializer(2) public {
 *         __ERC20Permit_init("MyToken");
 *     }
 * }
 * ```
 *
 * TIP: To avoid leaving the proxy in an uninitialized state, the initializer function should be called as early as
 * possible by providing the encoded function call as the `_data` argument to {ERC1967Proxy-constructor}.
 *
 * CAUTION: When used with inheritance, manual care must be taken to not invoke a parent initializer twice, or to ensure
 * that all initializers are idempotent. This is not verified automatically as constructors are by Solidity.
 *
 * [CAUTION]
 * ====
 * Avoid leaving a contract uninitialized.
 *
 * An uninitialized contract can be taken over by an attacker. This applies to both a proxy and its implementation
 * contract, which may impact the proxy. To prevent the implementation contract from being used, you should invoke
 * the {_disableInitializers} function in the constructor to automatically lock it when it is deployed:
 *
 * [.hljs-theme-light.nopadding]
 * ```
 * /// @custom:oz-upgrades-unsafe-allow constructor
 * constructor() {
 *     _disableInitializers();
 * }
 * ```
 * ====
 */
abstract contract Initializable {
    /**
     * @dev Storage of the initializable contract.
     *
     * It's implemented on a custom ERC-7201 namespace to reduce the risk of storage collisions
     * when using with upgradeable contracts.
     *
     * @custom:storage-location erc7201:openzeppelin.storage.Initializable
     */
    struct InitializableStorage {
        /**
         * @dev Indicates that the contract has been initialized.
         */
        uint64 _initialized;
        /**
         * @dev Indicates that the contract is in the process of being initialized.
         */
        bool _initializing;
    }

    // keccak256(abi.encode(uint256(keccak256("openzeppelin.storage.Initializable")) - 1)) & ~bytes32(uint256(0xff))
    bytes32 private constant INITIALIZABLE_STORAGE = 0xf0c57e16840df040f15088dc2f81fe391c3923bec73e23a9662efc9c229c6a00;

    /**
     * @dev The contract is already initialized.
     */
    error InvalidInitialization();

    /**
     * @dev The contract is not initializing.
     */
    error NotInitializing();

    /**
     * @dev Triggered when the contract has been initialized or reinitialized.
     */
    event Initialized(uint64 version);

    /**
     * @dev A modifier that defines a protected initializer function that can be invoked at most once. In its scope,
     * `onlyInitializing` functions can be used to initialize parent contracts.
     *
     * Similar to `reinitializer(1)`, except that in the context of a constructor an `initializer` may be invoked any
     * number of times. This behavior in the constructor can be useful during testing and is not expected to be used in
     * production.
     *
     * Emits an {Initialized} event.
     */
    modifier initializer() {
        // solhint-disable-next-line var-name-mixedcase
        InitializableStorage storage $ = _getInitializableStorage();

        // Cache values to avoid duplicated sloads
        bool isTopLevelCall = !$._initializing;
        uint64 initialized = $._initialized;

        // Allowed calls:
        // - initialSetup: the contract is not in the initializing state and no previous version was
        //                 initialized
        // - construction: the contract is initialized at version 1 (no reinitialization) and the
        //                 current contract is just being deployed
        bool initialSetup = initialized == 0 && isTopLevelCall;
        bool construction = initialized == 1 && address(this).code.length == 0;

        if (!initialSetup && !construction) {
            revert InvalidInitialization();
        }
        $._initialized = 1;
        if (isTopLevelCall) {
            $._initializing = true;
        }
        _;
        if (isTopLevelCall) {
            $._initializing = false;
            emit Initialized(1);
        }
    }

    /**
     * @dev A modifier that defines a protected reinitializer function that can be invoked at most once, and only if the
     * contract hasn't been initialized to a greater version before. In its scope, `onlyInitializing` functions can be
     * used to initialize parent contracts.
     *
     * A reinitializer may be used after the original initialization step. This is essential to configure modules that
     * are added through upgrades and that require initialization.
     *
     * When `version` is 1, this modifier is similar to `initializer`, except that functions marked with `reinitializer`
     * cannot be nested. If one is invoked in the context of another, execution will revert.
     *
     * Note that versions can jump in increments greater than 1; this implies that if multiple reinitializers coexist in
     * a contract, executing them in the right order is up to the developer or operator.
     *
     * WARNING: Setting the version to 2**64 - 1 will prevent any future reinitialization.
     *
     * Emits an {Initialized} event.
     */
    modifier reinitializer(uint64 version) {
        // solhint-disable-next-line var-name-mixedcase
        InitializableStorage storage $ = _getInitializableStorage();

        if ($._initializing || $._initialized >= version) {
            revert InvalidInitialization();
        }
        $._initialized = version;
        $._initializing = true;
        _;
        $._initializing = false;
        emit Initialized(version);
    }

    /**
     * @dev Modifier to protect an initialization function so that it can only be invoked by functions with the
     * {initializer} and {reinitializer} modifiers, directly or indirectly.
     */
    modifier onlyInitializing() {
        _checkInitializing();
        _;
    }

    /**
     * @dev Reverts if the contract is not in an initializing state. See {onlyInitializing}.
     */
    function _checkInitializing() internal view virtual {
        if (!_isInitializing()) {
            revert NotInitializing();
        }
    }

    /**
     * @dev Locks the contract, preventing any future reinitialization. This cannot be part of an initializer call.
     * Calling this in the constructor of a contract will prevent that contract from being initialized or reinitialized
     * to any version. It is recommended to use this to lock implementation contracts that are designed to be called
     * through proxies.
     *
     * Emits an {Initialized} event the first time it is successfully executed.
     */
    function _disableInitializers() internal virtual {
        // solhint-disable-next-line var-name-mixedcase
        InitializableStorage storage $ = _getInitializableStorage();

        if ($._initializing) {
            revert InvalidInitialization();
        }
        if ($._initialized != type(uint64).max) {
            $._initialized = type(uint64).max;
            emit Initialized(type(uint64).max);
        }
    }

    /**
     * @dev Returns the highest version that has been initialized. See {reinitializer}.
     */
    function _getInitializedVersion() internal view returns (uint64) {
        return _getInitializableStorage()._initialized;
    }

    /**
     * @dev Returns `true` if the contract is currently initializing. See {onlyInitializing}.
     */
    function _isInitializing() internal view returns (bool) {
        return _getInitializableStorage()._initializing;
    }

    /**
     * @dev Pointer to storage slot. Allows integrators to override it with a custom storage location.
     *
     * NOTE: Consider following the ERC-7201 formula to derive storage locations.
     */
    function _initializableStorageSlot() internal pure virtual returns (bytes32) {
        return INITIALIZABLE_STORAGE;
    }

    /**
     * @dev Returns a pointer to the storage namespace.
     */
    // solhint-disable-next-line var-name-mixedcase
    function _getInitializableStorage() private pure returns (InitializableStorage storage $) {
        bytes32 slot = _initializableStorageSlot();
        assembly {
            $.slot := slot
        }
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.3.0) (token/ERC1155/IERC1155.sol)

pragma solidity ^0.8.20;

import {IERC165} from "../../utils/introspection/IERC165.sol";

/**
 * @dev Required interface of an ERC-1155 compliant contract, as defined in the
 * https://eips.ethereum.org/EIPS/eip-1155[ERC].
 */
interface IERC1155 is IERC165 {
    /**
     * @dev Emitted when `value` amount of tokens of type `id` are transferred from `from` to `to` by `operator`.
     */
    event TransferSingle(address indexed operator, address indexed from, address indexed to, uint256 id, uint256 value);

    /**
     * @dev Equivalent to multiple {TransferSingle} events, where `operator`, `from` and `to` are the same for all
     * transfers.
     */
    event TransferBatch(
        address indexed operator,
        address indexed from,
        address indexed to,
        uint256[] ids,
        uint256[] values
    );

    /**
     * @dev Emitted when `account` grants or revokes permission to `operator` to transfer their tokens, according to
     * `approved`.
     */
    event ApprovalForAll(address indexed account, address indexed operator, bool approved);

    /**
     * @dev Emitted when the URI for token type `id` changes to `value`, if it is a non-programmatic URI.
     *
     * If an {URI} event was emitted for `id`, the standard
     * https://eips.ethereum.org/EIPS/eip-1155#metadata-extensions[guarantees] that `value` will equal the value
     * returned by {IERC1155MetadataURI-uri}.
     */
    event URI(string value, uint256 indexed id);

    /**
     * @dev Returns the value of tokens of token type `id` owned by `account`.
     */
    function balanceOf(address account, uint256 id) external view returns (uint256);

    /**
     * @dev xref:ROOT:erc1155.adoc#batch-operations[Batched] version of {balanceOf}.
     *
     * Requirements:
     *
     * - `accounts` and `ids` must have the same length.
     */
    function balanceOfBatch(
        address[] calldata accounts,
        uint256[] calldata ids
    ) external view returns (uint256[] memory);

    /**
     * @dev Grants or revokes permission to `operator` to transfer the caller's tokens, according to `approved`,
     *
     * Emits an {ApprovalForAll} event.
     *
     * Requirements:
     *
     * - `operator` cannot be the zero address.
     */
    function setApprovalForAll(address operator, bool approved) external;

    /**
     * @dev Returns true if `operator` is approved to transfer ``account``'s tokens.
     *
     * See {setApprovalForAll}.
     */
    function isApprovedForAll(address account, address operator) external view returns (bool);

    /**
     * @dev Transfers a `value` amount of tokens of type `id` from `from` to `to`.
     *
     * WARNING: This function can potentially allow a reentrancy attack when transferring tokens
     * to an untrusted contract, when invoking {IERC1155Receiver-onERC1155Received} on the receiver.
     * Ensure to follow the checks-effects-interactions pattern and consider employing
     * reentrancy guards when interacting with untrusted contracts.
     *
     * Emits a {TransferSingle} event.
     *
     * Requirements:
     *
     * - `to` cannot be the zero address.
     * - If the caller is not `from`, it must have been approved to spend ``from``'s tokens via {setApprovalForAll}.
     * - `from` must have a balance of tokens of type `id` of at least `value` amount.
     * - If `to` refers to a smart contract, it must implement {IERC1155Receiver-onERC1155Received} and return the
     * acceptance magic value.
     */
    function safeTransferFrom(address from, address to, uint256 id, uint256 value, bytes calldata data) external;

    /**
     * @dev xref:ROOT:erc1155.adoc#batch-operations[Batched] version of {safeTransferFrom}.
     *
     * WARNING: This function can potentially allow a reentrancy attack when transferring tokens
     * to an untrusted contract, when invoking {IERC1155Receiver-onERC1155BatchReceived} on the receiver.
     * Ensure to follow the checks-effects-interactions pattern and consider employing
     * reentrancy guards when interacting with untrusted contracts.
     *
     * Emits either a {TransferSingle} or a {TransferBatch} event, depending on the length of the array arguments.
     *
     * Requirements:
     *
     * - `ids` and `values` must have the same length.
     * - If `to` refers to a smart contract, it must implement {IERC1155Receiver-onERC1155BatchReceived} and return the
     * acceptance magic value.
     */
    function safeBatchTransferFrom(
        address from,
        address to,
        uint256[] calldata ids,
        uint256[] calldata values,
        bytes calldata data
    ) external;
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.1.0) (token/ERC1155/extensions/IERC1155MetadataURI.sol)

pragma solidity ^0.8.20;

import {IERC1155} from "../IERC1155.sol";

/**
 * @dev Interface of the optional ERC1155MetadataExtension interface, as defined
 * in the https://eips.ethereum.org/EIPS/eip-1155#metadata-extensions[ERC].
 */
interface IERC1155MetadataURI is IERC1155 {
    /**
     * @dev Returns the URI for token type `id`.
     *
     * If the `\{id\}` substring is present in the URI, it must be replaced by
     * clients with the actual token type ID.
     */
    function uri(uint256 id) external view returns (string memory);
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.3.0) (token/ERC1155/utils/ERC1155Utils.sol)

pragma solidity ^0.8.20;

import {IERC1155Receiver} from "../IERC1155Receiver.sol";
import {IERC1155Errors} from "../../../interfaces/draft-IERC6093.sol";

/**
 * @dev Library that provide common ERC-1155 utility functions.
 *
 * See https://eips.ethereum.org/EIPS/eip-1155[ERC-1155].
 *
 * _Available since v5.1._
 */
library ERC1155Utils {
    /**
     * @dev Performs an acceptance check for the provided `operator` by calling {IERC1155Receiver-onERC1155Received}
     * on the `to` address. The `operator` is generally the address that initiated the token transfer (i.e. `msg.sender`).
     *
     * The acceptance call is not executed and treated as a no-op if the target address doesn't contain code (i.e. an EOA).
     * Otherwise, the recipient must implement {IERC1155Receiver-onERC1155Received} and return the acceptance magic value to accept
     * the transfer.
     */
    function checkOnERC1155Received(
        address operator,
        address from,
        address to,
        uint256 id,
        uint256 value,
        bytes memory data
    ) internal {
        if (to.code.length > 0) {
            try IERC1155Receiver(to).onERC1155Received(operator, from, id, value, data) returns (bytes4 response) {
                if (response != IERC1155Receiver.onERC1155Received.selector) {
                    // Tokens rejected
                    revert IERC1155Errors.ERC1155InvalidReceiver(to);
                }
            } catch (bytes memory reason) {
                if (reason.length == 0) {
                    // non-IERC1155Receiver implementer
                    revert IERC1155Errors.ERC1155InvalidReceiver(to);
                } else {
                    assembly ("memory-safe") {
                        revert(add(32, reason), mload(reason))
                    }
                }
            }
        }
    }

    /**
     * @dev Performs a batch acceptance check for the provided `operator` by calling {IERC1155Receiver-onERC1155BatchReceived}
     * on the `to` address. The `operator` is generally the address that initiated the token transfer (i.e. `msg.sender`).
     *
     * The acceptance call is not executed and treated as a no-op if the target address doesn't contain code (i.e. an EOA).
     * Otherwise, the recipient must implement {IERC1155Receiver-onERC1155Received} and return the acceptance magic value to accept
     * the transfer.
     */
    function checkOnERC1155BatchReceived(
        address operator,
        address from,
        address to,
        uint256[] memory ids,
        uint256[] memory values,
        bytes memory data
    ) internal {
        if (to.code.length > 0) {
            try IERC1155Receiver(to).onERC1155BatchReceived(operator, from, ids, values, data) returns (
                bytes4 response
            ) {
                if (response != IERC1155Receiver.onERC1155BatchReceived.selector) {
                    // Tokens rejected
                    revert IERC1155Errors.ERC1155InvalidReceiver(to);
                }
            } catch (bytes memory reason) {
                if (reason.length == 0) {
                    // non-IERC1155Receiver implementer
                    revert IERC1155Errors.ERC1155InvalidReceiver(to);
                } else {
                    assembly ("memory-safe") {
                        revert(add(32, reason), mload(reason))
                    }
                }
            }
        }
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.1) (utils/Context.sol)

pragma solidity ^0.8.20;
import {Initializable} from "../proxy/utils/Initializable.sol";

/**
 * @dev Provides information about the current execution context, including the
 * sender of the transaction and its data. While these are generally available
 * via msg.sender and msg.data, they should not be accessed in such a direct
 * manner, since when dealing with meta-transactions the account sending and
 * paying for execution may not be the actual sender (as far as an application
 * is concerned).
