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// SPDX-License-Identifier: MIT
pragma solidity ^0.8.28;

import {PaintSwapUserNFTBase, ERC1155Upgradeable} from "./PaintSwapUserNFTBase.sol";
import {IERC165, IERC2981} from "../interfaces/IERC2981.sol";

contract PaintSwapUserNFTERC2981 is PaintSwapUserNFTBase, IERC2981 {
  event RoyaltyInfo(address recipient, uint128 royalty);

  error RoyaltyTooHigh();
  error RoyaltyAddressZero();
  error RoyaltyRecipientZero();

  uint256 private _royalty; // base 10000
  address private _royaltyRecipient;

  function _initialize(
    address /* marketplace */,
    address royaltyRecipient,
    uint128 royalty,
    address /* devAddr */,
    uint128 /* nftMintFee */,
    uint128 /* maxMints */,
    string calldata /* symbol */,
    string calldata /* name */,
    address /* contractOwner */
  ) internal override {
    require(royalty <= 2000, RoyaltyTooHigh()); // 20%
    require(royaltyRecipient != address(0), RoyaltyRecipientZero());
    _royalty = royalty;
    _royaltyRecipient = royaltyRecipient;
    emit RoyaltyInfo(royaltyRecipient, royalty);
  }

  function royaltyInfo(
    uint256,
    uint256 _salePrice
  ) external view override returns (address receiver, uint256 royaltyAmount) {
    uint256 amount = (_salePrice * _royalty) / 10000;
    return (_royaltyRecipient, amount);
  }

  function supportsInterface(bytes4 interfaceId) public view override(IERC165, ERC1155Upgradeable) returns (bool) {
    if (_royalty == 0) {
      return super.supportsInterface(interfaceId);
    }
    return interfaceId == type(IERC2981).interfaceId || super.supportsInterface(interfaceId);
  }

  function setRoyaltyRecipient(address royaltyRecipient) external onlyOwner {
    require(royaltyRecipient != address(0), RoyaltyAddressZero());
    _royaltyRecipient = royaltyRecipient;
  }
}

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

pragma solidity ^0.8.20;

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

/**
 * @dev Contract module which provides a basic access control mechanism, where
 * there is an account (an owner) that can be granted exclusive access to
 * specific functions.
 *
 * The initial owner is set to the address provided by the deployer. This can
 * later be changed with {transferOwnership}.
 *
 * This module is used through inheritance. It will make available the modifier
 * `onlyOwner`, which can be applied to your functions to restrict their use to
 * the owner.
 */
abstract contract OwnableUpgradeable is Initializable, ContextUpgradeable {
    /// @custom:storage-location erc7201:openzeppelin.storage.Ownable
    struct OwnableStorage {
        address _owner;
    }

    // keccak256(abi.encode(uint256(keccak256("openzeppelin.storage.Ownable")) - 1)) & ~bytes32(uint256(0xff))
    bytes32 private constant OwnableStorageLocation = 0x9016d09d72d40fdae2fd8ceac6b6234c7706214fd39c1cd1e609a0528c199300;

    function _getOwnableStorage() private pure returns (OwnableStorage storage $) {
        assembly ("memory-safe") {
            $.slot := OwnableStorageLocation
        }
    }

    /**
     * @dev The caller account is not authorized to perform an operation.
     */
    error OwnableUnauthorizedAccount(address account);

    /**
     * @dev The owner is not a valid owner account. (eg. `address(0)`)
     */
    error OwnableInvalidOwner(address owner);

    event OwnershipTransferred(address indexed previousOwner, address indexed newOwner);

    /**
     * @dev Initializes the contract setting the address provided by the deployer as the initial owner.
     */
    function __Ownable_init(address initialOwner) internal onlyInitializing {
        __Ownable_init_unchained(initialOwner);
    }

    function __Ownable_init_unchained(address initialOwner) internal onlyInitializing {
        if (initialOwner == address(0)) {
            revert OwnableInvalidOwner(address(0));
        }
        _transferOwnership(initialOwner);
    }

    /**
     * @dev Throws if called by any account other than the owner.
     */
    modifier onlyOwner() {
        _checkOwner();
        _;
    }

