// File: @openzeppelin/contracts/access/AccessControl.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.8.0) (access/AccessControl.sol)

pragma solidity ^0.8.0;

import "./IAccessControl.sol";
import "../utils/Context.sol";
import "../utils/Strings.sol";
import "../utils/introspection/ERC165.sol";

/**
 * @dev Contract module that allows children to implement role-based access
 * control mechanisms. This is a lightweight version that doesn't allow enumerating role
 * members except through off-chain means by accessing the contract event logs. Some
 * applications may benefit from on-chain enumerability, for those cases see
 * {AccessControlEnumerable}.
 *
 * Roles are referred to by their `bytes32` identifier. These should be exposed
 * in the external API and be unique. The best way to achieve this is by
 * using `public constant` hash digests:
 *
 * ```
 * bytes32 public constant MY_ROLE = keccak256("MY_ROLE");
 * ```
 *
 * Roles can be used to represent a set of permissions. To restrict access to a
 * function call, use {hasRole}:
 *
 * ```
 * function foo() public {
 *     require(hasRole(MY_ROLE, msg.sender));
 *     ...
 * }
 * ```
 *
 * Roles can be granted and revoked dynamically via the {grantRole} and
 * {revokeRole} functions. Each role has an associated admin role, and only
 * accounts that have a role's admin role can call {grantRole} and {revokeRole}.
 *
 * By default, the admin role for all roles is `DEFAULT_ADMIN_ROLE`, which means
 * that only accounts with this role will be able to grant or revoke other
 * roles. More complex role relationships can be created by using
 * {_setRoleAdmin}.
 *
 * WARNING: The `DEFAULT_ADMIN_ROLE` is also its own admin: it has permission to
 * grant and revoke this role. Extra precautions should be taken to secure
 * accounts that have been granted it.
 */
abstract contract AccessControl is Context, IAccessControl, ERC165 {
    struct RoleData {
        mapping(address => bool) members;
        bytes32 adminRole;
    }

    mapping(bytes32 => RoleData) private _roles;

    bytes32 public constant DEFAULT_ADMIN_ROLE = 0x00;

    /**
     * @dev Modifier that checks that an account has a specific role. Reverts
     * with a standardized message including the required role.
     *
     * The format of the revert reason is given by the following regular expression:
     *
     *  /^AccessControl: account (0x[0-9a-f]{40}) is missing role (0x[0-9a-f]{64})$/
     *
     * _Available since v4.1._
     */
    modifier onlyRole(bytes32 role) {
        _checkRole(role);
        _;
    }

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

    /**
     * @dev Returns `true` if `account` has been granted `role`.
     */
    function hasRole(bytes32 role, address account) public view virtual override returns (bool) {
        return _roles[role].members[account];
    }

    /**
     * @dev Revert with a standard message if `_msgSender()` is missing `role`.
     * Overriding this function changes the behavior of the {onlyRole} modifier.
     *
     * Format of the revert message is described in {_checkRole}.
     *
     * _Available since v4.6._
     */
    function _checkRole(bytes32 role) internal view virtual {
        _checkRole(role, _msgSender());
    }

    /**
     * @dev Revert with a standard message if `account` is missing `role`.
     *
     * The format of the revert reason is given by the following regular expression:
     *
     *  /^AccessControl: account (0x[0-9a-f]{40}) is missing role (0x[0-9a-f]{64})$/
     */
    function _checkRole(bytes32 role, address account) internal view virtual {
        if (!hasRole(role, account)) {
            revert(
                string(
                    abi.encodePacked(
                        "AccessControl: account ",
                        Strings.toHexString(account),
                        " is missing role ",
                        Strings.toHexString(uint256(role), 32)
                    )
                )
            );
        }
    }

    /**
     * @dev Returns the admin role that controls `role`. See {grantRole} and
     * {revokeRole}.
     *
     * To change a role's admin, use {_setRoleAdmin}.
     */
    function getRoleAdmin(bytes32 role) public view virtual override returns (bytes32) {
        return _roles[role].adminRole;
    }

    /**
     * @dev Grants `role` to `account`.
     *
     * If `account` had not been already granted `role`, emits a {RoleGranted}
     * event.
     *
     * Requirements:
     *
     * - the caller must have ``role``'s admin role.
     *
     * May emit a {RoleGranted} event.
     */
    function grantRole(bytes32 role, address account) public virtual override onlyRole(getRoleAdmin(role)) {
        _grantRole(role, account);
    }

    /**
     * @dev Revokes `role` from `account`.
     *
     * If `account` had been granted `role`, emits a {RoleRevoked} event.
     *
     * Requirements:
     *
     * - the caller must have ``role``'s admin role.
     *
     * May emit a {RoleRevoked} event.
     */
    function revokeRole(bytes32 role, address account) public virtual override onlyRole(getRoleAdmin(role)) {
        _revokeRole(role, account);
    }

    /**
     * @dev Revokes `role` from the calling account.
     *
     * Roles are often managed via {grantRole} and {revokeRole}: this function's
     * purpose is to provide a mechanism for accounts to lose their privileges
     * if they are compromised (such as when a trusted device is misplaced).
     *
     * If the calling account had been revoked `role`, emits a {RoleRevoked}
     * event.
     *
     * Requirements:
     *
     * - the caller must be `account`.
     *
     * May emit a {RoleRevoked} event.
     */
    function renounceRole(bytes32 role, address account) public virtual override {
        require(account == _msgSender(), "AccessControl: can only renounce roles for self");