 *
 * This contract is only required for intermediate, library-like contracts.
 */
abstract contract ContextUpgradeable is Initializable {
    function __Context_init() internal onlyInitializing {
    }

    function __Context_init_unchained() internal onlyInitializing {
    }
    function _msgSender() internal view virtual returns (address) {
        return msg.sender;
    }

    function _msgData() internal view virtual returns (bytes calldata) {
        return msg.data;
    }

    function _contextSuffixLength() internal view virtual returns (uint256) {
        return 0;
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.1.0) (utils/introspection/IERC165.sol)

pragma solidity ^0.8.20;

/**
 * @dev Interface of the ERC-165 standard, as defined in the
 * https://eips.ethereum.org/EIPS/eip-165[ERC].
 *
 * Implementers can declare support of contract interfaces, which can then be
 * queried by others ({ERC165Checker}).
 *
 * For an implementation, see {ERC165}.
 */
interface IERC165 {
    /**
     * @dev Returns true if this contract implements the interface defined by
     * `interfaceId`. See the corresponding
     * https://eips.ethereum.org/EIPS/eip-165#how-interfaces-are-identified[ERC section]
     * to learn more about how these ids are created.
     *
     * This function call must use less than 30 000 gas.
     */
    function supportsInterface(bytes4 interfaceId) external view returns (bool);
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.1.0) (utils/introspection/ERC165.sol)

pragma solidity ^0.8.20;

import {IERC165} from "@openzeppelin/contracts/utils/introspection/IERC165.sol";
import {Initializable} from "../../proxy/utils/Initializable.sol";

/**
 * @dev Implementation of the {IERC165} interface.
 *
 * Contracts that want to implement ERC-165 should inherit from this contract and override {supportsInterface} to check
 * for the additional interface id that will be supported. For example:
 *
 * ```solidity
 * function supportsInterface(bytes4 interfaceId) public view virtual override returns (bool) {
 *     return interfaceId == type(MyInterface).interfaceId || super.supportsInterface(interfaceId);
 * }
 * ```
 */
abstract contract ERC165Upgradeable is Initializable, IERC165 {
    function __ERC165_init() internal onlyInitializing {
    }

    function __ERC165_init_unchained() internal onlyInitializing {
    }
    /**
     * @dev See {IERC165-supportsInterface}.
     */
    function supportsInterface(bytes4 interfaceId) public view virtual returns (bool) {
        return interfaceId == type(IERC165).interfaceId;
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.3.0) (utils/Arrays.sol)
// This file was procedurally generated from scripts/generate/templates/Arrays.js.

pragma solidity ^0.8.20;

import {Comparators} from "./Comparators.sol";
import {SlotDerivation} from "./SlotDerivation.sol";
import {StorageSlot} from "./StorageSlot.sol";
import {Math} from "./math/Math.sol";

/**
 * @dev Collection of functions related to array types.
 */
library Arrays {
    using SlotDerivation for bytes32;
    using StorageSlot for bytes32;

    /**
     * @dev Sort an array of uint256 (in memory) following the provided comparator function.
     *
     * This function does the sorting "in place", meaning that it overrides the input. The object is returned for
     * convenience, but that returned value can be discarded safely if the caller has a memory pointer to the array.
     *
     * NOTE: this function's cost is `O(n · log(n))` in average and `O(n²)` in the worst case, with n the length of the
     * array. Using it in view functions that are executed through `eth_call` is safe, but one should be very careful
     * when executing this as part of a transaction. If the array being sorted is too large, the sort operation may
     * consume more gas than is available in a block, leading to potential DoS.
     *
     * IMPORTANT: Consider memory side-effects when using custom comparator functions that access memory in an unsafe way.
     */
    function sort(
        uint256[] memory array,
        function(uint256, uint256) pure returns (bool) comp
    ) internal pure returns (uint256[] memory) {
        _quickSort(_begin(array), _end(array), comp);
        return array;
    }

    /**
     * @dev Variant of {sort} that sorts an array of uint256 in increasing order.
     */
    function sort(uint256[] memory array) internal pure returns (uint256[] memory) {
        sort(array, Comparators.lt);
        return array;
    }

    /**
     * @dev Sort an array of address (in memory) following the provided comparator function.
     *
     * This function does the sorting "in place", meaning that it overrides the input. The object is returned for
     * convenience, but that returned value can be discarded safely if the caller has a memory pointer to the array.
     *
     * NOTE: this function's cost is `O(n · log(n))` in average and `O(n²)` in the worst case, with n the length of the
     * array. Using it in view functions that are executed through `eth_call` is safe, but one should be very careful
     * when executing this as part of a transaction. If the array being sorted is too large, the sort operation may
     * consume more gas than is available in a block, leading to potential DoS.
     *
     * IMPORTANT: Consider memory side-effects when using custom comparator functions that access memory in an unsafe way.
     */
    function sort(
        address[] memory array,
        function(address, address) pure returns (bool) comp
    ) internal pure returns (address[] memory) {
        sort(_castToUint256Array(array), _castToUint256Comp(comp));
        return array;
    }

    /**
     * @dev Variant of {sort} that sorts an array of address in increasing order.
     */
    function sort(address[] memory array) internal pure returns (address[] memory) {
        sort(_castToUint256Array(array), Comparators.lt);
        return array;
    }

    /**
     * @dev Sort an array of bytes32 (in memory) following the provided comparator function.
     *
     * This function does the sorting "in place", meaning that it overrides the input. The object is returned for
     * convenience, but that returned value can be discarded safely if the caller has a memory pointer to the array.
     *
     * NOTE: this function's cost is `O(n · log(n))` in average and `O(n²)` in the worst case, with n the length of the
     * array. Using it in view functions that are executed through `eth_call` is safe, but one should be very careful
     * when executing this as part of a transaction. If the array being sorted is too large, the sort operation may
     * consume more gas than is available in a block, leading to potential DoS.
     *
     * IMPORTANT: Consider memory side-effects when using custom comparator functions that access memory in an unsafe way.
     */
    function sort(
        bytes32[] memory array,
        function(bytes32, bytes32) pure returns (bool) comp
    ) internal pure returns (bytes32[] memory) {
        sort(_castToUint256Array(array), _castToUint256Comp(comp));
        return array;
    }

    /**
     * @dev Variant of {sort} that sorts an array of bytes32 in increasing order.
     */
    function sort(bytes32[] memory array) internal pure returns (bytes32[] memory) {
        sort(_castToUint256Array(array), Comparators.lt);
        return array;
    }

    /**
     * @dev Performs a quick sort of a segment of memory. The segment sorted starts at `begin` (inclusive), and stops
     * at end (exclusive). Sorting follows the `comp` comparator.
     *
     * Invariant: `begin <= end`. This is the case when initially called by {sort} and is preserved in subcalls.
     *
     * IMPORTANT: Memory locations between `begin` and `end` are not validated/zeroed. This function should
     * be used only if the limits are within a memory array.
     */
    function _quickSort(uint256 begin, uint256 end, function(uint256, uint256) pure returns (bool) comp) private pure {
        unchecked {
            if (end - begin < 0x40) return;

            // Use first element as pivot
            uint256 pivot = _mload(begin);
            // Position where the pivot should be at the end of the loop
            uint256 pos = begin;

            for (uint256 it = begin + 0x20; it < end; it += 0x20) {
                if (comp(_mload(it), pivot)) {
                    // If the value stored at the iterator's position comes before the pivot, we increment the
                    // position of the pivot and move the value there.
                    pos += 0x20;
                    _swap(pos, it);
                }
            }

            _swap(begin, pos); // Swap pivot into place
            _quickSort(begin, pos, comp); // Sort the left side of the pivot
            _quickSort(pos + 0x20, end, comp); // Sort the right side of the pivot
        }
    }

    /**
     * @dev Pointer to the memory location of the first element of `array`.
     */
    function _begin(uint256[] memory array) private pure returns (uint256 ptr) {
        assembly ("memory-safe") {
            ptr := add(array, 0x20)
        }
    }

    /**
     * @dev Pointer to the memory location of the first memory word (32bytes) after `array`. This is the memory word
     * that comes just after the last element of the array.
     */
    function _end(uint256[] memory array) private pure returns (uint256 ptr) {
        unchecked {
            return _begin(array) + array.length * 0x20;
        }
    }

    /**
     * @dev Load memory word (as a uint256) at location `ptr`.
     */
    function _mload(uint256 ptr) private pure returns (uint256 value) {
        assembly {
            value := mload(ptr)
        }
    }

    /**
     * @dev Swaps the elements memory location `ptr1` and `ptr2`.
     */
    function _swap(uint256 ptr1, uint256 ptr2) private pure {
        assembly {
            let value1 := mload(ptr1)
            let value2 := mload(ptr2)
            mstore(ptr1, value2)
            mstore(ptr2, value1)
        }
    }

    /// @dev Helper: low level cast address memory array to uint256 memory array
    function _castToUint256Array(address[] memory input) private pure returns (uint256[] memory output) {
        assembly {
            output := input
        }
    }

    /// @dev Helper: low level cast bytes32 memory array to uint256 memory array
    function _castToUint256Array(bytes32[] memory input) private pure returns (uint256[] memory output) {
        assembly {
            output := input
        }
    }

    /// @dev Helper: low level cast address comp function to uint256 comp function
    function _castToUint256Comp(
        function(address, address) pure returns (bool) input
    ) private pure returns (function(uint256, uint256) pure returns (bool) output) {
        assembly {
            output := input
        }
    }

    /// @dev Helper: low level cast bytes32 comp function to uint256 comp function
    function _castToUint256Comp(
        function(bytes32, bytes32) pure returns (bool) input
    ) private pure returns (function(uint256, uint256) pure returns (bool) output) {
        assembly {
            output := input
        }
    }

    /**
     * @dev Searches a sorted `array` and returns the first index that contains
     * a value greater or equal to `element`. If no such index exists (i.e. all
     * values in the array are strictly less than `element`), the array length is
     * returned. Time complexity O(log n).
     *
     * NOTE: The `array` is expected to be sorted in ascending order, and to
     * contain no repeated elements.
     *
     * IMPORTANT: Deprecated. This implementation behaves as {lowerBound} but lacks
     * support for repeated elements in the array. The {lowerBound} function should
     * be used instead.
     */
    function findUpperBound(uint256[] storage array, uint256 element) internal view returns (uint256) {
        uint256 low = 0;
        uint256 high = array.length;

        if (high == 0) {
            return 0;
        }

        while (low < high) {
            uint256 mid = Math.average(low, high);

            // Note that mid will always be strictly less than high (i.e. it will be a valid array index)
            // because Math.average rounds towards zero (it does integer division with truncation).
            if (unsafeAccess(array, mid).value > element) {
                high = mid;
            } else {
                low = mid + 1;
            }
        }

        // At this point `low` is the exclusive upper bound. We will return the inclusive upper bound.
        if (low > 0 && unsafeAccess(array, low - 1).value == element) {
            return low - 1;
        } else {
            return low;
        }
    }

    /**
     * @dev Searches an `array` sorted in ascending order and returns the first
     * index that contains a value greater or equal than `element`. If no such index
     * exists (i.e. all values in the array are strictly less than `element`), the array
     * length is returned. Time complexity O(log n).
     *
     * See C++'s https://en.cppreference.com/w/cpp/algorithm/lower_bound[lower_bound].
     */
    function lowerBound(uint256[] storage array, uint256 element) internal view returns (uint256) {
        uint256 low = 0;
        uint256 high = array.length;

        if (high == 0) {
            return 0;
        }

        while (low < high) {
            uint256 mid = Math.average(low, high);

            // Note that mid will always be strictly less than high (i.e. it will be a valid array index)
            // because Math.average rounds towards zero (it does integer division with truncation).
            if (unsafeAccess(array, mid).value < element) {
                // this cannot overflow because mid < high
                unchecked {
                    low = mid + 1;
                }
            } else {
                high = mid;
            }
        }

        return low;
    }

    /**
     * @dev Searches an `array` sorted in ascending order and returns the first
     * index that contains a value strictly greater than `element`. If no such index
     * exists (i.e. all values in the array are strictly less than `element`), the array
     * length is returned. Time complexity O(log n).
     *
     * See C++'s https://en.cppreference.com/w/cpp/algorithm/upper_bound[upper_bound].
     */
    function upperBound(uint256[] storage array, uint256 element) internal view returns (uint256) {
        uint256 low = 0;
        uint256 high = array.length;

        if (high == 0) {
            return 0;
        }

        while (low < high) {
            uint256 mid = Math.average(low, high);

            // Note that mid will always be strictly less than high (i.e. it will be a valid array index)
            // because Math.average rounds towards zero (it does integer division with truncation).
            if (unsafeAccess(array, mid).value > element) {
                high = mid;
            } else {
                // this cannot overflow because mid < high
                unchecked {
                    low = mid + 1;
                }
            }
        }

        return low;
    }

    /**
     * @dev Same as {lowerBound}, but with an array in memory.
     */
    function lowerBoundMemory(uint256[] memory array, uint256 element) internal pure returns (uint256) {
        uint256 low = 0;
        uint256 high = array.length;

        if (high == 0) {
            return 0;
        }

        while (low < high) {
            uint256 mid = Math.average(low, high);

            // Note that mid will always be strictly less than high (i.e. it will be a valid array index)
            // because Math.average rounds towards zero (it does integer division with truncation).
            if (unsafeMemoryAccess(array, mid) < element) {
                // this cannot overflow because mid < high
                unchecked {
                    low = mid + 1;
                }
            } else {
                high = mid;
            }
        }

        return low;
    }

    /**
     * @dev Same as {upperBound}, but with an array in memory.
     */
    function upperBoundMemory(uint256[] memory array, uint256 element) internal pure returns (uint256) {
        uint256 low = 0;
        uint256 high = array.length;

        if (high == 0) {
            return 0;
        }

        while (low < high) {
            uint256 mid = Math.average(low, high);

            // Note that mid will always be strictly less than high (i.e. it will be a valid array index)
            // because Math.average rounds towards zero (it does integer division with truncation).
            if (unsafeMemoryAccess(array, mid) > element) {
                high = mid;
            } else {
                // this cannot overflow because mid < high
                unchecked {
                    low = mid + 1;
                }
            }
        }

        return low;
    }

    /**
     * @dev Access an array in an "unsafe" way. Skips solidity "index-out-of-range" check.
     *
     * WARNING: Only use if you are certain `pos` is lower than the array length.
     */
    function unsafeAccess(address[] storage arr, uint256 pos) internal pure returns (StorageSlot.AddressSlot storage) {
        bytes32 slot;
        assembly ("memory-safe") {
            slot := arr.slot
        }
        return slot.deriveArray().offset(pos).getAddressSlot();
    }

    /**
     * @dev Access an array in an "unsafe" way. Skips solidity "index-out-of-range" check.
     *
     * WARNING: Only use if you are certain `pos` is lower than the array length.
     */
    function unsafeAccess(bytes32[] storage arr, uint256 pos) internal pure returns (StorageSlot.Bytes32Slot storage) {
        bytes32 slot;
        assembly ("memory-safe") {
            slot := arr.slot
        }
        return slot.deriveArray().offset(pos).getBytes32Slot();
    }

    /**
     * @dev Access an array in an "unsafe" way. Skips solidity "index-out-of-range" check.
     *
     * WARNING: Only use if you are certain `pos` is lower than the array length.