    /**
     * @dev Returns the address of the current owner.
     */
    function owner() public view virtual returns (address) {
        OwnableStorage storage $ = _getOwnableStorage();
        return $._owner;
    }

    /**
     * @dev Throws if the sender is not the owner.
     */
    function _checkOwner() internal view virtual {
        if (owner() != _msgSender()) {
            revert OwnableUnauthorizedAccount(_msgSender());
        }
    }

    /**
     * @dev Leaves the contract without owner. It will not be possible to call
     * `onlyOwner` functions. Can only be called by the current owner.
     *
     * NOTE: Renouncing ownership will leave the contract without an owner,
     * thereby disabling any functionality that is only available to the owner.
     */
    function renounceOwnership() public virtual onlyOwner {
        _transferOwnership(address(0));
    }

    /**
     * @dev Transfers ownership of the contract to a new account (`newOwner`).
     * Can only be called by the current owner.
     */
    function transferOwnership(address newOwner) public virtual onlyOwner {
        if (newOwner == address(0)) {
            revert OwnableInvalidOwner(address(0));
        }
        _transferOwnership(newOwner);
    }

    /**
     * @dev Transfers ownership of the contract to a new account (`newOwner`).
     * Internal function without access restriction.
     */
    function _transferOwnership(address newOwner) internal virtual {
        OwnableStorage storage $ = _getOwnableStorage();
        address oldOwner = $._owner;
        $._owner = newOwner;
        emit OwnershipTransferred(oldOwner, newOwner);
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.0) (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 reininitialization) 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 Returns a pointer to the storage namespace.
     */
    // solhint-disable-next-line var-name-mixedcase
    function _getInitializableStorage() private pure returns (InitializableStorage storage $) {
        assembly ("memory-safe") {
            $.slot := INITIALIZABLE_STORAGE
        }
    }
}

// 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 ("memory-safe") {
            $.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 v5.0.1) (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/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 v5.1.0) (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 v5.1.0) (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 v5.1.0) (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 {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 {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/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) (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 {IERC1155-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 {IERC1155-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 v5.1.0) (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 ("memory-safe") {
            value := mload(ptr)
        }
    }

    /**
     * @dev Swaps the elements memory location `ptr1` and `ptr2`.
     */
    function _swap(uint256 ptr1, uint256 ptr2) private pure {
        assembly ("memory-safe") {
            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 ("memory-safe") {
            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 ("memory-safe") {
            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 ("memory-safe") {
            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 ("memory-safe") {
            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 ("memory-safe") {
            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 ("memory-safe") {
            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 ("memory-safe") {
            res := mload(add(add(arr, 0x20), mul(pos, 0x20)))
        }
    }

    /**
     * @dev Helper to set the length of an 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 an 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 an 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) (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 v5.1.0) (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/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 Returns the addition of two unsigned integers, with an success flag (no overflow).
     */
    function tryAdd(uint256 a, uint256 b) internal pure returns (bool success, uint256 result) {
        unchecked {
            uint256 c = a + b;
            if (c < a) return (false, 0);
            return (true, c);
        }
    }

    /**
     * @dev Returns the subtraction of two unsigned integers, with an success flag (no overflow).
     */
    function trySub(uint256 a, uint256 b) internal pure returns (bool success, uint256 result) {
        unchecked {
            if (b > a) return (false, 0);
            return (true, a - b);
        }
    }

    /**
     * @dev Returns the multiplication of two unsigned integers, with an success flag (no overflow).
     */
    function tryMul(uint256 a, uint256 b) internal pure returns (bool success, uint256 result) {
        unchecked {
            // Gas optimization: this is cheaper than requiring 'a' not being zero, but the
            // benefit is lost if 'b' is also tested.
            // See: https://github.com/OpenZeppelin/openzeppelin-contracts/pull/522
            if (a == 0) return (true, 0);
            uint256 c = a * b;
            if (c / a != b) return (false, 0);
            return (true, c);
        }
    }

    /**
     * @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 {
            if (b == 0) return (false, 0);
            return (true, 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 {
            if (b == 0) return (false, 0);
            return (true, a % b);
        }
    }