        _revokeRole(role, account);
    }

    /**
     * @dev Grants `role` to `account`.
     *
     * If `account` had not been already granted `role`, emits a {RoleGranted}
     * event. Note that unlike {grantRole}, this function doesn't perform any
     * checks on the calling account.
     *
     * May emit a {RoleGranted} event.
     *
     * [WARNING]
     * ====
     * This function should only be called from the constructor when setting
     * up the initial roles for the system.
     *
     * Using this function in any other way is effectively circumventing the admin
     * system imposed by {AccessControl}.
     * ====
     *
     * NOTE: This function is deprecated in favor of {_grantRole}.
     */
    function _setupRole(bytes32 role, address account) internal virtual {
        _grantRole(role, account);
    }

    /**
     * @dev Sets `adminRole` as ``role``'s admin role.
     *
     * Emits a {RoleAdminChanged} event.
     */
    function _setRoleAdmin(bytes32 role, bytes32 adminRole) internal virtual {
        bytes32 previousAdminRole = getRoleAdmin(role);
        _roles[role].adminRole = adminRole;
        emit RoleAdminChanged(role, previousAdminRole, adminRole);
    }

    /**
     * @dev Grants `role` to `account`.
     *
     * Internal function without access restriction.
     *
     * May emit a {RoleGranted} event.
     */
    function _grantRole(bytes32 role, address account) internal virtual {
        if (!hasRole(role, account)) {
            _roles[role].members[account] = true;
            emit RoleGranted(role, account, _msgSender());
        }
    }

    /**
     * @dev Revokes `role` from `account`.
     *
     * Internal function without access restriction.
     *
     * May emit a {RoleRevoked} event.
     */
    function _revokeRole(bytes32 role, address account) internal virtual {
        if (hasRole(role, account)) {
            _roles[role].members[account] = false;
            emit RoleRevoked(role, account, _msgSender());
        }
    }
}

// File: @openzeppelin/contracts/access/IAccessControl.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (access/IAccessControl.sol)

pragma solidity ^0.8.0;

/**
 * @dev External interface of AccessControl declared to support ERC165 detection.
 */
interface IAccessControl {
    /**
     * @dev Emitted when `newAdminRole` is set as ``role``'s admin role, replacing `previousAdminRole`
     *
     * `DEFAULT_ADMIN_ROLE` is the starting admin for all roles, despite
     * {RoleAdminChanged} not being emitted signaling this.
     *
     * _Available since v3.1._
     */
    event RoleAdminChanged(bytes32 indexed role, bytes32 indexed previousAdminRole, bytes32 indexed newAdminRole);

    /**
     * @dev Emitted when `account` is granted `role`.
     *
     * `sender` is the account that originated the contract call, an admin role
     * bearer except when using {AccessControl-_setupRole}.
     */
    event RoleGranted(bytes32 indexed role, address indexed account, address indexed sender);

    /**
     * @dev Emitted when `account` is revoked `role`.
     *
     * `sender` is the account that originated the contract call:
     *   - if using `revokeRole`, it is the admin role bearer
     *   - if using `renounceRole`, it is the role bearer (i.e. `account`)
     */
    event RoleRevoked(bytes32 indexed role, address indexed account, address indexed sender);

    /**
     * @dev Returns `true` if `account` has been granted `role`.
     */
    function hasRole(bytes32 role, address account) external view returns (bool);

    /**
     * @dev Returns the admin role that controls `role`. See {grantRole} and
     * {revokeRole}.
     *
     * To change a role's admin, use {AccessControl-_setRoleAdmin}.
     */
    function getRoleAdmin(bytes32 role) external view returns (bytes32);

    /**
     * @dev Grants `role` to `account`.
     *
     * If `account` had not been already granted `role`, emits a {RoleGranted}
     * event.
     *
     * Requirements:
     *
     * - the caller must have ``role``'s admin role.
     */
    function grantRole(bytes32 role, address account) external;

    /**
     * @dev Revokes `role` from `account`.
     *
     * If `account` had been granted `role`, emits a {RoleRevoked} event.
     *
     * Requirements:
     *
     * - the caller must have ``role``'s admin role.
     */
    function revokeRole(bytes32 role, address account) external;

    /**
     * @dev Revokes `role` from the calling account.
     *
     * Roles are often managed via {grantRole} and {revokeRole}: this function's
     * purpose is to provide a mechanism for accounts to lose their privileges
     * if they are compromised (such as when a trusted device is misplaced).
     *
     * If the calling account had been granted `role`, emits a {RoleRevoked}
     * event.
     *
     * Requirements:
     *
     * - the caller must be `account`.
     */
    function renounceRole(bytes32 role, address account) external;
}

// File: @openzeppelin/contracts/security/ReentrancyGuard.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.8.0) (security/ReentrancyGuard.sol)

pragma solidity ^0.8.0;