     */
    function unsafeAccess(uint256[] storage arr, uint256 pos) internal pure returns (StorageSlot.Uint256Slot storage) {
        bytes32 slot;
        assembly ("memory-safe") {
            slot := arr.slot
        }
        return slot.deriveArray().offset(pos).getUint256Slot();
    }

    /**
     * @dev Access an array in an "unsafe" way. Skips solidity "index-out-of-range" check.
     *
     * WARNING: Only use if you are certain `pos` is lower than the array length.
     */
    function unsafeMemoryAccess(address[] memory arr, uint256 pos) internal pure returns (address res) {
        assembly {
            res := mload(add(add(arr, 0x20), mul(pos, 0x20)))
        }
    }

    /**
     * @dev Access an array in an "unsafe" way. Skips solidity "index-out-of-range" check.
     *
     * WARNING: Only use if you are certain `pos` is lower than the array length.
     */
    function unsafeMemoryAccess(bytes32[] memory arr, uint256 pos) internal pure returns (bytes32 res) {
        assembly {
            res := mload(add(add(arr, 0x20), mul(pos, 0x20)))
        }
    }

    /**
     * @dev Access an array in an "unsafe" way. Skips solidity "index-out-of-range" check.
     *
     * WARNING: Only use if you are certain `pos` is lower than the array length.
     */
    function unsafeMemoryAccess(uint256[] memory arr, uint256 pos) internal pure returns (uint256 res) {
        assembly {
            res := mload(add(add(arr, 0x20), mul(pos, 0x20)))
        }
    }

    /**
     * @dev Helper to set the length of a dynamic array. Directly writing to `.length` is forbidden.
     *
     * WARNING: this does not clear elements if length is reduced, of initialize elements if length is increased.
     */
    function unsafeSetLength(address[] storage array, uint256 len) internal {
        assembly ("memory-safe") {
            sstore(array.slot, len)
        }
    }

    /**
     * @dev Helper to set the length of a dynamic array. Directly writing to `.length` is forbidden.
     *
     * WARNING: this does not clear elements if length is reduced, of initialize elements if length is increased.
     */
    function unsafeSetLength(bytes32[] storage array, uint256 len) internal {
        assembly ("memory-safe") {
            sstore(array.slot, len)
        }
    }

    /**
     * @dev Helper to set the length of a dynamic array. Directly writing to `.length` is forbidden.
     *
     * WARNING: this does not clear elements if length is reduced, of initialize elements if length is increased.
     */
    function unsafeSetLength(uint256[] storage array, uint256 len) internal {
        assembly ("memory-safe") {
            sstore(array.slot, len)
        }
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.1.0) (interfaces/draft-IERC6093.sol)
pragma solidity ^0.8.20;

/**
 * @dev Standard ERC-20 Errors
 * Interface of the https://eips.ethereum.org/EIPS/eip-6093[ERC-6093] custom errors for ERC-20 tokens.
 */
interface IERC20Errors {
    /**
     * @dev Indicates an error related to the current `balance` of a `sender`. Used in transfers.
     * @param sender Address whose tokens are being transferred.
     * @param balance Current balance for the interacting account.
     * @param needed Minimum amount required to perform a transfer.
     */
    error ERC20InsufficientBalance(address sender, uint256 balance, uint256 needed);

    /**
     * @dev Indicates a failure with the token `sender`. Used in transfers.
     * @param sender Address whose tokens are being transferred.
     */
    error ERC20InvalidSender(address sender);

    /**
     * @dev Indicates a failure with the token `receiver`. Used in transfers.
     * @param receiver Address to which tokens are being transferred.
     */
    error ERC20InvalidReceiver(address receiver);

    /**
     * @dev Indicates a failure with the `spender`’s `allowance`. Used in transfers.
     * @param spender Address that may be allowed to operate on tokens without being their owner.
     * @param allowance Amount of tokens a `spender` is allowed to operate with.
     * @param needed Minimum amount required to perform a transfer.
     */
    error ERC20InsufficientAllowance(address spender, uint256 allowance, uint256 needed);

    /**
     * @dev Indicates a failure with the `approver` of a token to be approved. Used in approvals.
     * @param approver Address initiating an approval operation.
     */
    error ERC20InvalidApprover(address approver);

    /**
     * @dev Indicates a failure with the `spender` to be approved. Used in approvals.
     * @param spender Address that may be allowed to operate on tokens without being their owner.
     */
    error ERC20InvalidSpender(address spender);
}

/**
 * @dev Standard ERC-721 Errors
 * Interface of the https://eips.ethereum.org/EIPS/eip-6093[ERC-6093] custom errors for ERC-721 tokens.
 */
interface IERC721Errors {
    /**
     * @dev Indicates that an address can't be an owner. For example, `address(0)` is a forbidden owner in ERC-20.
     * Used in balance queries.
     * @param owner Address of the current owner of a token.
     */
    error ERC721InvalidOwner(address owner);

    /**
     * @dev Indicates a `tokenId` whose `owner` is the zero address.
     * @param tokenId Identifier number of a token.
     */
    error ERC721NonexistentToken(uint256 tokenId);

    /**
     * @dev Indicates an error related to the ownership over a particular token. Used in transfers.
     * @param sender Address whose tokens are being transferred.
     * @param tokenId Identifier number of a token.
     * @param owner Address of the current owner of a token.
     */
    error ERC721IncorrectOwner(address sender, uint256 tokenId, address owner);

    /**
     * @dev Indicates a failure with the token `sender`. Used in transfers.
     * @param sender Address whose tokens are being transferred.
     */
    error ERC721InvalidSender(address sender);

    /**
     * @dev Indicates a failure with the token `receiver`. Used in transfers.
     * @param receiver Address to which tokens are being transferred.
     */
    error ERC721InvalidReceiver(address receiver);

    /**
     * @dev Indicates a failure with the `operator`’s approval. Used in transfers.
     * @param operator Address that may be allowed to operate on tokens without being their owner.
     * @param tokenId Identifier number of a token.
     */
    error ERC721InsufficientApproval(address operator, uint256 tokenId);

    /**
     * @dev Indicates a failure with the `approver` of a token to be approved. Used in approvals.
     * @param approver Address initiating an approval operation.
     */
    error ERC721InvalidApprover(address approver);

    /**
     * @dev Indicates a failure with the `operator` to be approved. Used in approvals.
     * @param operator Address that may be allowed to operate on tokens without being their owner.
     */
    error ERC721InvalidOperator(address operator);
}

/**
 * @dev Standard ERC-1155 Errors
 * Interface of the https://eips.ethereum.org/EIPS/eip-6093[ERC-6093] custom errors for ERC-1155 tokens.
 */
interface IERC1155Errors {
    /**
     * @dev Indicates an error related to the current `balance` of a `sender`. Used in transfers.
     * @param sender Address whose tokens are being transferred.
     * @param balance Current balance for the interacting account.
     * @param needed Minimum amount required to perform a transfer.
     * @param tokenId Identifier number of a token.
     */
    error ERC1155InsufficientBalance(address sender, uint256 balance, uint256 needed, uint256 tokenId);

    /**
     * @dev Indicates a failure with the token `sender`. Used in transfers.
     * @param sender Address whose tokens are being transferred.
     */
    error ERC1155InvalidSender(address sender);

    /**
     * @dev Indicates a failure with the token `receiver`. Used in transfers.
     * @param receiver Address to which tokens are being transferred.
     */
    error ERC1155InvalidReceiver(address receiver);

    /**
     * @dev Indicates a failure with the `operator`’s approval. Used in transfers.
     * @param operator Address that may be allowed to operate on tokens without being their owner.
     * @param owner Address of the current owner of a token.
     */
    error ERC1155MissingApprovalForAll(address operator, address owner);

    /**
     * @dev Indicates a failure with the `approver` of a token to be approved. Used in approvals.
     * @param approver Address initiating an approval operation.
     */
    error ERC1155InvalidApprover(address approver);

    /**
     * @dev Indicates a failure with the `operator` to be approved. Used in approvals.
     * @param operator Address that may be allowed to operate on tokens without being their owner.
     */
    error ERC1155InvalidOperator(address operator);

    /**
     * @dev Indicates an array length mismatch between ids and values in a safeBatchTransferFrom operation.
     * Used in batch transfers.
     * @param idsLength Length of the array of token identifiers
     * @param valuesLength Length of the array of token amounts
     */
    error ERC1155InvalidArrayLength(uint256 idsLength, uint256 valuesLength);
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.3.0) (utils/cryptography/Hashes.sol)

pragma solidity ^0.8.20;

/**
 * @dev Library of standard hash functions.
 *
 * _Available since v5.1._
 */
library Hashes {
    /**
     * @dev Commutative Keccak256 hash of a sorted pair of bytes32. Frequently used when working with merkle proofs.
     *
     * NOTE: Equivalent to the `standardNodeHash` in our https://github.com/OpenZeppelin/merkle-tree[JavaScript library].
     */
    function commutativeKeccak256(bytes32 a, bytes32 b) internal pure returns (bytes32) {
        return a < b ? efficientKeccak256(a, b) : efficientKeccak256(b, a);
    }

    /**
     * @dev Implementation of keccak256(abi.encode(a, b)) that doesn't allocate or expand memory.
     */
    function efficientKeccak256(bytes32 a, bytes32 b) internal pure returns (bytes32 value) {
        assembly ("memory-safe") {
            mstore(0x00, a)
            mstore(0x20, b)
            value := keccak256(0x00, 0x40)
        }
    }
}

// SPDX-License-Identifier: BUSL-1.1
pragma solidity ^0.8.28;

/// @title IAccess
/// @author kexley, Cap Labs
/// @notice Interface for Access contract
interface IAccess {
    /// @dev Access storage
    /// @param accessControl Access control address
    struct AccessStorage {
        address accessControl;
    }

    /// @notice Access is denied for the caller
    error AccessDenied();
}

// SPDX-License-Identifier: BUSL-1.1
pragma solidity ^0.8.28;

/// @title IAccessControl
/// @author kexley, Cap Labs
/// @notice Interface for granular access control system that manages permissions for specific function selectors on contracts
interface IAccessControl {
    /// @notice Error thrown when trying to revoke own revocation role
    error CannotRevokeSelf();

    /// @notice Initialize the access control system with a default admin
    /// @param _admin Address to be granted the default admin role and initial access management permissions
    function initialize(address _admin) external;

    /// @notice Grant access to a specific method on a contract
    /// @param _selector Function selector (4-byte identifier) of the method to grant access to
    /// @param _contract Address of the contract containing the method
    /// @param _address Address to grant access to
    function grantAccess(bytes4 _selector, address _contract, address _address) external;

    /// @notice Revoke access to a specific method on a contract
    /// @param _selector Function selector (4-byte identifier) of the method to revoke access from
    /// @param _contract Address of the contract containing the method
    /// @param _address Address to revoke access from
    function revokeAccess(bytes4 _selector, address _contract, address _address) external;

    /// @notice Check if a specific method access is granted to an address
    /// @param _selector Function selector (4-byte identifier) of the method to check
    /// @param _contract Address of the contract containing the method
    /// @param _caller Address to check permissions for
    /// @return hasAccess True if access is granted, false otherwise
    function checkAccess(bytes4 _selector, address _contract, address _caller) external view returns (bool hasAccess);

    /// @notice Get the role identifier for a specific function selector on a contract
    /// @dev The role identifier is a unique identifier derived packing the selector and contract address
    /// @param _selector Function selector (4-byte identifier) of the method
    /// @param _contract Address of the contract containing the method
    /// @return roleId Unique role identifier derived from the selector and contract address
    function role(bytes4 _selector, address _contract) external pure returns (bytes32 roleId);
}

// SPDX-License-Identifier: BUSL-1.1
pragma solidity ^0.8.28;

import { IAccess } from "../interfaces/IAccess.sol";

/// @title Access Storage Utils
/// @author kexley, Cap Labs
/// @notice Storage utilities for access control
abstract contract AccessStorageUtils {
    /// @dev keccak256(abi.encode(uint256(keccak256("cap.storage.Access")) - 1)) & ~bytes32(uint256(0xff))
    bytes32 private constant AccessStorageLocation = 0xb413d65cb88f23816c329284a0d3eb15a99df7963ab7402ade4c5da22bff6b00;

    /// @dev Get access storage
    /// @return $ Storage pointer
    function getAccessStorage() internal pure returns (IAccess.AccessStorage storage $) {
        assembly {
            $.slot := AccessStorageLocation
        }
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.0) (proxy/beacon/IBeacon.sol)

pragma solidity ^0.8.20;

/**
 * @dev This is the interface that {BeaconProxy} expects of its beacon.
 */
interface IBeacon {
    /**
     * @dev Must return an address that can be used as a delegate call target.
     *
     * {UpgradeableBeacon} will check that this address is a contract.
     */
    function implementation() external view returns (address);
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.0) (interfaces/IERC1967.sol)

pragma solidity ^0.8.20;

/**
 * @dev ERC-1967: Proxy Storage Slots. This interface contains the events defined in the ERC.
 */
interface IERC1967 {
    /**
     * @dev Emitted when the implementation is upgraded.
     */
    event Upgraded(address indexed implementation);

    /**
     * @dev Emitted when the admin account has changed.
     */
    event AdminChanged(address previousAdmin, address newAdmin);

    /**
     * @dev Emitted when the beacon is changed.
     */
    event BeaconUpgraded(address indexed beacon);
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.2.0) (utils/Address.sol)

pragma solidity ^0.8.20;

import {Errors} from "./Errors.sol";

/**
 * @dev Collection of functions related to the address type
 */
library Address {
    /**
     * @dev There's no code at `target` (it is not a contract).
     */
    error AddressEmptyCode(address target);

    /**
     * @dev Replacement for Solidity's `transfer`: sends `amount` wei to
     * `recipient`, forwarding all available gas and reverting on errors.
     *
     * https://eips.ethereum.org/EIPS/eip-1884[EIP1884] increases the gas cost
     * of certain opcodes, possibly making contracts go over the 2300 gas limit
     * imposed by `transfer`, making them unable to receive funds via
     * `transfer`. {sendValue} removes this limitation.
     *
     * https://consensys.net/diligence/blog/2019/09/stop-using-soliditys-transfer-now/[Learn more].
     *
     * IMPORTANT: because control is transferred to `recipient`, care must be
     * taken to not create reentrancy vulnerabilities. Consider using
     * {ReentrancyGuard} or the
     * https://solidity.readthedocs.io/en/v0.8.20/security-considerations.html#use-the-checks-effects-interactions-pattern[checks-effects-interactions pattern].
     */
    function sendValue(address payable recipient, uint256 amount) internal {
        if (address(this).balance < amount) {
            revert Errors.InsufficientBalance(address(this).balance, amount);
        }

        (bool success, bytes memory returndata) = recipient.call{value: amount}("");
        if (!success) {
            _revert(returndata);
        }
    }

    /**
     * @dev Performs a Solidity function call using a low level `call`. A
     * plain `call` is an unsafe replacement for a function call: use this
     * function instead.
     *
     * If `target` reverts with a revert reason or custom error, it is bubbled
     * up by this function (like regular Solidity function calls). However, if
     * the call reverted with no returned reason, this function reverts with a
     * {Errors.FailedCall} error.