    /**
     * @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 {
            // 512-bit multiply [prod1 prod0] = 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 = prod1 * 2²⁵⁶ + prod0.
            uint256 prod0 = x * y; // Least significant 256 bits of the product
            uint256 prod1; // Most significant 256 bits of the product
            assembly ("memory-safe") {
                let mm := mulmod(x, y, not(0))
                prod1 := sub(sub(mm, prod0), lt(mm, prod0))
            }

            // Handle non-overflow cases, 256 by 256 division.
            if (prod1 == 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 prod0 / denominator;
            }

            // Make sure the result is less than 2²⁵⁶. Also prevents denominator == 0.
            if (denominator <= prod1) {
                Panic.panic(ternary(denominator == 0, Panic.DIVISION_BY_ZERO, Panic.UNDER_OVERFLOW));
            }

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

            // Make division exact by subtracting the remainder from [prod1 prod0].
            uint256 remainder;
            assembly ("memory-safe") {
                // Compute remainder using mulmod.
                remainder := mulmod(x, y, denominator)

                // Subtract 256 bit number from 512 bit number.
                prod1 := sub(prod1, gt(remainder, prod0))
                prod0 := sub(prod0, 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 [prod1 prod0] by twos.
                prod0 := div(prod0, 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 prod1 into prod0.
            prod0 |= prod1 * 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 prod1
            // is no longer required.
            result = prod0 * 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 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 value) internal pure returns (uint256) {
        uint256 result = 0;
        uint256 exp;
        unchecked {
            exp = 128 * SafeCast.toUint(value > (1 << 128) - 1);
            value >>= exp;
            result += exp;

            exp = 64 * SafeCast.toUint(value > (1 << 64) - 1);
            value >>= exp;
            result += exp;

            exp = 32 * SafeCast.toUint(value > (1 << 32) - 1);
            value >>= exp;
            result += exp;

            exp = 16 * SafeCast.toUint(value > (1 << 16) - 1);
            value >>= exp;
            result += exp;

            exp = 8 * SafeCast.toUint(value > (1 << 8) - 1);
            value >>= exp;
            result += exp;

            exp = 4 * SafeCast.toUint(value > (1 << 4) - 1);
            value >>= exp;
            result += exp;

            exp = 2 * SafeCast.toUint(value > (1 << 2) - 1);
            value >>= exp;
            result += exp;

            result += SafeCast.toUint(value > 1);
        }
        return result;
    }

    /**
     * @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 value) internal pure returns (uint256) {
        uint256 result = 0;
        uint256 isGt;
        unchecked {
            isGt = SafeCast.toUint(value > (1 << 128) - 1);
            value >>= isGt * 128;
            result += isGt * 16;

            isGt = SafeCast.toUint(value > (1 << 64) - 1);
            value >>= isGt * 64;
            result += isGt * 8;

            isGt = SafeCast.toUint(value > (1 << 32) - 1);
            value >>= isGt * 32;
            result += isGt * 4;

            isGt = SafeCast.toUint(value > (1 << 16) - 1);
            value >>= isGt * 16;
            result += isGt * 2;

            result += SafeCast.toUint(value > (1 << 8) - 1);
        }
        return result;
    }

    /**
     * @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/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))
        }
    }
}

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

pragma solidity ^0.8.20;

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

/**
 * @dev Standard signed math utilities missing in the Solidity language.
 */
library SignedMath {
    /**
     * @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, int256 a, int256 b) internal pure returns (int256) {
        unchecked {
            // branchless ternary works because:
            // b ^ (a ^ b) == a
            // b ^ 0 == b
            return b ^ ((a ^ b) * int256(SafeCast.toUint(condition)));
        }
    }

    /**
     * @dev Returns the largest of two signed numbers.
     */
    function max(int256 a, int256 b) internal pure returns (int256) {
        return ternary(a > b, a, b);
    }

    /**
     * @dev Returns the smallest of two signed numbers.
     */
    function min(int256 a, int256 b) internal pure returns (int256) {
        return ternary(a < b, a, b);
    }

    /**
     * @dev Returns the average of two signed numbers without overflow.
     * The result is rounded towards zero.
     */
    function average(int256 a, int256 b) internal pure returns (int256) {
        // Formula from the book "Hacker's Delight"
        int256 x = (a & b) + ((a ^ b) >> 1);
        return x + (int256(uint256(x) >> 255) & (a ^ b));
    }