/**
 * @dev Contract module that helps prevent reentrant calls to a function.
 *
 * Inheriting from `ReentrancyGuard` will make the {nonReentrant} modifier
 * available, which can be applied to functions to make sure there are no nested
 * (reentrant) calls to them.
 *
 * Note that because there is a single `nonReentrant` guard, functions marked as
 * `nonReentrant` may not call one another. This can be worked around by making
 * those functions `private`, and then adding `external` `nonReentrant` entry
 * points to them.
 *
 * TIP: If you would like to learn more about reentrancy and alternative ways
 * to protect against it, check out our blog post
 * https://blog.openzeppelin.com/reentrancy-after-istanbul/[Reentrancy After Istanbul].
 */
abstract contract ReentrancyGuard {
    // Booleans are more expensive than uint256 or any type that takes up a full
    // word because each write operation emits an extra SLOAD to first read the
    // slot's contents, replace the bits taken up by the boolean, and then write
    // back. This is the compiler's defense against contract upgrades and
    // pointer aliasing, and it cannot be disabled.

    // The values being non-zero value makes deployment a bit more expensive,
    // but in exchange the refund on every call to nonReentrant will be lower in
    // amount. Since refunds are capped to a percentage of the total
    // transaction's gas, it is best to keep them low in cases like this one, to
    // increase the likelihood of the full refund coming into effect.
    uint256 private constant _NOT_ENTERED = 1;
    uint256 private constant _ENTERED = 2;

    uint256 private _status;

    constructor() {
        _status = _NOT_ENTERED;
    }

    /**
     * @dev Prevents a contract from calling itself, directly or indirectly.
     * Calling a `nonReentrant` function from another `nonReentrant`
     * function is not supported. It is possible to prevent this from happening
     * by making the `nonReentrant` function external, and making it call a
     * `private` function that does the actual work.
     */
    modifier nonReentrant() {
        _nonReentrantBefore();
        _;
        _nonReentrantAfter();
    }

    function _nonReentrantBefore() private {
        // On the first call to nonReentrant, _status will be _NOT_ENTERED
        require(_status != _ENTERED, "ReentrancyGuard: reentrant call");

        // Any calls to nonReentrant after this point will fail
        _status = _ENTERED;
    }

    function _nonReentrantAfter() private {
        // By storing the original value once again, a refund is triggered (see
        // https://eips.ethereum.org/EIPS/eip-2200)
        _status = _NOT_ENTERED;
    }
}

// File: @openzeppelin/contracts/token/ERC721/ERC721.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.8.0) (token/ERC721/ERC721.sol)

pragma solidity ^0.8.0;

import "./IERC721.sol";
import "./IERC721Receiver.sol";
import "./extensions/IERC721Metadata.sol";
import "../../utils/Address.sol";
import "../../utils/Context.sol";
import "../../utils/Strings.sol";
import "../../utils/introspection/ERC165.sol";

/**
 * @dev Implementation of https://eips.ethereum.org/EIPS/eip-721[ERC721] Non-Fungible Token Standard, including
 * the Metadata extension, but not including the Enumerable extension, which is available separately as
 * {ERC721Enumerable}.
 */
contract ERC721 is Context, ERC165, IERC721, IERC721Metadata {
    using Address for address;
    using Strings for uint256;

    // Token name
    string private _name;

    // Token symbol
    string private _symbol;

    // Mapping from token ID to owner address
    mapping(uint256 => address) private _owners;

    // Mapping owner address to token count
    mapping(address => uint256) private _balances;

    // Mapping from token ID to approved address
    mapping(uint256 => address) private _tokenApprovals;

    // Mapping from owner to operator approvals
    mapping(address => mapping(address => bool)) private _operatorApprovals;

    /**
     * @dev Initializes the contract by setting a `name` and a `symbol` to the token collection.
     */
    constructor(string memory name_, string memory symbol_) {
        _name = name_;
        _symbol = symbol_;
    }

    /**
     * @dev See {IERC165-supportsInterface}.
     */
    function supportsInterface(bytes4 interfaceId) public view virtual override(ERC165, IERC165) returns (bool) {
        return
            interfaceId == type(IERC721).interfaceId ||
            interfaceId == type(IERC721Metadata).interfaceId ||
            super.supportsInterface(interfaceId);
    }

    /**
     * @dev See {IERC721-balanceOf}.
     */
    function balanceOf(address owner) public view virtual override returns (uint256) {
        require(owner != address(0), "ERC721: address zero is not a valid owner");
        return _balances[owner];
    }

    /**
     * @dev See {IERC721-ownerOf}.
     */
    function ownerOf(uint256 tokenId) public view virtual override returns (address) {
        address owner = _ownerOf(tokenId);
        require(owner != address(0), "ERC721: invalid token ID");
        return owner;
    }

    /**
     * @dev See {IERC721Metadata-name}.
     */
    function name() public view virtual override returns (string memory) {
        return _name;
    }

    /**
     * @dev See {IERC721Metadata-symbol}.
     */
    function symbol() public view virtual override returns (string memory) {
        return _symbol;
    }

    /**
     * @dev See {IERC721Metadata-tokenURI}.
     */
    function tokenURI(uint256 tokenId) public view virtual override returns (string memory) {
        _requireMinted(tokenId);

        string memory baseURI = _baseURI();
        return bytes(baseURI).length > 0 ? string(abi.encodePacked(baseURI, tokenId.toString())) : "";
    }