     *
     * Returns the raw returned data. To convert to the expected return value,
     * use https://solidity.readthedocs.io/en/latest/units-and-global-variables.html?highlight=abi.decode#abi-encoding-and-decoding-functions[`abi.decode`].
     *
     * Requirements:
     *
     * - `target` must be a contract.
     * - calling `target` with `data` must not revert.
     */
    function functionCall(address target, bytes memory data) internal returns (bytes memory) {
        return functionCallWithValue(target, data, 0);
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`],
     * but also transferring `value` wei to `target`.
     *
     * Requirements:
     *
     * - the calling contract must have an ETH balance of at least `value`.
     * - the called Solidity function must be `payable`.
     */
    function functionCallWithValue(address target, bytes memory data, uint256 value) internal returns (bytes memory) {
        if (address(this).balance < value) {
            revert Errors.InsufficientBalance(address(this).balance, value);
        }
        (bool success, bytes memory returndata) = target.call{value: value}(data);
        return verifyCallResultFromTarget(target, success, returndata);
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`],
     * but performing a static call.
     */
    function functionStaticCall(address target, bytes memory data) internal view returns (bytes memory) {
        (bool success, bytes memory returndata) = target.staticcall(data);
        return verifyCallResultFromTarget(target, success, returndata);
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`],
     * but performing a delegate call.
     */
    function functionDelegateCall(address target, bytes memory data) internal returns (bytes memory) {
        (bool success, bytes memory returndata) = target.delegatecall(data);
        return verifyCallResultFromTarget(target, success, returndata);
    }

    /**
     * @dev Tool to verify that a low level call to smart-contract was successful, and reverts if the target
     * was not a contract or bubbling up the revert reason (falling back to {Errors.FailedCall}) in case
     * of an unsuccessful call.
     */
    function verifyCallResultFromTarget(
        address target,
        bool success,
        bytes memory returndata
    ) internal view returns (bytes memory) {
        if (!success) {
            _revert(returndata);
        } else {
            // only check if target is a contract if the call was successful and the return data is empty
            // otherwise we already know that it was a contract
            if (returndata.length == 0 && target.code.length == 0) {
                revert AddressEmptyCode(target);
            }
            return returndata;
        }
    }

    /**
     * @dev Tool to verify that a low level call was successful, and reverts if it wasn't, either by bubbling the
     * revert reason or with a default {Errors.FailedCall} error.
     */
    function verifyCallResult(bool success, bytes memory returndata) internal pure returns (bytes memory) {
        if (!success) {
            _revert(returndata);
        } else {
            return returndata;
        }
    }

    /**
     * @dev Reverts with returndata if present. Otherwise reverts with {Errors.FailedCall}.
     */
    function _revert(bytes memory returndata) private pure {
        // Look for revert reason and bubble it up if present
        if (returndata.length > 0) {
            // The easiest way to bubble the revert reason is using memory via assembly
            assembly ("memory-safe") {
                let returndata_size := mload(returndata)
                revert(add(32, returndata), returndata_size)
            }
        } else {
            revert Errors.FailedCall();
        }
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.1.0) (utils/StorageSlot.sol)
// This file was procedurally generated from scripts/generate/templates/StorageSlot.js.

pragma solidity ^0.8.20;

/**
 * @dev Library for reading and writing primitive types to specific storage slots.
 *
 * Storage slots are often used to avoid storage conflict when dealing with upgradeable contracts.
 * This library helps with reading and writing to such slots without the need for inline assembly.
 *
 * The functions in this library return Slot structs that contain a `value` member that can be used to read or write.
 *
 * Example usage to set ERC-1967 implementation slot:
 * ```solidity
 * contract ERC1967 {
 *     // Define the slot. Alternatively, use the SlotDerivation library to derive the slot.
 *     bytes32 internal constant _IMPLEMENTATION_SLOT = 0x360894a13ba1a3210667c828492db98dca3e2076cc3735a920a3ca505d382bbc;
 *
 *     function _getImplementation() internal view returns (address) {
 *         return StorageSlot.getAddressSlot(_IMPLEMENTATION_SLOT).value;
 *     }
 *
 *     function _setImplementation(address newImplementation) internal {
 *         require(newImplementation.code.length > 0);
 *         StorageSlot.getAddressSlot(_IMPLEMENTATION_SLOT).value = newImplementation;
 *     }
 * }
 * ```
 *
 * TIP: Consider using this library along with {SlotDerivation}.
 */
library StorageSlot {
    struct AddressSlot {
        address value;
    }

    struct BooleanSlot {
        bool value;
    }

    struct Bytes32Slot {
        bytes32 value;
    }

    struct Uint256Slot {
        uint256 value;
    }

    struct Int256Slot {
        int256 value;
    }

    struct StringSlot {
        string value;
    }

    struct BytesSlot {
        bytes value;
    }

    /**
     * @dev Returns an `AddressSlot` with member `value` located at `slot`.
     */
    function getAddressSlot(bytes32 slot) internal pure returns (AddressSlot storage r) {
        assembly ("memory-safe") {
            r.slot := slot
        }
    }

    /**
     * @dev Returns a `BooleanSlot` with member `value` located at `slot`.
     */
    function getBooleanSlot(bytes32 slot) internal pure returns (BooleanSlot storage r) {
        assembly ("memory-safe") {
            r.slot := slot
        }
    }

    /**
     * @dev Returns a `Bytes32Slot` with member `value` located at `slot`.
     */
    function getBytes32Slot(bytes32 slot) internal pure returns (Bytes32Slot storage r) {
        assembly ("memory-safe") {
            r.slot := slot
        }
    }

    /**
     * @dev Returns a `Uint256Slot` with member `value` located at `slot`.
     */
    function getUint256Slot(bytes32 slot) internal pure returns (Uint256Slot storage r) {
        assembly ("memory-safe") {
            r.slot := slot
        }
    }

    /**
     * @dev Returns a `Int256Slot` with member `value` located at `slot`.
     */
    function getInt256Slot(bytes32 slot) internal pure returns (Int256Slot storage r) {
        assembly ("memory-safe") {
            r.slot := slot
        }
    }

    /**
     * @dev Returns a `StringSlot` with member `value` located at `slot`.
     */
    function getStringSlot(bytes32 slot) internal pure returns (StringSlot storage r) {
        assembly ("memory-safe") {
            r.slot := slot
        }
    }

    /**
     * @dev Returns an `StringSlot` representation of the string storage pointer `store`.
     */
    function getStringSlot(string storage store) internal pure returns (StringSlot storage r) {
        assembly ("memory-safe") {
            r.slot := store.slot
        }
    }

    /**
     * @dev Returns a `BytesSlot` with member `value` located at `slot`.
     */
    function getBytesSlot(bytes32 slot) internal pure returns (BytesSlot storage r) {
        assembly ("memory-safe") {
            r.slot := slot
        }
    }

    /**
     * @dev Returns an `BytesSlot` representation of the bytes storage pointer `store`.
     */
    function getBytesSlot(bytes storage store) internal pure returns (BytesSlot storage r) {
        assembly ("memory-safe") {
            r.slot := store.slot
        }
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.1.0) (token/ERC1155/IERC1155Receiver.sol)

pragma solidity ^0.8.20;

import {IERC165} from "../../utils/introspection/IERC165.sol";

/**
 * @dev Interface that must be implemented by smart contracts in order to receive
 * ERC-1155 token transfers.
 */
interface IERC1155Receiver is IERC165 {
    /**
     * @dev Handles the receipt of a single ERC-1155 token type. This function is
     * called at the end of a `safeTransferFrom` after the balance has been updated.
     *
     * NOTE: To accept the transfer, this must return
     * `bytes4(keccak256("onERC1155Received(address,address,uint256,uint256,bytes)"))`
     * (i.e. 0xf23a6e61, or its own function selector).
     *
     * @param operator The address which initiated the transfer (i.e. msg.sender)
     * @param from The address which previously owned the token
     * @param id The ID of the token being transferred
     * @param value The amount of tokens being transferred
     * @param data Additional data with no specified format
     * @return `bytes4(keccak256("onERC1155Received(address,address,uint256,uint256,bytes)"))` if transfer is allowed
     */
    function onERC1155Received(
        address operator,
        address from,
        uint256 id,
        uint256 value,
        bytes calldata data
    ) external returns (bytes4);

    /**
     * @dev Handles the receipt of a multiple ERC-1155 token types. This function
     * is called at the end of a `safeBatchTransferFrom` after the balances have
     * been updated.
     *
     * NOTE: To accept the transfer(s), this must return
     * `bytes4(keccak256("onERC1155BatchReceived(address,address,uint256[],uint256[],bytes)"))`
     * (i.e. 0xbc197c81, or its own function selector).
     *
     * @param operator The address which initiated the batch transfer (i.e. msg.sender)
     * @param from The address which previously owned the token
     * @param ids An array containing ids of each token being transferred (order and length must match values array)
     * @param values An array containing amounts of each token being transferred (order and length must match ids array)
     * @param data Additional data with no specified format
     * @return `bytes4(keccak256("onERC1155BatchReceived(address,address,uint256[],uint256[],bytes)"))` if transfer is allowed
     */
    function onERC1155BatchReceived(
        address operator,
        address from,
        uint256[] calldata ids,
        uint256[] calldata values,
        bytes calldata data
    ) external returns (bytes4);
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.1.0) (utils/Comparators.sol)

pragma solidity ^0.8.20;

/**
 * @dev Provides a set of functions to compare values.
 *
 * _Available since v5.1._
 */
library Comparators {
    function lt(uint256 a, uint256 b) internal pure returns (bool) {
        return a < b;
    }

    function gt(uint256 a, uint256 b) internal pure returns (bool) {
        return a > b;
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.3.0) (utils/SlotDerivation.sol)
// This file was procedurally generated from scripts/generate/templates/SlotDerivation.js.

pragma solidity ^0.8.20;

/**
 * @dev Library for computing storage (and transient storage) locations from namespaces and deriving slots
 * corresponding to standard patterns. The derivation method for array and mapping matches the storage layout used by
 * the solidity language / compiler.
 *
 * See https://docs.soliditylang.org/en/v0.8.20/internals/layout_in_storage.html#mappings-and-dynamic-arrays[Solidity docs for mappings and dynamic arrays.].
 *
 * Example usage:
 * ```solidity
 * contract Example {
 *     // Add the library methods
 *     using StorageSlot for bytes32;
 *     using SlotDerivation for bytes32;
 *
 *     // Declare a namespace
 *     string private constant _NAMESPACE = "<namespace>"; // eg. OpenZeppelin.Slot
 *
 *     function setValueInNamespace(uint256 key, address newValue) internal {
 *         _NAMESPACE.erc7201Slot().deriveMapping(key).getAddressSlot().value = newValue;
 *     }
 *
 *     function getValueInNamespace(uint256 key) internal view returns (address) {
 *         return _NAMESPACE.erc7201Slot().deriveMapping(key).getAddressSlot().value;
 *     }
 * }
 * ```
 *
 * TIP: Consider using this library along with {StorageSlot}.
 *
 * NOTE: This library provides a way to manipulate storage locations in a non-standard way. Tooling for checking
 * upgrade safety will ignore the slots accessed through this library.
 *
 * _Available since v5.1._
 */
library SlotDerivation {
    /**
     * @dev Derive an ERC-7201 slot from a string (namespace).
     */
    function erc7201Slot(string memory namespace) internal pure returns (bytes32 slot) {
        assembly ("memory-safe") {
            mstore(0x00, sub(keccak256(add(namespace, 0x20), mload(namespace)), 1))
            slot := and(keccak256(0x00, 0x20), not(0xff))
        }
    }

    /**
     * @dev Add an offset to a slot to get the n-th element of a structure or an array.
     */
    function offset(bytes32 slot, uint256 pos) internal pure returns (bytes32 result) {
        unchecked {
            return bytes32(uint256(slot) + pos);
        }
    }

    /**
     * @dev Derive the location of the first element in an array from the slot where the length is stored.
     */
    function deriveArray(bytes32 slot) internal pure returns (bytes32 result) {
        assembly ("memory-safe") {
            mstore(0x00, slot)
            result := keccak256(0x00, 0x20)
        }
    }

    /**
     * @dev Derive the location of a mapping element from the key.
     */
    function deriveMapping(bytes32 slot, address key) internal pure returns (bytes32 result) {
        assembly ("memory-safe") {
            mstore(0x00, and(key, shr(96, not(0))))
            mstore(0x20, slot)
            result := keccak256(0x00, 0x40)
        }
    }

    /**
     * @dev Derive the location of a mapping element from the key.
     */
    function deriveMapping(bytes32 slot, bool key) internal pure returns (bytes32 result) {
        assembly ("memory-safe") {
            mstore(0x00, iszero(iszero(key)))
            mstore(0x20, slot)
            result := keccak256(0x00, 0x40)
        }
    }

    /**
     * @dev Derive the location of a mapping element from the key.
     */
    function deriveMapping(bytes32 slot, bytes32 key) internal pure returns (bytes32 result) {
        assembly ("memory-safe") {
            mstore(0x00, key)
            mstore(0x20, slot)
            result := keccak256(0x00, 0x40)
        }
    }

    /**
     * @dev Derive the location of a mapping element from the key.
     */
    function deriveMapping(bytes32 slot, uint256 key) internal pure returns (bytes32 result) {
        assembly ("memory-safe") {
            mstore(0x00, key)
            mstore(0x20, slot)
            result := keccak256(0x00, 0x40)
        }
    }

    /**
     * @dev Derive the location of a mapping element from the key.
     */
    function deriveMapping(bytes32 slot, int256 key) internal pure returns (bytes32 result) {
        assembly ("memory-safe") {
            mstore(0x00, key)
            mstore(0x20, slot)
            result := keccak256(0x00, 0x40)
        }
    }

    /**
     * @dev Derive the location of a mapping element from the key.
     */
    function deriveMapping(bytes32 slot, string memory key) internal pure returns (bytes32 result) {
        assembly ("memory-safe") {
            let length := mload(key)
            let begin := add(key, 0x20)
            let end := add(begin, length)
            let cache := mload(end)
            mstore(end, slot)
            result := keccak256(begin, add(length, 0x20))
            mstore(end, cache)
        }
    }

    /**
     * @dev Derive the location of a mapping element from the key.
     */
    function deriveMapping(bytes32 slot, bytes memory key) internal pure returns (bytes32 result) {
        assembly ("memory-safe") {
            let length := mload(key)
            let begin := add(key, 0x20)
            let end := add(begin, length)
            let cache := mload(end)
            mstore(end, slot)
            result := keccak256(begin, add(length, 0x20))
            mstore(end, cache)
        }
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.3.0) (utils/math/Math.sol)

pragma solidity ^0.8.20;

import {Panic} from "../Panic.sol";
import {SafeCast} from "./SafeCast.sol";

/**
 * @dev Standard math utilities missing in the Solidity language.
 */
library Math {
    enum Rounding {
        Floor, // Toward negative infinity
        Ceil, // Toward positive infinity
        Trunc, // Toward zero
        Expand // Away from zero
    }

    /**
     * @dev Return the 512-bit addition of two uint256.
     *
     * The result is stored in two 256 variables such that sum = high * 2²⁵⁶ + low.
     */
    function add512(uint256 a, uint256 b) internal pure returns (uint256 high, uint256 low) {
        assembly ("memory-safe") {
            low := add(a, b)
            high := lt(low, a)
        }
    }

    /**
     * @dev Return the 512-bit multiplication of two uint256.