    /**
     * @dev Returns the absolute unsigned value of a signed value.
     */
    function abs(int256 n) internal pure returns (uint256) {
        unchecked {
            // Formula from the "Bit Twiddling Hacks" by Sean Eron Anderson.
            // Since `n` is a signed integer, the generated bytecode will use the SAR opcode to perform the right shift,
            // taking advantage of the most significant (or "sign" bit) in two's complement representation.
            // This opcode adds new most significant bits set to the value of the previous most significant bit. As a result,
            // the mask will either be `bytes32(0)` (if n is positive) or `~bytes32(0)` (if n is negative).
            int256 mask = n >> 255;

            // A `bytes32(0)` mask leaves the input unchanged, while a `~bytes32(0)` mask complements it.
            return uint256((n + mask) ^ mask);
        }
    }
}

// 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/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 v5.1.0) (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) (utils/Strings.sol)

pragma solidity ^0.8.20;

import {Math} from "./math/Math.sol";
import {SignedMath} from "./math/SignedMath.sol";

/**
 * @dev String operations.
 */
library Strings {
    bytes16 private constant HEX_DIGITS = "0123456789abcdef";
    uint8 private constant ADDRESS_LENGTH = 20;

    /**
     * @dev The `value` string doesn't fit in the specified `length`.
     */
    error StringsInsufficientHexLength(uint256 value, uint256 length);

    /**
     * @dev Converts a `uint256` to its ASCII `string` decimal representation.
     */
    function toString(uint256 value) internal pure returns (string memory) {
        unchecked {
            uint256 length = Math.log10(value) + 1;
            string memory buffer = new string(length);
            uint256 ptr;
            assembly ("memory-safe") {
                ptr := add(buffer, add(32, length))
            }
            while (true) {
                ptr--;
                assembly ("memory-safe") {
                    mstore8(ptr, byte(mod(value, 10), HEX_DIGITS))
                }
                value /= 10;
                if (value == 0) break;
            }
            return buffer;
        }
    }

    /**
     * @dev Converts a `int256` to its ASCII `string` decimal representation.
     */
    function toStringSigned(int256 value) internal pure returns (string memory) {
        return string.concat(value < 0 ? "-" : "", toString(SignedMath.abs(value)));
    }

    /**
     * @dev Converts a `uint256` to its ASCII `string` hexadecimal representation.
     */
    function toHexString(uint256 value) internal pure returns (string memory) {
        unchecked {
            return toHexString(value, Math.log256(value) + 1);
        }
    }

    /**
     * @dev Converts a `uint256` to its ASCII `string` hexadecimal representation with fixed length.
     */
    function toHexString(uint256 value, uint256 length) internal pure returns (string memory) {
        uint256 localValue = value;
        bytes memory buffer = new bytes(2 * length + 2);
        buffer[0] = "0";
        buffer[1] = "x";
        for (uint256 i = 2 * length + 1; i > 1; --i) {
            buffer[i] = HEX_DIGITS[localValue & 0xf];
            localValue >>= 4;
        }
        if (localValue != 0) {
            revert StringsInsufficientHexLength(value, length);
        }
        return string(buffer);
    }

    /**
     * @dev Converts an `address` with fixed length of 20 bytes to its not checksummed ASCII `string` hexadecimal
     * representation.
     */
    function toHexString(address addr) internal pure returns (string memory) {
        return toHexString(uint256(uint160(addr)), ADDRESS_LENGTH);
    }

    /**
     * @dev Converts an `address` with fixed length of 20 bytes to its checksummed ASCII `string` hexadecimal
     * representation, according to EIP-55.
     */
    function toChecksumHexString(address addr) internal pure returns (string memory) {
        bytes memory buffer = bytes(toHexString(addr));

        // hash the hex part of buffer (skip length + 2 bytes, length 40)
        uint256 hashValue;
        assembly ("memory-safe") {
            hashValue := shr(96, keccak256(add(buffer, 0x22), 40))
        }

        for (uint256 i = 41; i > 1; --i) {
            // possible values for buffer[i] are 48 (0) to 57 (9) and 97 (a) to 102 (f)
            if (hashValue & 0xf > 7 && uint8(buffer[i]) > 96) {
                // case shift by xoring with 0x20
                buffer[i] ^= 0x20;
            }
            hashValue >>= 4;
        }
        return string(buffer);
    }