    /**
     * @dev Base URI for computing {tokenURI}. If set, the resulting URI for each
     * token will be the concatenation of the `baseURI` and the `tokenId`. Empty
     * by default, can be overridden in child contracts.
     */
    function _baseURI() internal view virtual returns (string memory) {
        return "";
    }

    /**
     * @dev See {IERC721-approve}.
     */
    function approve(address to, uint256 tokenId) public virtual override {
        address owner = ERC721.ownerOf(tokenId);
        require(to != owner, "ERC721: approval to current owner");

        require(
            _msgSender() == owner || isApprovedForAll(owner, _msgSender()),
            "ERC721: approve caller is not token owner or approved for all"
        );

        _approve(to, tokenId);
    }

    /**
     * @dev See {IERC721-getApproved}.
     */
    function getApproved(uint256 tokenId) public view virtual override returns (address) {
        _requireMinted(tokenId);

        return _tokenApprovals[tokenId];
    }

    /**
     * @dev See {IERC721-setApprovalForAll}.
     */
    function setApprovalForAll(address operator, bool approved) public virtual override {
        _setApprovalForAll(_msgSender(), operator, approved);
    }

    /**
     * @dev See {IERC721-isApprovedForAll}.
     */
    function isApprovedForAll(address owner, address operator) public view virtual override returns (bool) {
        return _operatorApprovals[owner][operator];
    }

    /**
     * @dev See {IERC721-transferFrom}.
     */
    function transferFrom(
        address from,
        address to,
        uint256 tokenId
    ) public virtual override {
        //solhint-disable-next-line max-line-length
        require(_isApprovedOrOwner(_msgSender(), tokenId), "ERC721: caller is not token owner or approved");

        _transfer(from, to, tokenId);
    }

    /**
     * @dev See {IERC721-safeTransferFrom}.
     */
    function safeTransferFrom(
        address from,
        address to,
        uint256 tokenId
    ) public virtual override {
        safeTransferFrom(from, to, tokenId, "");
    }

    /**
     * @dev See {IERC721-safeTransferFrom}.
     */
    function safeTransferFrom(
        address from,
        address to,
        uint256 tokenId,
        bytes memory data
    ) public virtual override {
        require(_isApprovedOrOwner(_msgSender(), tokenId), "ERC721: caller is not token owner or approved");
        _safeTransfer(from, to, tokenId, data);
    }

    /**
     * @dev Safely transfers `tokenId` token from `from` to `to`, checking first that contract recipients
     * are aware of the ERC721 protocol to prevent tokens from being forever locked.
     *
     * `data` is additional data, it has no specified format and it is sent in call to `to`.
     *
     * This internal function is equivalent to {safeTransferFrom}, and can be used to e.g.
     * implement alternative mechanisms to perform token transfer, such as signature-based.
     *
     * Requirements:
     *
     * - `from` cannot be the zero address.
     * - `to` cannot be the zero address.
     * - `tokenId` token must exist and be owned by `from`.
     * - If `to` refers to a smart contract, it must implement {IERC721Receiver-onERC721Received}, which is called upon a safe transfer.
     *
     * Emits a {Transfer} event.
     */
    function _safeTransfer(
        address from,
        address to,
        uint256 tokenId,
        bytes memory data
    ) internal virtual {
        _transfer(from, to, tokenId);
        require(_checkOnERC721Received(from, to, tokenId, data), "ERC721: transfer to non ERC721Receiver implementer");
    }

    /**
     * @dev Returns the owner of the `tokenId`. Does NOT revert if token doesn't exist
     */
    function _ownerOf(uint256 tokenId) internal view virtual returns (address) {
        return _owners[tokenId];
    }

    /**
     * @dev Returns whether `tokenId` exists.
     *
     * Tokens can be managed by their owner or approved accounts via {approve} or {setApprovalForAll}.
     *
     * Tokens start existing when they are minted (`_mint`),
     * and stop existing when they are burned (`_burn`).
     */
    function _exists(uint256 tokenId) internal view virtual returns (bool) {
        return _ownerOf(tokenId) != address(0);
    }

    /**
     * @dev Returns whether `spender` is allowed to manage `tokenId`.
     *
     * Requirements:
     *
     * - `tokenId` must exist.
     */
    function _isApprovedOrOwner(address spender, uint256 tokenId) internal view virtual returns (bool) {
        address owner = ERC721.ownerOf(tokenId);
        return (spender == owner || isApprovedForAll(owner, spender) || getApproved(tokenId) == spender);
    }

    /**
     * @dev Safely mints `tokenId` and transfers it to `to`.
     *
     * Requirements:
     *
     * - `tokenId` must not exist.
     * - If `to` refers to a smart contract, it must implement {IERC721Receiver-onERC721Received}, which is called upon a safe transfer.
     *
     * Emits a {Transfer} event.
     */
    function _safeMint(address to, uint256 tokenId) internal virtual {
        _safeMint(to, tokenId, "");
    }

    /**
     * @dev Same as {xref-ERC721-_safeMint-address-uint256-}[`_safeMint`], with an additional `data` parameter which is
     * forwarded in {IERC721Receiver-onERC721Received} to contract recipients.
     */
    function _safeMint(
        address to,
        uint256 tokenId,
        bytes memory data
    ) internal virtual {
        _mint(to, tokenId);
        require(
            _checkOnERC721Received(address(0), to, tokenId, data),
            "ERC721: transfer to non ERC721Receiver implementer"
        );
    }