     *
     * The result is stored in two 256 variables such that product = high * 2²⁵⁶ + low.
     */
    function mul512(uint256 a, uint256 b) internal pure returns (uint256 high, uint256 low) {
        // 512-bit multiply [high low] = x * y. Compute the product mod 2²⁵⁶ and mod 2²⁵⁶ - 1, then use
        // the Chinese Remainder Theorem to reconstruct the 512 bit result. The result is stored in two 256
        // variables such that product = high * 2²⁵⁶ + low.
        assembly ("memory-safe") {
            let mm := mulmod(a, b, not(0))
            low := mul(a, b)
            high := sub(sub(mm, low), lt(mm, low))
        }
    }

    /**
     * @dev Returns the addition of two unsigned integers, with a success flag (no overflow).
     */
    function tryAdd(uint256 a, uint256 b) internal pure returns (bool success, uint256 result) {
        unchecked {
            uint256 c = a + b;
            success = c >= a;
            result = c * SafeCast.toUint(success);
        }
    }

    /**
     * @dev Returns the subtraction of two unsigned integers, with a success flag (no overflow).
     */
    function trySub(uint256 a, uint256 b) internal pure returns (bool success, uint256 result) {
        unchecked {
            uint256 c = a - b;
            success = c <= a;
            result = c * SafeCast.toUint(success);
        }
    }

    /**
     * @dev Returns the multiplication of two unsigned integers, with a success flag (no overflow).
     */
    function tryMul(uint256 a, uint256 b) internal pure returns (bool success, uint256 result) {
        unchecked {
            uint256 c = a * b;
            assembly ("memory-safe") {
                // Only true when the multiplication doesn't overflow
                // (c / a == b) || (a == 0)
                success := or(eq(div(c, a), b), iszero(a))
            }
            // equivalent to: success ? c : 0
            result = c * SafeCast.toUint(success);
        }
    }

    /**
     * @dev Returns the division of two unsigned integers, with a success flag (no division by zero).
     */
    function tryDiv(uint256 a, uint256 b) internal pure returns (bool success, uint256 result) {
        unchecked {
            success = b > 0;
            assembly ("memory-safe") {
                // The `DIV` opcode returns zero when the denominator is 0.
                result := div(a, b)
            }
        }
    }

    /**
     * @dev Returns the remainder of dividing two unsigned integers, with a success flag (no division by zero).
     */
    function tryMod(uint256 a, uint256 b) internal pure returns (bool success, uint256 result) {
        unchecked {
            success = b > 0;
            assembly ("memory-safe") {
                // The `MOD` opcode returns zero when the denominator is 0.
                result := mod(a, b)
            }
        }
    }

    /**
     * @dev Unsigned saturating addition, bounds to `2²⁵⁶ - 1` instead of overflowing.
     */
    function saturatingAdd(uint256 a, uint256 b) internal pure returns (uint256) {
        (bool success, uint256 result) = tryAdd(a, b);
        return ternary(success, result, type(uint256).max);
    }

    /**
     * @dev Unsigned saturating subtraction, bounds to zero instead of overflowing.
     */
    function saturatingSub(uint256 a, uint256 b) internal pure returns (uint256) {
        (, uint256 result) = trySub(a, b);
        return result;
    }

    /**
     * @dev Unsigned saturating multiplication, bounds to `2²⁵⁶ - 1` instead of overflowing.
     */
    function saturatingMul(uint256 a, uint256 b) internal pure returns (uint256) {
        (bool success, uint256 result) = tryMul(a, b);
        return ternary(success, result, type(uint256).max);
    }

    /**
     * @dev Branchless ternary evaluation for `a ? b : c`. Gas costs are constant.
     *
     * IMPORTANT: This function may reduce bytecode size and consume less gas when used standalone.
     * However, the compiler may optimize Solidity ternary operations (i.e. `a ? b : c`) to only compute
     * one branch when needed, making this function more expensive.
     */
    function ternary(bool condition, uint256 a, uint256 b) internal pure returns (uint256) {
        unchecked {
            // branchless ternary works because:
            // b ^ (a ^ b) == a
            // b ^ 0 == b
            return b ^ ((a ^ b) * SafeCast.toUint(condition));
        }
    }

    /**
     * @dev Returns the largest of two numbers.
     */
    function max(uint256 a, uint256 b) internal pure returns (uint256) {
        return ternary(a > b, a, b);
    }

    /**
     * @dev Returns the smallest of two numbers.
     */
    function min(uint256 a, uint256 b) internal pure returns (uint256) {
        return ternary(a < b, a, b);
    }

    /**
     * @dev Returns the average of two numbers. The result is rounded towards
     * zero.
     */
    function average(uint256 a, uint256 b) internal pure returns (uint256) {
        // (a + b) / 2 can overflow.
        return (a & b) + (a ^ b) / 2;
    }

    /**
     * @dev Returns the ceiling of the division of two numbers.
     *
     * This differs from standard division with `/` in that it rounds towards infinity instead
     * of rounding towards zero.
     */
    function ceilDiv(uint256 a, uint256 b) internal pure returns (uint256) {
        if (b == 0) {
            // Guarantee the same behavior as in a regular Solidity division.
            Panic.panic(Panic.DIVISION_BY_ZERO);
        }

        // The following calculation ensures accurate ceiling division without overflow.
        // Since a is non-zero, (a - 1) / b will not overflow.
        // The largest possible result occurs when (a - 1) / b is type(uint256).max,
        // but the largest value we can obtain is type(uint256).max - 1, which happens
        // when a = type(uint256).max and b = 1.
        unchecked {
            return SafeCast.toUint(a > 0) * ((a - 1) / b + 1);
        }
    }

    /**
     * @dev Calculates floor(x * y / denominator) with full precision. Throws if result overflows a uint256 or
     * denominator == 0.
     *
     * Original credit to Remco Bloemen under MIT license (https://xn--2-umb.com/21/muldiv) with further edits by
     * Uniswap Labs also under MIT license.
     */
    function mulDiv(uint256 x, uint256 y, uint256 denominator) internal pure returns (uint256 result) {
        unchecked {
            (uint256 high, uint256 low) = mul512(x, y);

            // Handle non-overflow cases, 256 by 256 division.
            if (high == 0) {
                // Solidity will revert if denominator == 0, unlike the div opcode on its own.
                // The surrounding unchecked block does not change this fact.
                // See https://docs.soliditylang.org/en/latest/control-structures.html#checked-or-unchecked-arithmetic.
                return low / denominator;
            }

            // Make sure the result is less than 2²⁵⁶. Also prevents denominator == 0.
            if (denominator <= high) {
                Panic.panic(ternary(denominator == 0, Panic.DIVISION_BY_ZERO, Panic.UNDER_OVERFLOW));
            }

            ///////////////////////////////////////////////
            // 512 by 256 division.
            ///////////////////////////////////////////////

            // Make division exact by subtracting the remainder from [high low].
            uint256 remainder;
            assembly ("memory-safe") {
                // Compute remainder using mulmod.
                remainder := mulmod(x, y, denominator)

                // Subtract 256 bit number from 512 bit number.
                high := sub(high, gt(remainder, low))
                low := sub(low, remainder)
            }

            // Factor powers of two out of denominator and compute largest power of two divisor of denominator.
            // Always >= 1. See https://cs.stackexchange.com/q/138556/92363.

            uint256 twos = denominator & (0 - denominator);
            assembly ("memory-safe") {
                // Divide denominator by twos.
                denominator := div(denominator, twos)

                // Divide [high low] by twos.
                low := div(low, twos)

                // Flip twos such that it is 2²⁵⁶ / twos. If twos is zero, then it becomes one.
                twos := add(div(sub(0, twos), twos), 1)
            }

            // Shift in bits from high into low.
            low |= high * twos;

            // Invert denominator mod 2²⁵⁶. Now that denominator is an odd number, it has an inverse modulo 2²⁵⁶ such
            // that denominator * inv ≡ 1 mod 2²⁵⁶. Compute the inverse by starting with a seed that is correct for
            // four bits. That is, denominator * inv ≡ 1 mod 2⁴.
            uint256 inverse = (3 * denominator) ^ 2;

            // Use the Newton-Raphson iteration to improve the precision. Thanks to Hensel's lifting lemma, this also
            // works in modular arithmetic, doubling the correct bits in each step.
            inverse *= 2 - denominator * inverse; // inverse mod 2⁸
            inverse *= 2 - denominator * inverse; // inverse mod 2¹⁶
            inverse *= 2 - denominator * inverse; // inverse mod 2³²
            inverse *= 2 - denominator * inverse; // inverse mod 2⁶⁴
            inverse *= 2 - denominator * inverse; // inverse mod 2¹²⁸
            inverse *= 2 - denominator * inverse; // inverse mod 2²⁵⁶

            // Because the division is now exact we can divide by multiplying with the modular inverse of denominator.
            // This will give us the correct result modulo 2²⁵⁶. Since the preconditions guarantee that the outcome is
            // less than 2²⁵⁶, this is the final result. We don't need to compute the high bits of the result and high
            // is no longer required.
            result = low * inverse;
            return result;
        }
    }

    /**
     * @dev Calculates x * y / denominator with full precision, following the selected rounding direction.
     */
    function mulDiv(uint256 x, uint256 y, uint256 denominator, Rounding rounding) internal pure returns (uint256) {
        return mulDiv(x, y, denominator) + SafeCast.toUint(unsignedRoundsUp(rounding) && mulmod(x, y, denominator) > 0);
    }

    /**
     * @dev Calculates floor(x * y >> n) with full precision. Throws if result overflows a uint256.
     */
    function mulShr(uint256 x, uint256 y, uint8 n) internal pure returns (uint256 result) {
        unchecked {
            (uint256 high, uint256 low) = mul512(x, y);
            if (high >= 1 << n) {
                Panic.panic(Panic.UNDER_OVERFLOW);
            }
            return (high << (256 - n)) | (low >> n);
        }
    }

    /**
     * @dev Calculates x * y >> n with full precision, following the selected rounding direction.
     */
    function mulShr(uint256 x, uint256 y, uint8 n, Rounding rounding) internal pure returns (uint256) {
        return mulShr(x, y, n) + SafeCast.toUint(unsignedRoundsUp(rounding) && mulmod(x, y, 1 << n) > 0);
    }

    /**
     * @dev Calculate the modular multiplicative inverse of a number in Z/nZ.
     *
     * If n is a prime, then Z/nZ is a field. In that case all elements are inversible, except 0.
     * If n is not a prime, then Z/nZ is not a field, and some elements might not be inversible.
     *
     * If the input value is not inversible, 0 is returned.
     *
     * NOTE: If you know for sure that n is (big) a prime, it may be cheaper to use Fermat's little theorem and get the
     * inverse using `Math.modExp(a, n - 2, n)`. See {invModPrime}.
     */
    function invMod(uint256 a, uint256 n) internal pure returns (uint256) {
        unchecked {
            if (n == 0) return 0;

            // The inverse modulo is calculated using the Extended Euclidean Algorithm (iterative version)
            // Used to compute integers x and y such that: ax + ny = gcd(a, n).
            // When the gcd is 1, then the inverse of a modulo n exists and it's x.
            // ax + ny = 1
            // ax = 1 + (-y)n
            // ax ≡ 1 (mod n) # x is the inverse of a modulo n

            // If the remainder is 0 the gcd is n right away.
            uint256 remainder = a % n;
            uint256 gcd = n;

            // Therefore the initial coefficients are:
            // ax + ny = gcd(a, n) = n
            // 0a + 1n = n
            int256 x = 0;
            int256 y = 1;

            while (remainder != 0) {
                uint256 quotient = gcd / remainder;

                (gcd, remainder) = (
                    // The old remainder is the next gcd to try.
                    remainder,
                    // Compute the next remainder.
                    // Can't overflow given that (a % gcd) * (gcd // (a % gcd)) <= gcd
                    // where gcd is at most n (capped to type(uint256).max)
                    gcd - remainder * quotient
                );

                (x, y) = (
                    // Increment the coefficient of a.
                    y,
                    // Decrement the coefficient of n.
                    // Can overflow, but the result is casted to uint256 so that the
                    // next value of y is "wrapped around" to a value between 0 and n - 1.
                    x - y * int256(quotient)
                );
            }

            if (gcd != 1) return 0; // No inverse exists.
            return ternary(x < 0, n - uint256(-x), uint256(x)); // Wrap the result if it's negative.
        }
    }

    /**
     * @dev Variant of {invMod}. More efficient, but only works if `p` is known to be a prime greater than `2`.
     *
     * From https://en.wikipedia.org/wiki/Fermat%27s_little_theorem[Fermat's little theorem], we know that if p is
     * prime, then `a**(p-1) ≡ 1 mod p`. As a consequence, we have `a * a**(p-2) ≡ 1 mod p`, which means that
     * `a**(p-2)` is the modular multiplicative inverse of a in Fp.
     *
     * NOTE: this function does NOT check that `p` is a prime greater than `2`.
     */
    function invModPrime(uint256 a, uint256 p) internal view returns (uint256) {
        unchecked {
            return Math.modExp(a, p - 2, p);
        }
    }

    /**
     * @dev Returns the modular exponentiation of the specified base, exponent and modulus (b ** e % m)
     *
     * Requirements:
     * - modulus can't be zero
     * - underlying staticcall to precompile must succeed
     *
     * IMPORTANT: The result is only valid if the underlying call succeeds. When using this function, make
     * sure the chain you're using it on supports the precompiled contract for modular exponentiation
     * at address 0x05 as specified in https://eips.ethereum.org/EIPS/eip-198[EIP-198]. Otherwise,
     * the underlying function will succeed given the lack of a revert, but the result may be incorrectly
     * interpreted as 0.
     */
    function modExp(uint256 b, uint256 e, uint256 m) internal view returns (uint256) {
        (bool success, uint256 result) = tryModExp(b, e, m);
        if (!success) {
            Panic.panic(Panic.DIVISION_BY_ZERO);
        }
        return result;
    }

    /**
     * @dev Returns the modular exponentiation of the specified base, exponent and modulus (b ** e % m).
     * It includes a success flag indicating if the operation succeeded. Operation will be marked as failed if trying
     * to operate modulo 0 or if the underlying precompile reverted.
     *
     * IMPORTANT: The result is only valid if the success flag is true. When using this function, make sure the chain
     * you're using it on supports the precompiled contract for modular exponentiation at address 0x05 as specified in
     * https://eips.ethereum.org/EIPS/eip-198[EIP-198]. Otherwise, the underlying function will succeed given the lack
     * of a revert, but the result may be incorrectly interpreted as 0.
     */
    function tryModExp(uint256 b, uint256 e, uint256 m) internal view returns (bool success, uint256 result) {
        if (m == 0) return (false, 0);
        assembly ("memory-safe") {
            let ptr := mload(0x40)
            // | Offset    | Content    | Content (Hex)                                                      |
            // |-----------|------------|--------------------------------------------------------------------|
            // | 0x00:0x1f | size of b  | 0x0000000000000000000000000000000000000000000000000000000000000020 |
            // | 0x20:0x3f | size of e  | 0x0000000000000000000000000000000000000000000000000000000000000020 |
            // | 0x40:0x5f | size of m  | 0x0000000000000000000000000000000000000000000000000000000000000020 |
            // | 0x60:0x7f | value of b | 0x<.............................................................b> |
            // | 0x80:0x9f | value of e | 0x<.............................................................e> |
            // | 0xa0:0xbf | value of m | 0x<.............................................................m> |
            mstore(ptr, 0x20)
            mstore(add(ptr, 0x20), 0x20)
            mstore(add(ptr, 0x40), 0x20)
            mstore(add(ptr, 0x60), b)
            mstore(add(ptr, 0x80), e)
            mstore(add(ptr, 0xa0), m)

            // Given the result < m, it's guaranteed to fit in 32 bytes,
            // so we can use the memory scratch space located at offset 0.
            success := staticcall(gas(), 0x05, ptr, 0xc0, 0x00, 0x20)
            result := mload(0x00)
        }
    }

    /**
     * @dev Variant of {modExp} that supports inputs of arbitrary length.