    /**
     * @dev Returns true if the two strings are equal.
     */
    function equal(string memory a, string memory b) internal pure returns (bool) {
        return bytes(a).length == bytes(b).length && keccak256(bytes(a)) == keccak256(bytes(b));
    }
}

// SPDX-License-Identifier: MIT
pragma solidity ^0.8.28;

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

interface IERC2981 is IERC165 {
  /// @notice Called with the sale price to determine how much royalty
  //          is owed and to whom.
  /// @param tokenId - the NFT asset queried for royalty information
  /// @param salePrice - the sale price of the NFT asset specified by _tokenId
  /// @return receiver - address of who should be sent the royalty payment
  /// @return royaltyAmount - the royalty payment amount for _salePrice
  function royaltyInfo(
    uint256 tokenId,
    uint256 salePrice
  ) external view returns (address receiver, uint256 royaltyAmount);
}

// SPDX-License-Identifier: MIT
pragma solidity ^0.8.28;

interface InitializeUserNFT {
  function initialize(
    address marketplace,
    address royaltyRecipient,
    uint128 royalty,
    address devAddr,
    uint128 mintFee,
    uint128 maxMints,
    string calldata symbol,
    string calldata name,
    address owner
  ) external;
}

// SPDX-License-Identifier: MIT
pragma solidity ^0.8.28;

import {ERC1155Upgradeable} from "@openzeppelin/contracts-upgradeable/token/ERC1155/ERC1155Upgradeable.sol";
import {Strings} from "@openzeppelin/contracts/utils/Strings.sol";
import {OwnableUpgradeable} from "@openzeppelin/contracts-upgradeable/access/OwnableUpgradeable.sol";
import {InitializeUserNFT} from "../interfaces/InitializeUserNFT.sol";

abstract contract PaintSwapUserNFTBase is ERC1155Upgradeable, InitializeUserNFT, OwnableUpgradeable {
  using Strings for uint256;

  event IsInitialized(string symbol, string name);
  event MaxMintsReached();
  event UpdateName(string name);
  event Ignore(bool ignore);

  error NameTooLong();
  error TokenDoesNotExist(uint256 tokenId);
  error NotEnoughFtm(uint256 mintFee);
  error NotEnoughFtmBatch(uint256 mintFee, uint256 length);
  error LengthMismatch();
  error MintAmountExceedsMaxMints(uint128 maxMints);
  error CoinTransferFailed(address to);

  string private constant _baseUri = "ipfs://";
  uint256 private _tokenIds;

  // PaintSwap Marketplace V2 contract address to allow skipping approval process when selling nfts
  address internal _marketplace;
  // The fee for minting
  uint256 private _mintFee;
  // The destination adddress
  address private _devAddr;
  // Maximum number of individual nft tokenIds that can be created
  uint128 private _maxMints;
  mapping(uint256 tokenId => string uri) internal _tokenURIs;

  string private _symbol;
  string private _name;

  /// @custom:oz-upgrades-unsafe-allow constructor
  constructor() {
    _disableInitializers();
  }

  function initialize(
    address marketplace,
    address royaltyRecipient,
    uint128 royalty,
    address devAddr,
    uint128 nftMintFee,
    uint128 maxMints,
    string calldata nftSymbol,
    string calldata nftName,
    address contractOwner
  ) external override initializer {
    __Ownable_init(contractOwner);
    __ERC1155_init("");

    _marketplace = marketplace;
    _mintFee = nftMintFee;
    _devAddr = devAddr;
    _maxMints = maxMints == 0 ? type(uint128).max : maxMints;
    require(bytes(nftName).length <= 32, NameTooLong());
    _name = nftName;
    _symbol = nftSymbol;