    /**
     * @dev Mints `tokenId` and transfers it to `to`.
     *
     * WARNING: Usage of this method is discouraged, use {_safeMint} whenever possible
     *
     * Requirements:
     *
     * - `tokenId` must not exist.
     * - `to` cannot be the zero address.
     *
     * Emits a {Transfer} event.
     */
    function _mint(address to, uint256 tokenId) internal virtual {
        require(to != address(0), "ERC721: mint to the zero address");
        require(!_exists(tokenId), "ERC721: token already minted");

        _beforeTokenTransfer(address(0), to, tokenId, 1);

        // Check that tokenId was not minted by `_beforeTokenTransfer` hook
        require(!_exists(tokenId), "ERC721: token already minted");

        unchecked {
            // Will not overflow unless all 2**256 token ids are minted to the same owner.
            // Given that tokens are minted one by one, it is impossible in practice that
            // this ever happens. Might change if we allow batch minting.
            // The ERC fails to describe this case.
            _balances[to] += 1;
        }

        _owners[tokenId] = to;

        emit Transfer(address(0), to, tokenId);

        _afterTokenTransfer(address(0), to, tokenId, 1);
    }

    /**
     * @dev Destroys `tokenId`.
     * The approval is cleared when the token is burned.
     * This is an internal function that does not check if the sender is authorized to operate on the token.
     *
     * Requirements:
     *
     * - `tokenId` must exist.
     *
     * Emits a {Transfer} event.
     */
    function _burn(uint256 tokenId) internal virtual {
        address owner = ERC721.ownerOf(tokenId);

        _beforeTokenTransfer(owner, address(0), tokenId, 1);

        // Update ownership in case tokenId was transferred by `_beforeTokenTransfer` hook
        owner = ERC721.ownerOf(tokenId);

        // Clear approvals
        delete _tokenApprovals[tokenId];

        unchecked {
            // Cannot overflow, as that would require more tokens to be burned/transferred
            // out than the owner initially received through minting and transferring in.
            _balances[owner] -= 1;
        }
        delete _owners[tokenId];

        emit Transfer(owner, address(0), tokenId);

        _afterTokenTransfer(owner, address(0), tokenId, 1);
    }

    /**
     * @dev Transfers `tokenId` from `from` to `to`.
     *  As opposed to {transferFrom}, this imposes no restrictions on msg.sender.
     *
     * Requirements:
     *
     * - `to` cannot be the zero address.
     * - `tokenId` token must be owned by `from`.
     *
     * Emits a {Transfer} event.
     */
    function _transfer(
        address from,
        address to,
        uint256 tokenId
    ) internal virtual {
        require(ERC721.ownerOf(tokenId) == from, "ERC721: transfer from incorrect owner");
        require(to != address(0), "ERC721: transfer to the zero address");

        _beforeTokenTransfer(from, to, tokenId, 1);

        // Check that tokenId was not transferred by `_beforeTokenTransfer` hook
        require(ERC721.ownerOf(tokenId) == from, "ERC721: transfer from incorrect owner");

        // Clear approvals from the previous owner
        delete _tokenApprovals[tokenId];

        unchecked {
            // `_balances[from]` cannot overflow for the same reason as described in `_burn`:
            // `from`'s balance is the number of token held, which is at least one before the current
            // transfer.
            // `_balances[to]` could overflow in the conditions described in `_mint`. That would require
            // all 2**256 token ids to be minted, which in practice is impossible.
            _balances[from] -= 1;
            _balances[to] += 1;
        }
        _owners[tokenId] = to;

        emit Transfer(from, to, tokenId);

        _afterTokenTransfer(from, to, tokenId, 1);
    }

    /**
     * @dev Approve `to` to operate on `tokenId`
     *
     * Emits an {Approval} event.
     */
    function _approve(address to, uint256 tokenId) internal virtual {
        _tokenApprovals[tokenId] = to;
        emit Approval(ERC721.ownerOf(tokenId), to, tokenId);
    }

    /**
     * @dev Approve `operator` to operate on all of `owner` tokens
     *
     * Emits an {ApprovalForAll} event.
     */
    function _setApprovalForAll(
        address owner,
        address operator,
        bool approved
    ) internal virtual {
        require(owner != operator, "ERC721: approve to caller");
        _operatorApprovals[owner][operator] = approved;
        emit ApprovalForAll(owner, operator, approved);
    }

    /**
     * @dev Reverts if the `tokenId` has not been minted yet.
     */
    function _requireMinted(uint256 tokenId) internal view virtual {
        require(_exists(tokenId), "ERC721: invalid token ID");
    }

    /**
     * @dev Internal function to invoke {IERC721Receiver-onERC721Received} on a target address.
     * The call is not executed if the target address is not a contract.
     *
     * @param from address representing the previous owner of the given token ID
     * @param to target address that will receive the tokens
     * @param tokenId uint256 ID of the token to be transferred
     * @param data bytes optional data to send along with the call
     * @return bool whether the call correctly returned the expected magic value
     */
    function _checkOnERC721Received(
        address from,
        address to,
        uint256 tokenId,
        bytes memory data
    ) private returns (bool) {
        if (to.isContract()) {
            try IERC721Receiver(to).onERC721Received(_msgSender(), from, tokenId, data) returns (bytes4 retval) {
                return retval == IERC721Receiver.onERC721Received.selector;
            } catch (bytes memory reason) {
                if (reason.length == 0) {
                    revert("ERC721: transfer to non ERC721Receiver implementer");
                } else {
                    /// @solidity memory-safe-assembly
                    assembly {
                        revert(add(32, reason), mload(reason))
                    }
                }
            }
        } else {
            return true;
        }
    }