     */
    function modExp(bytes memory b, bytes memory e, bytes memory m) internal view returns (bytes memory) {
        (bool success, bytes memory result) = tryModExp(b, e, m);
        if (!success) {
            Panic.panic(Panic.DIVISION_BY_ZERO);
        }
        return result;
    }

    /**
     * @dev Variant of {tryModExp} that supports inputs of arbitrary length.
     */
    function tryModExp(
        bytes memory b,
        bytes memory e,
        bytes memory m
    ) internal view returns (bool success, bytes memory result) {
        if (_zeroBytes(m)) return (false, new bytes(0));

        uint256 mLen = m.length;

        // Encode call args in result and move the free memory pointer
        result = abi.encodePacked(b.length, e.length, mLen, b, e, m);

        assembly ("memory-safe") {
            let dataPtr := add(result, 0x20)
            // Write result on top of args to avoid allocating extra memory.
            success := staticcall(gas(), 0x05, dataPtr, mload(result), dataPtr, mLen)
            // Overwrite the length.
            // result.length > returndatasize() is guaranteed because returndatasize() == m.length
            mstore(result, mLen)
            // Set the memory pointer after the returned data.
            mstore(0x40, add(dataPtr, mLen))
        }
    }

    /**
     * @dev Returns whether the provided byte array is zero.
     */
    function _zeroBytes(bytes memory byteArray) private pure returns (bool) {
        for (uint256 i = 0; i < byteArray.length; ++i) {
            if (byteArray[i] != 0) {
                return false;
            }
        }
        return true;
    }

    /**
     * @dev Returns the square root of a number. If the number is not a perfect square, the value is rounded
     * towards zero.
     *
     * This method is based on Newton's method for computing square roots; the algorithm is restricted to only
     * using integer operations.
     */
    function sqrt(uint256 a) internal pure returns (uint256) {
        unchecked {
            // Take care of easy edge cases when a == 0 or a == 1
            if (a <= 1) {
                return a;
            }

            // In this function, we use Newton's method to get a root of `f(x) := x² - a`. It involves building a
            // sequence x_n that converges toward sqrt(a). For each iteration x_n, we also define the error between
            // the current value as `ε_n = | x_n - sqrt(a) |`.
            //
            // For our first estimation, we consider `e` the smallest power of 2 which is bigger than the square root
            // of the target. (i.e. `2**(e-1) ≤ sqrt(a) < 2**e`). We know that `e ≤ 128` because `(2¹²⁸)² = 2²⁵⁶` is
            // bigger than any uint256.
            //
            // By noticing that
            // `2**(e-1) ≤ sqrt(a) < 2**e → (2**(e-1))² ≤ a < (2**e)² → 2**(2*e-2) ≤ a < 2**(2*e)`
            // we can deduce that `e - 1` is `log2(a) / 2`. We can thus compute `x_n = 2**(e-1)` using a method similar
            // to the msb function.
            uint256 aa = a;
            uint256 xn = 1;

            if (aa >= (1 << 128)) {
                aa >>= 128;
                xn <<= 64;
            }
            if (aa >= (1 << 64)) {
                aa >>= 64;
                xn <<= 32;
            }
            if (aa >= (1 << 32)) {
                aa >>= 32;
                xn <<= 16;
            }
            if (aa >= (1 << 16)) {
                aa >>= 16;
                xn <<= 8;
            }
            if (aa >= (1 << 8)) {
                aa >>= 8;
                xn <<= 4;
            }
            if (aa >= (1 << 4)) {
                aa >>= 4;
                xn <<= 2;
            }
            if (aa >= (1 << 2)) {
                xn <<= 1;
            }

            // We now have x_n such that `x_n = 2**(e-1) ≤ sqrt(a) < 2**e = 2 * x_n`. This implies ε_n ≤ 2**(e-1).
            //
            // We can refine our estimation by noticing that the middle of that interval minimizes the error.
            // If we move x_n to equal 2**(e-1) + 2**(e-2), then we reduce the error to ε_n ≤ 2**(e-2).
            // This is going to be our x_0 (and ε_0)
            xn = (3 * xn) >> 1; // ε_0 := | x_0 - sqrt(a) | ≤ 2**(e-2)

            // From here, Newton's method give us:
            // x_{n+1} = (x_n + a / x_n) / 2
            //
            // One should note that:
            // x_{n+1}² - a = ((x_n + a / x_n) / 2)² - a
            //              = ((x_n² + a) / (2 * x_n))² - a
            //              = (x_n⁴ + 2 * a * x_n² + a²) / (4 * x_n²) - a
            //              = (x_n⁴ + 2 * a * x_n² + a² - 4 * a * x_n²) / (4 * x_n²)
            //              = (x_n⁴ - 2 * a * x_n² + a²) / (4 * x_n²)
            //              = (x_n² - a)² / (2 * x_n)²
            //              = ((x_n² - a) / (2 * x_n))²
            //              ≥ 0
            // Which proves that for all n ≥ 1, sqrt(a) ≤ x_n
            //
            // This gives us the proof of quadratic convergence of the sequence:
            // ε_{n+1} = | x_{n+1} - sqrt(a) |
            //         = | (x_n + a / x_n) / 2 - sqrt(a) |
            //         = | (x_n² + a - 2*x_n*sqrt(a)) / (2 * x_n) |
            //         = | (x_n - sqrt(a))² / (2 * x_n) |
            //         = | ε_n² / (2 * x_n) |
            //         = ε_n² / | (2 * x_n) |
            //
            // For the first iteration, we have a special case where x_0 is known:
            // ε_1 = ε_0² / | (2 * x_0) |
            //     ≤ (2**(e-2))² / (2 * (2**(e-1) + 2**(e-2)))
            //     ≤ 2**(2*e-4) / (3 * 2**(e-1))
            //     ≤ 2**(e-3) / 3
            //     ≤ 2**(e-3-log2(3))
            //     ≤ 2**(e-4.5)
            //
            // For the following iterations, we use the fact that, 2**(e-1) ≤ sqrt(a) ≤ x_n:
            // ε_{n+1} = ε_n² / | (2 * x_n) |
            //         ≤ (2**(e-k))² / (2 * 2**(e-1))
            //         ≤ 2**(2*e-2*k) / 2**e
            //         ≤ 2**(e-2*k)
            xn = (xn + a / xn) >> 1; // ε_1 := | x_1 - sqrt(a) | ≤ 2**(e-4.5)  -- special case, see above
            xn = (xn + a / xn) >> 1; // ε_2 := | x_2 - sqrt(a) | ≤ 2**(e-9)    -- general case with k = 4.5
            xn = (xn + a / xn) >> 1; // ε_3 := | x_3 - sqrt(a) | ≤ 2**(e-18)   -- general case with k = 9
            xn = (xn + a / xn) >> 1; // ε_4 := | x_4 - sqrt(a) | ≤ 2**(e-36)   -- general case with k = 18
            xn = (xn + a / xn) >> 1; // ε_5 := | x_5 - sqrt(a) | ≤ 2**(e-72)   -- general case with k = 36
            xn = (xn + a / xn) >> 1; // ε_6 := | x_6 - sqrt(a) | ≤ 2**(e-144)  -- general case with k = 72

            // Because e ≤ 128 (as discussed during the first estimation phase), we know have reached a precision
            // ε_6 ≤ 2**(e-144) < 1. Given we're operating on integers, then we can ensure that xn is now either
            // sqrt(a) or sqrt(a) + 1.
            return xn - SafeCast.toUint(xn > a / xn);
        }
    }

    /**
     * @dev Calculates sqrt(a), following the selected rounding direction.
     */
    function sqrt(uint256 a, Rounding rounding) internal pure returns (uint256) {
        unchecked {
            uint256 result = sqrt(a);
            return result + SafeCast.toUint(unsignedRoundsUp(rounding) && result * result < a);
        }
    }

    /**
     * @dev Return the log in base 2 of a positive value rounded towards zero.
     * Returns 0 if given 0.
     */
    function log2(uint256 x) internal pure returns (uint256 r) {
        // If value has upper 128 bits set, log2 result is at least 128
        r = SafeCast.toUint(x > 0xffffffffffffffffffffffffffffffff) << 7;
        // If upper 64 bits of 128-bit half set, add 64 to result
        r |= SafeCast.toUint((x >> r) > 0xffffffffffffffff) << 6;
        // If upper 32 bits of 64-bit half set, add 32 to result
        r |= SafeCast.toUint((x >> r) > 0xffffffff) << 5;
        // If upper 16 bits of 32-bit half set, add 16 to result
        r |= SafeCast.toUint((x >> r) > 0xffff) << 4;
        // If upper 8 bits of 16-bit half set, add 8 to result
        r |= SafeCast.toUint((x >> r) > 0xff) << 3;
        // If upper 4 bits of 8-bit half set, add 4 to result
        r |= SafeCast.toUint((x >> r) > 0xf) << 2;

        // Shifts value right by the current result and use it as an index into this lookup table:
        //
        // | x (4 bits) |  index  | table[index] = MSB position |
        // |------------|---------|-----------------------------|
        // |    0000    |    0    |        table[0] = 0         |
        // |    0001    |    1    |        table[1] = 0         |
        // |    0010    |    2    |        table[2] = 1         |
        // |    0011    |    3    |        table[3] = 1         |
        // |    0100    |    4    |        table[4] = 2         |
        // |    0101    |    5    |        table[5] = 2         |
        // |    0110    |    6    |        table[6] = 2         |
        // |    0111    |    7    |        table[7] = 2         |
        // |    1000    |    8    |        table[8] = 3         |
        // |    1001    |    9    |        table[9] = 3         |
        // |    1010    |   10    |        table[10] = 3        |
        // |    1011    |   11    |        table[11] = 3        |
        // |    1100    |   12    |        table[12] = 3        |
        // |    1101    |   13    |        table[13] = 3        |
        // |    1110    |   14    |        table[14] = 3        |
        // |    1111    |   15    |        table[15] = 3        |
        //
        // The lookup table is represented as a 32-byte value with the MSB positions for 0-15 in the last 16 bytes.
        assembly ("memory-safe") {
            r := or(r, byte(shr(r, x), 0x0000010102020202030303030303030300000000000000000000000000000000))
        }
    }

    /**
     * @dev Return the log in base 2, following the selected rounding direction, of a positive value.
     * Returns 0 if given 0.
     */
    function log2(uint256 value, Rounding rounding) internal pure returns (uint256) {
        unchecked {
            uint256 result = log2(value);
            return result + SafeCast.toUint(unsignedRoundsUp(rounding) && 1 << result < value);
        }
    }

    /**
     * @dev Return the log in base 10 of a positive value rounded towards zero.
     * Returns 0 if given 0.
     */
    function log10(uint256 value) internal pure returns (uint256) {
        uint256 result = 0;
        unchecked {
            if (value >= 10 ** 64) {
                value /= 10 ** 64;
                result += 64;
            }
            if (value >= 10 ** 32) {
                value /= 10 ** 32;
                result += 32;
            }
            if (value >= 10 ** 16) {
                value /= 10 ** 16;
                result += 16;
            }
            if (value >= 10 ** 8) {
                value /= 10 ** 8;
                result += 8;
            }
            if (value >= 10 ** 4) {
                value /= 10 ** 4;
                result += 4;
            }
            if (value >= 10 ** 2) {
                value /= 10 ** 2;
                result += 2;
            }
            if (value >= 10 ** 1) {
                result += 1;
            }
        }
        return result;
    }

    /**
     * @dev Return the log in base 10, following the selected rounding direction, of a positive value.
     * Returns 0 if given 0.
     */
    function log10(uint256 value, Rounding rounding) internal pure returns (uint256) {
        unchecked {
            uint256 result = log10(value);
            return result + SafeCast.toUint(unsignedRoundsUp(rounding) && 10 ** result < value);
        }
    }

    /**
     * @dev Return the log in base 256 of a positive value rounded towards zero.
     * Returns 0 if given 0.
     *
     * Adding one to the result gives the number of pairs of hex symbols needed to represent `value` as a hex string.
     */
    function log256(uint256 x) internal pure returns (uint256 r) {
        // If value has upper 128 bits set, log2 result is at least 128
        r = SafeCast.toUint(x > 0xffffffffffffffffffffffffffffffff) << 7;
        // If upper 64 bits of 128-bit half set, add 64 to result
        r |= SafeCast.toUint((x >> r) > 0xffffffffffffffff) << 6;
        // If upper 32 bits of 64-bit half set, add 32 to result
        r |= SafeCast.toUint((x >> r) > 0xffffffff) << 5;
        // If upper 16 bits of 32-bit half set, add 16 to result
        r |= SafeCast.toUint((x >> r) > 0xffff) << 4;
        // Add 1 if upper 8 bits of 16-bit half set, and divide accumulated result by 8
        return (r >> 3) | SafeCast.toUint((x >> r) > 0xff);
    }

    /**
     * @dev Return the log in base 256, following the selected rounding direction, of a positive value.
     * Returns 0 if given 0.
     */
    function log256(uint256 value, Rounding rounding) internal pure returns (uint256) {
        unchecked {
            uint256 result = log256(value);
            return result + SafeCast.toUint(unsignedRoundsUp(rounding) && 1 << (result << 3) < value);
        }
    }

    /**
     * @dev Returns whether a provided rounding mode is considered rounding up for unsigned integers.
     */
    function unsignedRoundsUp(Rounding rounding) internal pure returns (bool) {
        return uint8(rounding) % 2 == 1;
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.1.0) (utils/Errors.sol)

pragma solidity ^0.8.20;

/**
 * @dev Collection of common custom errors used in multiple contracts
 *
 * IMPORTANT: Backwards compatibility is not guaranteed in future versions of the library.
 * It is recommended to avoid relying on the error API for critical functionality.
 *
 * _Available since v5.1._
 */
library Errors {
    /**
     * @dev The ETH balance of the account is not enough to perform the operation.
     */
    error InsufficientBalance(uint256 balance, uint256 needed);

    /**
     * @dev A call to an address target failed. The target may have reverted.
     */
    error FailedCall();

    /**
     * @dev The deployment failed.
     */
    error FailedDeployment();

    /**
     * @dev A necessary precompile is missing.
     */
    error MissingPrecompile(address);
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.1.0) (utils/Panic.sol)

pragma solidity ^0.8.20;

/**
 * @dev Helper library for emitting standardized panic codes.
 *
 * ```solidity
 * contract Example {
 *      using Panic for uint256;
 *
 *      // Use any of the declared internal constants
 *      function foo() { Panic.GENERIC.panic(); }
 *
 *      // Alternatively
 *      function foo() { Panic.panic(Panic.GENERIC); }
 * }
 * ```
 *
 * Follows the list from https://github.com/ethereum/solidity/blob/v0.8.24/libsolutil/ErrorCodes.h[libsolutil].