    _initialize(
      marketplace,
      royaltyRecipient,
      royalty,
      devAddr,
      nftMintFee,
      maxMints,
      nftSymbol,
      nftName,
      contractOwner
    );

    emit IsInitialized(nftSymbol, nftName);
  }

  function _initialize(
    address marketplace,
    address /* _royaltyRecipient */,
    uint128 /* _royalty */,
    address devAddr,
    uint128 nftMintFee,
    uint128 maxMints,
    string calldata symbol,
    string calldata name,
    address contractOwner
  ) internal virtual;

  function mintFee() external view returns (uint256) {
    return _mintFee;
  }

  function symbol() external view returns (string memory) {
    return _symbol;
  }

  function name() external view returns (string memory) {
    return _name;
  }

  function getMaxMints() external view returns (uint128) {
    return _maxMints;
  }

  function uri(uint256 tokenId) public view virtual override returns (string memory) {
    require(_exists(tokenId), TokenDoesNotExist(tokenId));

    // If there is no base URI, return the token URI.
    if (bytes(_baseUri).length == 0) {
      return _tokenURIs[tokenId];
    }
    // If both are set, concatenate the baseURI and tokenURI (via abi.encodePacked).
    if (bytes(_tokenURIs[tokenId]).length != 0) {
      return string(abi.encodePacked(_baseUri, _tokenURIs[tokenId]));
    }

    return super.uri(tokenId);
  }

  function batchMint(address to, uint256[] memory amounts, string[] memory tokenURIs) external payable onlyOwner {
    uint256 mintQuantity = amounts.length;
    require(mintQuantity == tokenURIs.length, LengthMismatch());
    require(msg.value == _mintFee * mintQuantity, NotEnoughFtmBatch(_mintFee, mintQuantity));

    uint256 current = _tokenIds;
    uint128 maxMints = _maxMints;
    require(current + mintQuantity <= maxMints, MintAmountExceedsMaxMints(maxMints));
    uint256[] memory ids = new uint256[](mintQuantity);
    for (uint256 i = 0; i < mintQuantity; ++i) {
      ++current;
      uint256 id = current;
      ids[i] = id;
      _tokenURIs[id] = tokenURIs[i];
    }

    if (current + mintQuantity == maxMints) {
      emit MaxMintsReached();
    }

    _mintBatch(to, ids, amounts, "");

    // Send FTM fee to fee recipient
    (bool success, ) = _devAddr.call{value: msg.value}("");
    require(success, CoinTransferFailed(_devAddr));
  }

  // The uri must be in the form of ipfs:// where the ipfs:// prefix has been stripped
  function mint(address to, uint256 amount, string memory tokenURI) external payable onlyOwner {
    require(msg.value == _mintFee, "Not enough ftm");

    uint256 id = ++_tokenIds;
    _mint(to, id, amount, "");
    _tokenURIs[id] = tokenURI;

    require(id <= _maxMints);
    if (id == _maxMints) {
      emit MaxMintsReached();
    }

    // Send FTM fee to recipient
    (bool success, ) = _devAddr.call{value: msg.value}("");
    require(success, "Transfer failed");
  }

  // Anyone can burn their NFT if they have sufficient balance
  function burn(uint256 id, uint256 amount) external {
    require(balanceOf(_msgSender(), id) >= amount);
    _burn(_msgSender(), id, amount);
  }

  function updateName(string calldata updatedName) external onlyOwner {
    _name = updatedName;
    emit UpdateName(updatedName);
  }

  function ignore(bool _ignore) external onlyOwner {
    emit Ignore(_ignore);
  }

  /**
   * Override isApprovedForAll to whitelist the PaintSwap marketplace to enable listings without needing approval.
   * Just makes it easier for users
   */
  function isApprovedForAll(address nftOwner, address _operator) public view override returns (bool isOperator) {
    if (_operator == _marketplace) {
      return true;
    }

    return ERC1155Upgradeable.isApprovedForAll(nftOwner, _operator);
  }

  function _exists(uint256 tokenId) private view returns (bool) {
    return bytes(_tokenURIs[tokenId]).length != 0;
  }
}

{
  "optimizer": {
    "enabled": true,
    "runs": 9999999,
    "details": {
      "yul": true
    }
  },
  "evmVersion": "cancun",
  "viaIR": true,
  "outputSelection": {
    "*": {
      "*": [
        "evm.bytecode",
        "evm.deployedBytecode",
        "devdoc",
        "userdoc",
        "metadata",
        "abi"
      ]
    }
  },
  "libraries": {}
}

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