    /**
     * @dev Hook that is called before any token transfer. This includes minting and burning. If {ERC721Consecutive} is
     * used, the hook may be called as part of a consecutive (batch) mint, as indicated by `batchSize` greater than 1.
     *
     * Calling conditions:
     *
     * - When `from` and `to` are both non-zero, ``from``'s tokens will be transferred to `to`.
     * - When `from` is zero, the tokens will be minted for `to`.
     * - When `to` is zero, ``from``'s tokens will be burned.
     * - `from` and `to` are never both zero.
     * - `batchSize` is non-zero.
     *
     * To learn more about hooks, head to xref:ROOT:extending-contracts.adoc#using-hooks[Using Hooks].
     */
    function _beforeTokenTransfer(
        address from,
        address to,
        uint256, /* firstTokenId */
        uint256 batchSize
    ) internal virtual {
        if (batchSize > 1) {
            if (from != address(0)) {
                _balances[from] -= batchSize;
            }
            if (to != address(0)) {
                _balances[to] += batchSize;
            }
        }
    }

    /**
     * @dev Hook that is called after any token transfer. This includes minting and burning. If {ERC721Consecutive} is
     * used, the hook may be called as part of a consecutive (batch) mint, as indicated by `batchSize` greater than 1.
     *
     * Calling conditions:
     *
     * - When `from` and `to` are both non-zero, ``from``'s tokens were transferred to `to`.
     * - When `from` is zero, the tokens were minted for `to`.
     * - When `to` is zero, ``from``'s tokens were burned.
     * - `from` and `to` are never both zero.
     * - `batchSize` is non-zero.
     *
     * To learn more about hooks, head to xref:ROOT:extending-contracts.adoc#using-hooks[Using Hooks].
     */
    function _afterTokenTransfer(
        address from,
        address to,
        uint256 firstTokenId,
        uint256 batchSize
    ) internal virtual {}
}

// File: @openzeppelin/contracts/token/ERC721/extensions/IERC721Metadata.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (token/ERC721/extensions/IERC721Metadata.sol)

pragma solidity ^0.8.0;

import "../IERC721.sol";

/**
 * @title ERC-721 Non-Fungible Token Standard, optional metadata extension
 * @dev See https://eips.ethereum.org/EIPS/eip-721
 */
interface IERC721Metadata is IERC721 {
    /**
     * @dev Returns the token collection name.
     */
    function name() external view returns (string memory);

    /**
     * @dev Returns the token collection symbol.
     */
    function symbol() external view returns (string memory);

    /**
     * @dev Returns the Uniform Resource Identifier (URI) for `tokenId` token.
     */
    function tokenURI(uint256 tokenId) external view returns (string memory);
}

// File: @openzeppelin/contracts/token/ERC721/IERC721.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.8.0) (token/ERC721/IERC721.sol)

pragma solidity ^0.8.0;

import "../../utils/introspection/IERC165.sol";

/**
 * @dev Required interface of an ERC721 compliant contract.
 */
interface IERC721 is IERC165 {
    /**
     * @dev Emitted when `tokenId` token is transferred from `from` to `to`.
     */
    event Transfer(address indexed from, address indexed to, uint256 indexed tokenId);

    /**
     * @dev Emitted when `owner` enables `approved` to manage the `tokenId` token.
     */
    event Approval(address indexed owner, address indexed approved, uint256 indexed tokenId);

    /**
     * @dev Emitted when `owner` enables or disables (`approved`) `operator` to manage all of its assets.
     */
    event ApprovalForAll(address indexed owner, address indexed operator, bool approved);

    /**
     * @dev Returns the number of tokens in ``owner``'s account.
     */
    function balanceOf(address owner) external view returns (uint256 balance);

    /**
     * @dev Returns the owner of the `tokenId` token.
     *
     * Requirements:
     *
     * - `tokenId` must exist.
     */
    function ownerOf(uint256 tokenId) external view returns (address owner);

    /**
     * @dev Safely transfers `tokenId` token from `from` to `to`.
     *
     * Requirements:
     *
     * - `from` cannot be the zero address.
     * - `to` cannot be the zero address.
     * - `tokenId` token must exist and be owned by `from`.
     * - If the caller is not `from`, it must be approved to move this token by either {approve} or {setApprovalForAll}.
     * - If `to` refers to a smart contract, it must implement {IERC721Receiver-onERC721Received}, which is called upon a safe transfer.
     *
     * Emits a {Transfer} event.
     */
    function safeTransferFrom(
        address from,
        address to,
        uint256 tokenId,
        bytes calldata data
    ) external;