 *
 * _Available since v5.1._
 */
// slither-disable-next-line unused-state
library Panic {
    /// @dev generic / unspecified error
    uint256 internal constant GENERIC = 0x00;
    /// @dev used by the assert() builtin
    uint256 internal constant ASSERT = 0x01;
    /// @dev arithmetic underflow or overflow
    uint256 internal constant UNDER_OVERFLOW = 0x11;
    /// @dev division or modulo by zero
    uint256 internal constant DIVISION_BY_ZERO = 0x12;
    /// @dev enum conversion error
    uint256 internal constant ENUM_CONVERSION_ERROR = 0x21;
    /// @dev invalid encoding in storage
    uint256 internal constant STORAGE_ENCODING_ERROR = 0x22;
    /// @dev empty array pop
    uint256 internal constant EMPTY_ARRAY_POP = 0x31;
    /// @dev array out of bounds access
    uint256 internal constant ARRAY_OUT_OF_BOUNDS = 0x32;
    /// @dev resource error (too large allocation or too large array)
    uint256 internal constant RESOURCE_ERROR = 0x41;
    /// @dev calling invalid internal function
    uint256 internal constant INVALID_INTERNAL_FUNCTION = 0x51;

    /// @dev Reverts with a panic code. Recommended to use with
    /// the internal constants with predefined codes.
    function panic(uint256 code) internal pure {
        assembly ("memory-safe") {
            mstore(0x00, 0x4e487b71)
            mstore(0x20, code)
            revert(0x1c, 0x24)
        }
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.1.0) (utils/math/SafeCast.sol)
// This file was procedurally generated from scripts/generate/templates/SafeCast.js.

pragma solidity ^0.8.20;

/**
 * @dev Wrappers over Solidity's uintXX/intXX/bool casting operators with added overflow
 * checks.
 *
 * Downcasting from uint256/int256 in Solidity does not revert on overflow. This can
 * easily result in undesired exploitation or bugs, since developers usually
 * assume that overflows raise errors. `SafeCast` restores this intuition by
 * reverting the transaction when such an operation overflows.
 *
 * Using this library instead of the unchecked operations eliminates an entire
 * class of bugs, so it's recommended to use it always.
 */
library SafeCast {
    /**
     * @dev Value doesn't fit in an uint of `bits` size.
     */
    error SafeCastOverflowedUintDowncast(uint8 bits, uint256 value);

    /**
     * @dev An int value doesn't fit in an uint of `bits` size.
     */
    error SafeCastOverflowedIntToUint(int256 value);

    /**
     * @dev Value doesn't fit in an int of `bits` size.
     */
    error SafeCastOverflowedIntDowncast(uint8 bits, int256 value);

    /**
     * @dev An uint value doesn't fit in an int of `bits` size.
     */
    error SafeCastOverflowedUintToInt(uint256 value);

    /**
     * @dev Returns the downcasted uint248 from uint256, reverting on
     * overflow (when the input is greater than largest uint248).
     *
     * Counterpart to Solidity's `uint248` operator.
     *
     * Requirements:
     *
     * - input must fit into 248 bits
     */
    function toUint248(uint256 value) internal pure returns (uint248) {
        if (value > type(uint248).max) {
            revert SafeCastOverflowedUintDowncast(248, value);
        }
        return uint248(value);
    }

    /**
     * @dev Returns the downcasted uint240 from uint256, reverting on
     * overflow (when the input is greater than largest uint240).
     *
     * Counterpart to Solidity's `uint240` operator.
     *
     * Requirements:
     *
     * - input must fit into 240 bits
     */
    function toUint240(uint256 value) internal pure returns (uint240) {
        if (value > type(uint240).max) {
            revert SafeCastOverflowedUintDowncast(240, value);
        }
        return uint240(value);
    }

    /**
     * @dev Returns the downcasted uint232 from uint256, reverting on
     * overflow (when the input is greater than largest uint232).
     *
     * Counterpart to Solidity's `uint232` operator.
     *
     * Requirements:
     *
     * - input must fit into 232 bits
     */
    function toUint232(uint256 value) internal pure returns (uint232) {
        if (value > type(uint232).max) {
            revert SafeCastOverflowedUintDowncast(232, value);
        }
        return uint232(value);
    }

    /**
     * @dev Returns the downcasted uint224 from uint256, reverting on
     * overflow (when the input is greater than largest uint224).
     *
     * Counterpart to Solidity's `uint224` operator.
     *
     * Requirements:
     *
     * - input must fit into 224 bits
     */
    function toUint224(uint256 value) internal pure returns (uint224) {
        if (value > type(uint224).max) {
            revert SafeCastOverflowedUintDowncast(224, value);
        }
        return uint224(value);
    }

    /**
     * @dev Returns the downcasted uint216 from uint256, reverting on
     * overflow (when the input is greater than largest uint216).
     *
     * Counterpart to Solidity's `uint216` operator.
     *
     * Requirements:
     *
     * - input must fit into 216 bits
     */
    function toUint216(uint256 value) internal pure returns (uint216) {
        if (value > type(uint216).max) {
            revert SafeCastOverflowedUintDowncast(216, value);
        }
        return uint216(value);
    }

    /**
     * @dev Returns the downcasted uint208 from uint256, reverting on
     * overflow (when the input is greater than largest uint208).
     *
     * Counterpart to Solidity's `uint208` operator.
     *
     * Requirements:
     *
     * - input must fit into 208 bits
     */
    function toUint208(uint256 value) internal pure returns (uint208) {
        if (value > type(uint208).max) {
            revert SafeCastOverflowedUintDowncast(208, value);
        }
        return uint208(value);
    }

    /**
     * @dev Returns the downcasted uint200 from uint256, reverting on
     * overflow (when the input is greater than largest uint200).
     *
     * Counterpart to Solidity's `uint200` operator.
     *
     * Requirements:
     *
     * - input must fit into 200 bits
     */
    function toUint200(uint256 value) internal pure returns (uint200) {
        if (value > type(uint200).max) {
            revert SafeCastOverflowedUintDowncast(200, value);
        }
        return uint200(value);
    }

    /**
     * @dev Returns the downcasted uint192 from uint256, reverting on
     * overflow (when the input is greater than largest uint192).
     *
     * Counterpart to Solidity's `uint192` operator.
     *
     * Requirements:
     *
     * - input must fit into 192 bits
     */
    function toUint192(uint256 value) internal pure returns (uint192) {
        if (value > type(uint192).max) {
            revert SafeCastOverflowedUintDowncast(192, value);
        }
        return uint192(value);
    }

    /**
     * @dev Returns the downcasted uint184 from uint256, reverting on
     * overflow (when the input is greater than largest uint184).
     *
     * Counterpart to Solidity's `uint184` operator.
     *
     * Requirements:
     *
     * - input must fit into 184 bits
     */
    function toUint184(uint256 value) internal pure returns (uint184) {
        if (value > type(uint184).max) {
            revert SafeCastOverflowedUintDowncast(184, value);
        }
        return uint184(value);
    }

    /**
     * @dev Returns the downcasted uint176 from uint256, reverting on
     * overflow (when the input is greater than largest uint176).
     *
     * Counterpart to Solidity's `uint176` operator.
     *
     * Requirements:
     *
     * - input must fit into 176 bits
     */
    function toUint176(uint256 value) internal pure returns (uint176) {
        if (value > type(uint176).max) {
            revert SafeCastOverflowedUintDowncast(176, value);
        }
        return uint176(value);
    }

    /**
     * @dev Returns the downcasted uint168 from uint256, reverting on
     * overflow (when the input is greater than largest uint168).
     *
     * Counterpart to Solidity's `uint168` operator.
     *
     * Requirements:
     *
     * - input must fit into 168 bits
     */
    function toUint168(uint256 value) internal pure returns (uint168) {
        if (value > type(uint168).max) {
            revert SafeCastOverflowedUintDowncast(168, value);
        }
        return uint168(value);
    }

    /**
     * @dev Returns the downcasted uint160 from uint256, reverting on
     * overflow (when the input is greater than largest uint160).
     *
     * Counterpart to Solidity's `uint160` operator.
     *
     * Requirements:
     *
     * - input must fit into 160 bits
     */
    function toUint160(uint256 value) internal pure returns (uint160) {
        if (value > type(uint160).max) {
            revert SafeCastOverflowedUintDowncast(160, value);
        }
        return uint160(value);
    }

    /**
     * @dev Returns the downcasted uint152 from uint256, reverting on
     * overflow (when the input is greater than largest uint152).
     *
     * Counterpart to Solidity's `uint152` operator.
     *
     * Requirements:
     *
     * - input must fit into 152 bits
     */
    function toUint152(uint256 value) internal pure returns (uint152) {
        if (value > type(uint152).max) {
            revert SafeCastOverflowedUintDowncast(152, value);
        }
        return uint152(value);
    }

    /**
     * @dev Returns the downcasted uint144 from uint256, reverting on
     * overflow (when the input is greater than largest uint144).
     *
     * Counterpart to Solidity's `uint144` operator.
     *
     * Requirements:
     *
     * - input must fit into 144 bits
     */
    function toUint144(uint256 value) internal pure returns (uint144) {
        if (value > type(uint144).max) {
            revert SafeCastOverflowedUintDowncast(144, value);
        }
        return uint144(value);
    }

    /**
     * @dev Returns the downcasted uint136 from uint256, reverting on
     * overflow (when the input is greater than largest uint136).
     *
     * Counterpart to Solidity's `uint136` operator.
     *
     * Requirements:
     *
     * - input must fit into 136 bits
     */
    function toUint136(uint256 value) internal pure returns (uint136) {
        if (value > type(uint136).max) {
            revert SafeCastOverflowedUintDowncast(136, value);
        }
        return uint136(value);
    }

    /**
     * @dev Returns the downcasted uint128 from uint256, reverting on
     * overflow (when the input is greater than largest uint128).
     *
     * Counterpart to Solidity's `uint128` operator.
     *
     * Requirements:
     *
     * - input must fit into 128 bits
     */
    function toUint128(uint256 value) internal pure returns (uint128) {
        if (value > type(uint128).max) {
            revert SafeCastOverflowedUintDowncast(128, value);
        }
        return uint128(value);
    }

    /**
     * @dev Returns the downcasted uint120 from uint256, reverting on
     * overflow (when the input is greater than largest uint120).
     *
     * Counterpart to Solidity's `uint120` operator.
     *
     * Requirements:
     *
     * - input must fit into 120 bits
     */
    function toUint120(uint256 value) internal pure returns (uint120) {
        if (value > type(uint120).max) {
            revert SafeCastOverflowedUintDowncast(120, value);
        }
        return uint120(value);
    }

    /**
     * @dev Returns the downcasted uint112 from uint256, reverting on
     * overflow (when the input is greater than largest uint112).
     *
     * Counterpart to Solidity's `uint112` operator.
     *
     * Requirements:
     *
     * - input must fit into 112 bits
     */
    function toUint112(uint256 value) internal pure returns (uint112) {
        if (value > type(uint112).max) {
            revert SafeCastOverflowedUintDowncast(112, value);
        }
        return uint112(value);
    }

    /**
     * @dev Returns the downcasted uint104 from uint256, reverting on
     * overflow (when the input is greater than largest uint104).
     *
     * Counterpart to Solidity's `uint104` operator.
     *
     * Requirements:
     *
     * - input must fit into 104 bits
     */
    function toUint104(uint256 value) internal pure returns (uint104) {
        if (value > type(uint104).max) {
            revert SafeCastOverflowedUintDowncast(104, value);
        }
        return uint104(value);
    }

    /**
     * @dev Returns the downcasted uint96 from uint256, reverting on
     * overflow (when the input is greater than largest uint96).
     *
     * Counterpart to Solidity's `uint96` operator.
     *
     * Requirements:
     *
     * - input must fit into 96 bits
     */
    function toUint96(uint256 value) internal pure returns (uint96) {
        if (value > type(uint96).max) {
            revert SafeCastOverflowedUintDowncast(96, value);
        }
        return uint96(value);
    }

    /**
     * @dev Returns the downcasted uint88 from uint256, reverting on
     * overflow (when the input is greater than largest uint88).
     *
     * Counterpart to Solidity's `uint88` operator.
     *
     * Requirements:
     *
     * - input must fit into 88 bits
     */
    function toUint88(uint256 value) internal pure returns (uint88) {
        if (value > type(uint88).max) {
            revert SafeCastOverflowedUintDowncast(88, value);
        }
        return uint88(value);
    }

    /**
     * @dev Returns the downcasted uint80 from uint256, reverting on
     * overflow (when the input is greater than largest uint80).
     *
     * Counterpart to Solidity's `uint80` operator.
     *
     * Requirements:
     *
     * - input must fit into 80 bits
     */
    function toUint80(uint256 value) internal pure returns (uint80) {
        if (value > type(uint80).max) {
            revert SafeCastOverflowedUintDowncast(80, value);
        }
        return uint80(value);
    }

    /**
     * @dev Returns the downcasted uint72 from uint256, reverting on
     * overflow (when the input is greater than largest uint72).
     *
     * Counterpart to Solidity's `uint72` operator.
     *
     * Requirements:
     *
     * - input must fit into 72 bits
     */
    function toUint72(uint256 value) internal pure returns (uint72) {
        if (value > type(uint72).max) {
            revert SafeCastOverflowedUintDowncast(72, value);
        }
        return uint72(value);
    }

    /**
     * @dev Returns the downcasted uint64 from uint256, reverting on
     * overflow (when the input is greater than largest uint64).
     *
     * Counterpart to Solidity's `uint64` operator.
     *
     * Requirements:
     *
     * - input must fit into 64 bits
     */
    function toUint64(uint256 value) internal pure returns (uint64) {
        if (value > type(uint64).max) {
            revert SafeCastOverflowedUintDowncast(64, value);
        }
        return uint64(value);
    }

    /**
     * @dev Returns the downcasted uint56 from uint256, reverting on
     * overflow (when the input is greater than largest uint56).
     *
     * Counterpart to Solidity's `uint56` operator.
     *
     * Requirements:
     *
     * - input must fit into 56 bits
     */
    function toUint56(uint256 value) internal pure returns (uint56) {
        if (value > type(uint56).max) {
            revert SafeCastOverflowedUintDowncast(56, value);
        }
        return uint56(value);
    }

    /**
     * @dev Returns the downcasted uint48 from uint256, reverting on
     * overflow (when the input is greater than largest uint48).
     *
     * Counterpart to Solidity's `uint48` operator.
     *
     * Requirements:
     *
     * - input must fit into 48 bits
     */
    function toUint48(uint256 value) internal pure returns (uint48) {
        if (value > type(uint48).max) {
            revert SafeCastOverflowedUintDowncast(48, value);
        }
        return uint48(value);
    }

    /**
     * @dev Returns the downcasted uint40 from uint256, reverting on
     * overflow (when the input is greater than largest uint40).
     *
     * Counterpart to Solidity's `uint40` operator.
     *
     * Requirements:
     *
     * - input must fit into 40 bits
     */
    function toUint40(uint256 value) internal pure returns (uint40) {
        if (value > type(uint40).max) {
            revert SafeCastOverflowedUintDowncast(40, value);
        }
        return uint40(value);
    }

    /**
     * @dev Returns the downcasted uint32 from uint256, reverting on
     * overflow (when the input is greater than largest uint32).