    /**
     * @dev Safely transfers `tokenId` token from `from` to `to`, checking first that contract recipients
     * are aware of the ERC721 protocol to prevent tokens from being forever locked.
     *
     * Requirements:
     *
     * - `from` cannot be the zero address.
     * - `to` cannot be the zero address.
     * - `tokenId` token must exist and be owned by `from`.
     * - If the caller is not `from`, it must have been allowed to move this token by either {approve} or {setApprovalForAll}.
     * - If `to` refers to a smart contract, it must implement {IERC721Receiver-onERC721Received}, which is called upon a safe transfer.
     *
     * Emits a {Transfer} event.
     */
    function safeTransferFrom(
        address from,
        address to,
        uint256 tokenId
    ) external;

    /**
     * @dev Transfers `tokenId` token from `from` to `to`.
     *
     * WARNING: Note that the caller is responsible to confirm that the recipient is capable of receiving ERC721
     * or else they may be permanently lost. Usage of {safeTransferFrom} prevents loss, though the caller must
     * understand this adds an external call which potentially creates a reentrancy vulnerability.
     *
     * Requirements:
     *
     * - `from` cannot be the zero address.
     * - `to` cannot be the zero address.
     * - `tokenId` token must be owned by `from`.
     * - If the caller is not `from`, it must be approved to move this token by either {approve} or {setApprovalForAll}.
     *
     * Emits a {Transfer} event.
     */
    function transferFrom(
        address from,
        address to,
        uint256 tokenId
    ) external;

    /**
     * @dev Gives permission to `to` to transfer `tokenId` token to another account.
     * The approval is cleared when the token is transferred.
     *
     * Only a single account can be approved at a time, so approving the zero address clears previous approvals.
     *
     * Requirements:
     *
     * - The caller must own the token or be an approved operator.
     * - `tokenId` must exist.
     *
     * Emits an {Approval} event.
     */
    function approve(address to, uint256 tokenId) external;

    /**
     * @dev Approve or remove `operator` as an operator for the caller.
     * Operators can call {transferFrom} or {safeTransferFrom} for any token owned by the caller.
     *
     * Requirements:
     *
     * - The `operator` cannot be the caller.
     *
     * Emits an {ApprovalForAll} event.
     */
    function setApprovalForAll(address operator, bool _approved) external;

    /**
     * @dev Returns the account approved for `tokenId` token.
     *
     * Requirements:
     *
     * - `tokenId` must exist.
     */
    function getApproved(uint256 tokenId) external view returns (address operator);

    /**
     * @dev Returns if the `operator` is allowed to manage all of the assets of `owner`.
     *
     * See {setApprovalForAll}
     */
    function isApprovedForAll(address owner, address operator) external view returns (bool);
}

// File: @openzeppelin/contracts/token/ERC721/IERC721Receiver.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.6.0) (token/ERC721/IERC721Receiver.sol)

pragma solidity ^0.8.0;

/**
 * @title ERC721 token receiver interface
 * @dev Interface for any contract that wants to support safeTransfers
 * from ERC721 asset contracts.
 */
interface IERC721Receiver {
    /**
     * @dev Whenever an {IERC721} `tokenId` token is transferred to this contract via {IERC721-safeTransferFrom}
     * by `operator` from `from`, this function is called.
     *
     * It must return its Solidity selector to confirm the token transfer.
     * If any other value is returned or the interface is not implemented by the recipient, the transfer will be reverted.
     *
     * The selector can be obtained in Solidity with `IERC721Receiver.onERC721Received.selector`.
     */
    function onERC721Received(
        address operator,
        address from,
        uint256 tokenId,
        bytes calldata data
    ) external returns (bytes4);
}

// File: @openzeppelin/contracts/utils/Address.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.8.0) (utils/Address.sol)

pragma solidity ^0.8.1;

/**
 * @dev Collection of functions related to the address type
 */
library Address {
    /**
     * @dev Returns true if `account` is a contract.
     *
     * [IMPORTANT]
     * ====
     * It is unsafe to assume that an address for which this function returns
     * false is an externally-owned account (EOA) and not a contract.
     *
     * Among others, `isContract` will return false for the following
     * types of addresses:
     *
     *  - an externally-owned account
     *  - a contract in construction
     *  - an address where a contract will be created
     *  - an address where a contract lived, but was destroyed
     * ====
     *
     * [IMPORTANT]
     * ====
     * You shouldn't rely on `isContract` to protect against flash loan attacks!
     *
     * Preventing calls from contracts is highly discouraged. It breaks composability, breaks support for smart wallets
     * like Gnosis Safe, and does not provide security since it can be circumvented by calling from a contract
     * constructor.
     * ====
     */
    function isContract(address account) internal view returns (bool) {
        // This method relies on extcodesize/address.code.length, which returns 0
        // for contracts in construction, since the code is only stored at the end
        // of the constructor execution.

        return account.code.length > 0;
    }

    /**
     * @dev Replacement for Solidity's `transfer`: sends `amount` wei to
     * `recipient`, forwarding all available gas and reverting on errors.
     *
     * https://eips.ethereum.org/EIPS/eip-1884[EIP1884] increases the gas cost
     * of certain opcodes, possibly making contracts go over the 2300 gas limit
     * imposed by `transfer`, making them unable to receive funds via
     * `transfer`. {sendValue} removes this limitation.
     *
     * https://diligence.consensys.net/posts/2019/09/stop-using-soliditys-transfer-now/[Learn more].
     *
     * IMPORTANT: because control is transferred to `recipient`, care must be
     * taken to not create reentrancy vulnerabilities. Consider using
     * {ReentrancyGuard} or the
     * https://solidity.readthedocs.io/en/v0.5.11/security-considerations.html#use-the-checks-effects-interactions-pattern[checks-effects-interactions pattern].
     */
    function sendValue(address payable recipient, uint256 amount) internal {
        require(address(this).balance >= amount, "Address: insufficient balance");