     *
     * Counterpart to Solidity's `uint32` operator.
     *
     * Requirements:
     *
     * - input must fit into 32 bits
     */
    function toUint32(uint256 value) internal pure returns (uint32) {
        if (value > type(uint32).max) {
            revert SafeCastOverflowedUintDowncast(32, value);
        }
        return uint32(value);
    }

    /**
     * @dev Returns the downcasted uint24 from uint256, reverting on
     * overflow (when the input is greater than largest uint24).
     *
     * Counterpart to Solidity's `uint24` operator.
     *
     * Requirements:
     *
     * - input must fit into 24 bits
     */
    function toUint24(uint256 value) internal pure returns (uint24) {
        if (value > type(uint24).max) {
            revert SafeCastOverflowedUintDowncast(24, value);
        }
        return uint24(value);
    }

    /**
     * @dev Returns the downcasted uint16 from uint256, reverting on
     * overflow (when the input is greater than largest uint16).
     *
     * Counterpart to Solidity's `uint16` operator.
     *
     * Requirements:
     *
     * - input must fit into 16 bits
     */
    function toUint16(uint256 value) internal pure returns (uint16) {
        if (value > type(uint16).max) {
            revert SafeCastOverflowedUintDowncast(16, value);
        }
        return uint16(value);
    }

    /**
     * @dev Returns the downcasted uint8 from uint256, reverting on
     * overflow (when the input is greater than largest uint8).
     *
     * Counterpart to Solidity's `uint8` operator.
     *
     * Requirements:
     *
     * - input must fit into 8 bits
     */
    function toUint8(uint256 value) internal pure returns (uint8) {
        if (value > type(uint8).max) {
            revert SafeCastOverflowedUintDowncast(8, value);
        }
        return uint8(value);
    }

    /**
     * @dev Converts a signed int256 into an unsigned uint256.
     *
     * Requirements:
     *
     * - input must be greater than or equal to 0.
     */
    function toUint256(int256 value) internal pure returns (uint256) {
        if (value < 0) {
            revert SafeCastOverflowedIntToUint(value);
        }
        return uint256(value);
    }

    /**
     * @dev Returns the downcasted int248 from int256, reverting on
     * overflow (when the input is less than smallest int248 or
     * greater than largest int248).
     *
     * Counterpart to Solidity's `int248` operator.
     *
     * Requirements:
     *
     * - input must fit into 248 bits
     */
    function toInt248(int256 value) internal pure returns (int248 downcasted) {
        downcasted = int248(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(248, value);
        }
    }

    /**
     * @dev Returns the downcasted int240 from int256, reverting on
     * overflow (when the input is less than smallest int240 or
     * greater than largest int240).
     *
     * Counterpart to Solidity's `int240` operator.
     *
     * Requirements:
     *
     * - input must fit into 240 bits
     */
    function toInt240(int256 value) internal pure returns (int240 downcasted) {
        downcasted = int240(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(240, value);
        }
    }

    /**
     * @dev Returns the downcasted int232 from int256, reverting on
     * overflow (when the input is less than smallest int232 or
     * greater than largest int232).
     *
     * Counterpart to Solidity's `int232` operator.
     *
     * Requirements:
     *
     * - input must fit into 232 bits
     */
    function toInt232(int256 value) internal pure returns (int232 downcasted) {
        downcasted = int232(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(232, value);
        }
    }

    /**
     * @dev Returns the downcasted int224 from int256, reverting on
     * overflow (when the input is less than smallest int224 or
     * greater than largest int224).
     *
     * Counterpart to Solidity's `int224` operator.
     *
     * Requirements:
     *
     * - input must fit into 224 bits
     */
    function toInt224(int256 value) internal pure returns (int224 downcasted) {
        downcasted = int224(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(224, value);
        }
    }

    /**
     * @dev Returns the downcasted int216 from int256, reverting on
     * overflow (when the input is less than smallest int216 or
     * greater than largest int216).
     *
     * Counterpart to Solidity's `int216` operator.
     *
     * Requirements:
     *
     * - input must fit into 216 bits
     */
    function toInt216(int256 value) internal pure returns (int216 downcasted) {
        downcasted = int216(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(216, value);
        }
    }

    /**
     * @dev Returns the downcasted int208 from int256, reverting on
     * overflow (when the input is less than smallest int208 or
     * greater than largest int208).
     *
     * Counterpart to Solidity's `int208` operator.
     *
     * Requirements:
     *
     * - input must fit into 208 bits
     */
    function toInt208(int256 value) internal pure returns (int208 downcasted) {
        downcasted = int208(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(208, value);
        }
    }

    /**
     * @dev Returns the downcasted int200 from int256, reverting on
     * overflow (when the input is less than smallest int200 or
     * greater than largest int200).
     *
     * Counterpart to Solidity's `int200` operator.
     *
     * Requirements:
     *
     * - input must fit into 200 bits
     */
    function toInt200(int256 value) internal pure returns (int200 downcasted) {
        downcasted = int200(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(200, value);
        }
    }

    /**
     * @dev Returns the downcasted int192 from int256, reverting on
     * overflow (when the input is less than smallest int192 or
     * greater than largest int192).
     *
     * Counterpart to Solidity's `int192` operator.
     *
     * Requirements:
     *
     * - input must fit into 192 bits
     */
    function toInt192(int256 value) internal pure returns (int192 downcasted) {
        downcasted = int192(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(192, value);
        }
    }

    /**
     * @dev Returns the downcasted int184 from int256, reverting on
     * overflow (when the input is less than smallest int184 or
     * greater than largest int184).
     *
     * Counterpart to Solidity's `int184` operator.
     *
     * Requirements:
     *
     * - input must fit into 184 bits
     */
    function toInt184(int256 value) internal pure returns (int184 downcasted) {
        downcasted = int184(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(184, value);
        }
    }

    /**
     * @dev Returns the downcasted int176 from int256, reverting on
     * overflow (when the input is less than smallest int176 or
     * greater than largest int176).
     *
     * Counterpart to Solidity's `int176` operator.
     *
     * Requirements:
     *
     * - input must fit into 176 bits
     */
    function toInt176(int256 value) internal pure returns (int176 downcasted) {
        downcasted = int176(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(176, value);
        }
    }

    /**
     * @dev Returns the downcasted int168 from int256, reverting on
     * overflow (when the input is less than smallest int168 or
     * greater than largest int168).
     *
     * Counterpart to Solidity's `int168` operator.
     *
     * Requirements:
     *
     * - input must fit into 168 bits
     */
    function toInt168(int256 value) internal pure returns (int168 downcasted) {
        downcasted = int168(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(168, value);
        }
    }

    /**
     * @dev Returns the downcasted int160 from int256, reverting on
     * overflow (when the input is less than smallest int160 or
     * greater than largest int160).
     *
     * Counterpart to Solidity's `int160` operator.
     *
     * Requirements:
     *
     * - input must fit into 160 bits
     */
    function toInt160(int256 value) internal pure returns (int160 downcasted) {
        downcasted = int160(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(160, value);
        }
    }

    /**
     * @dev Returns the downcasted int152 from int256, reverting on
     * overflow (when the input is less than smallest int152 or
     * greater than largest int152).
     *
     * Counterpart to Solidity's `int152` operator.
     *
     * Requirements:
     *
     * - input must fit into 152 bits
     */
    function toInt152(int256 value) internal pure returns (int152 downcasted) {
        downcasted = int152(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(152, value);
        }
    }

    /**
     * @dev Returns the downcasted int144 from int256, reverting on
     * overflow (when the input is less than smallest int144 or
     * greater than largest int144).
     *
     * Counterpart to Solidity's `int144` operator.
     *
     * Requirements:
     *
     * - input must fit into 144 bits
     */
    function toInt144(int256 value) internal pure returns (int144 downcasted) {
        downcasted = int144(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(144, value);
        }
    }

    /**
     * @dev Returns the downcasted int136 from int256, reverting on
     * overflow (when the input is less than smallest int136 or
     * greater than largest int136).
     *
     * Counterpart to Solidity's `int136` operator.
     *
     * Requirements:
     *
     * - input must fit into 136 bits
     */
    function toInt136(int256 value) internal pure returns (int136 downcasted) {
        downcasted = int136(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(136, value);
        }
    }

    /**
     * @dev Returns the downcasted int128 from int256, reverting on
     * overflow (when the input is less than smallest int128 or
     * greater than largest int128).
     *
     * Counterpart to Solidity's `int128` operator.
     *
     * Requirements:
     *
     * - input must fit into 128 bits
     */
    function toInt128(int256 value) internal pure returns (int128 downcasted) {
        downcasted = int128(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(128, value);
        }
    }

    /**
     * @dev Returns the downcasted int120 from int256, reverting on
     * overflow (when the input is less than smallest int120 or
     * greater than largest int120).
     *
     * Counterpart to Solidity's `int120` operator.
     *
     * Requirements:
     *
     * - input must fit into 120 bits
     */
    function toInt120(int256 value) internal pure returns (int120 downcasted) {
        downcasted = int120(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(120, value);
        }
    }

    /**
     * @dev Returns the downcasted int112 from int256, reverting on
     * overflow (when the input is less than smallest int112 or
     * greater than largest int112).
     *
     * Counterpart to Solidity's `int112` operator.
     *
     * Requirements:
     *
     * - input must fit into 112 bits
     */
    function toInt112(int256 value) internal pure returns (int112 downcasted) {
        downcasted = int112(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(112, value);
        }
    }

    /**
     * @dev Returns the downcasted int104 from int256, reverting on
     * overflow (when the input is less than smallest int104 or
     * greater than largest int104).
     *
     * Counterpart to Solidity's `int104` operator.
     *
     * Requirements:
     *
     * - input must fit into 104 bits
     */
    function toInt104(int256 value) internal pure returns (int104 downcasted) {
        downcasted = int104(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(104, value);
        }
    }

    /**
     * @dev Returns the downcasted int96 from int256, reverting on
     * overflow (when the input is less than smallest int96 or
     * greater than largest int96).
     *
     * Counterpart to Solidity's `int96` operator.
     *
     * Requirements:
     *
     * - input must fit into 96 bits
     */
    function toInt96(int256 value) internal pure returns (int96 downcasted) {
        downcasted = int96(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(96, value);
        }
    }

    /**
     * @dev Returns the downcasted int88 from int256, reverting on
     * overflow (when the input is less than smallest int88 or
     * greater than largest int88).
     *
     * Counterpart to Solidity's `int88` operator.
     *
     * Requirements:
     *
     * - input must fit into 88 bits
     */
    function toInt88(int256 value) internal pure returns (int88 downcasted) {
        downcasted = int88(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(88, value);
        }
    }

    /**
     * @dev Returns the downcasted int80 from int256, reverting on
     * overflow (when the input is less than smallest int80 or
     * greater than largest int80).
     *
     * Counterpart to Solidity's `int80` operator.
     *
     * Requirements:
     *
     * - input must fit into 80 bits
     */
    function toInt80(int256 value) internal pure returns (int80 downcasted) {
        downcasted = int80(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(80, value);
        }
    }

    /**
     * @dev Returns the downcasted int72 from int256, reverting on
     * overflow (when the input is less than smallest int72 or
     * greater than largest int72).
     *
     * Counterpart to Solidity's `int72` operator.
     *
     * Requirements:
     *
     * - input must fit into 72 bits
     */
    function toInt72(int256 value) internal pure returns (int72 downcasted) {
        downcasted = int72(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(72, value);
        }
    }

    /**
     * @dev Returns the downcasted int64 from int256, reverting on
     * overflow (when the input is less than smallest int64 or
     * greater than largest int64).
     *
     * Counterpart to Solidity's `int64` operator.
     *
     * Requirements:
     *
     * - input must fit into 64 bits
     */
    function toInt64(int256 value) internal pure returns (int64 downcasted) {
        downcasted = int64(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(64, value);
        }
    }

    /**
     * @dev Returns the downcasted int56 from int256, reverting on
     * overflow (when the input is less than smallest int56 or
     * greater than largest int56).
     *
     * Counterpart to Solidity's `int56` operator.
     *
     * Requirements:
     *
     * - input must fit into 56 bits
     */
    function toInt56(int256 value) internal pure returns (int56 downcasted) {
        downcasted = int56(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(56, value);
        }
    }

    /**
     * @dev Returns the downcasted int48 from int256, reverting on
     * overflow (when the input is less than smallest int48 or
     * greater than largest int48).
     *
     * Counterpart to Solidity's `int48` operator.
     *
     * Requirements:
     *
     * - input must fit into 48 bits
     */
    function toInt48(int256 value) internal pure returns (int48 downcasted) {
        downcasted = int48(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(48, value);
        }
    }

    /**
     * @dev Returns the downcasted int40 from int256, reverting on
     * overflow (when the input is less than smallest int40 or
     * greater than largest int40).
     *
     * Counterpart to Solidity's `int40` operator.
     *
     * Requirements:
     *
     * - input must fit into 40 bits
     */
    function toInt40(int256 value) internal pure returns (int40 downcasted) {
        downcasted = int40(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(40, value);
        }
    }

    /**
     * @dev Returns the downcasted int32 from int256, reverting on
     * overflow (when the input is less than smallest int32 or
     * greater than largest int32).
     *
     * Counterpart to Solidity's `int32` operator.
     *
     * Requirements:
     *
     * - input must fit into 32 bits
     */
    function toInt32(int256 value) internal pure returns (int32 downcasted) {
        downcasted = int32(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(32, value);
        }
    }

    /**
     * @dev Returns the downcasted int24 from int256, reverting on
     * overflow (when the input is less than smallest int24 or
     * greater than largest int24).
     *
     * Counterpart to Solidity's `int24` operator.
     *
     * Requirements:
     *
     * - input must fit into 24 bits
     */
    function toInt24(int256 value) internal pure returns (int24 downcasted) {
        downcasted = int24(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(24, value);
        }
    }

    /**
     * @dev Returns the downcasted int16 from int256, reverting on
     * overflow (when the input is less than smallest int16 or
     * greater than largest int16).
     *
     * Counterpart to Solidity's `int16` operator.
     *
     * Requirements:
     *
     * - input must fit into 16 bits
     */
    function toInt16(int256 value) internal pure returns (int16 downcasted) {
        downcasted = int16(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(16, value);
        }
    }

    /**
     * @dev Returns the downcasted int8 from int256, reverting on
     * overflow (when the input is less than smallest int8 or
     * greater than largest int8).
     *
     * Counterpart to Solidity's `int8` operator.
     *
     * Requirements:
     *
     * - input must fit into 8 bits
     */
    function toInt8(int256 value) internal pure returns (int8 downcasted) {
        downcasted = int8(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(8, value);
        }
    }

    /**
     * @dev Converts an unsigned uint256 into a signed int256.
     *
     * Requirements:
     *
     * - input must be less than or equal to maxInt256.
     */
    function toInt256(uint256 value) internal pure returns (int256) {
        // Note: Unsafe cast below is okay because `type(int256).max` is guaranteed to be positive
        if (value > uint256(type(int256).max)) {
            revert SafeCastOverflowedUintToInt(value);
        }
        return int256(value);
    }

    /**
     * @dev Cast a boolean (false or true) to a uint256 (0 or 1) with no jump.
     */
    function toUint(bool b) internal pure returns (uint256 u) {
        assembly ("memory-safe") {
            u := iszero(iszero(b))
        }
    }
}