        (bool success, ) = recipient.call{value: amount}("");
        require(success, "Address: unable to send value, recipient may have reverted");
    }

    /**
     * @dev Performs a Solidity function call using a low level `call`. A
     * plain `call` is an unsafe replacement for a function call: use this
     * function instead.
     *
     * If `target` reverts with a revert reason, it is bubbled up by this
     * function (like regular Solidity function calls).
     *
     * Returns the raw returned data. To convert to the expected return value,
     * use https://solidity.readthedocs.io/en/latest/units-and-global-variables.html?highlight=abi.decode#abi-encoding-and-decoding-functions[`abi.decode`].
     *
     * Requirements:
     *
     * - `target` must be a contract.
     * - calling `target` with `data` must not revert.
     *
     * _Available since v3.1._
     */
    function functionCall(address target, bytes memory data) internal returns (bytes memory) {
        return functionCallWithValue(target, data, 0, "Address: low-level call failed");
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`], but with
     * `errorMessage` as a fallback revert reason when `target` reverts.
     *
     * _Available since v3.1._
     */
    function functionCall(
        address target,
        bytes memory data,
        string memory errorMessage
    ) internal returns (bytes memory) {
        return functionCallWithValue(target, data, 0, errorMessage);
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`],
     * but also transferring `value` wei to `target`.
     *
     * Requirements:
     *
     * - the calling contract must have an ETH balance of at least `value`.
     * - the called Solidity function must be `payable`.
     *
     * _Available since v3.1._
     */
    function functionCallWithValue(
        address target,
        bytes memory data,
        uint256 value
    ) internal returns (bytes memory) {
        return functionCallWithValue(target, data, value, "Address: low-level call with value failed");
    }

    /**
     * @dev Same as {xref-Address-functionCallWithValue-address-bytes-uint256-}[`functionCallWithValue`], but
     * with `errorMessage` as a fallback revert reason when `target` reverts.
     *
     * _Available since v3.1._
     */
    function functionCallWithValue(
        address target,
        bytes memory data,
        uint256 value,
        string memory errorMessage
    ) internal returns (bytes memory) {
        require(address(this).balance >= value, "Address: insufficient balance for call");
        (bool success, bytes memory returndata) = target.call{value: value}(data);
        return verifyCallResultFromTarget(target, success, returndata, errorMessage);
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`],
     * but performing a static call.
     *
     * _Available since v3.3._
     */
    function functionStaticCall(address target, bytes memory data) internal view returns (bytes memory) {
        return functionStaticCall(target, data, "Address: low-level static call failed");
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-string-}[`functionCall`],
     * but performing a static call.
     *
     * _Available since v3.3._
     */
    function functionStaticCall(
        address target,
        bytes memory data,
        string memory errorMessage
    ) internal view returns (bytes memory) {
        (bool success, bytes memory returndata) = target.staticcall(data);
        return verifyCallResultFromTarget(target, success, returndata, errorMessage);
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`],
     * but performing a delegate call.
     *
     * _Available since v3.4._
     */
    function functionDelegateCall(address target, bytes memory data) internal returns (bytes memory) {
        return functionDelegateCall(target, data, "Address: low-level delegate call failed");
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-string-}[`functionCall`],
     * but performing a delegate call.
     *
     * _Available since v3.4._
     */
    function functionDelegateCall(
        address target,
        bytes memory data,
        string memory errorMessage
    ) internal returns (bytes memory) {
        (bool success, bytes memory returndata) = target.delegatecall(data);
        return verifyCallResultFromTarget(target, success, returndata, errorMessage);
    }

    /**
     * @dev Tool to verify that a low level call to smart-contract was successful, and revert (either by bubbling
     * the revert reason or using the provided one) in case of unsuccessful call or if target was not a contract.
     *
     * _Available since v4.8._
     */
    function verifyCallResultFromTarget(
        address target,
        bool success,
        bytes memory returndata,
        string memory errorMessage
    ) internal view returns (bytes memory) {
        if (success) {
            if (returndata.length == 0) {
                // only check isContract if the call was successful and the return data is empty
                // otherwise we already know that it was a contract
                require(isContract(target), "Address: call to non-contract");
            }
            return returndata;
        } else {
            _revert(returndata, errorMessage);
        }
    }

    /**
     * @dev Tool to verify that a low level call was successful, and revert if it wasn't, either by bubbling the
     * revert reason or using the provided one.
     *
     * _Available since v4.3._
     */
    function verifyCallResult(
        bool success,
        bytes memory returndata,
        string memory errorMessage
    ) internal pure returns (bytes memory) {
        if (success) {
            return returndata;
        } else {
            _revert(returndata, errorMessage);
        }
    }

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

// File: @openzeppelin/contracts/utils/Checkpoints.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.8.1) (utils/Checkpoints.sol)
// This file was procedurally generated from scripts/generate/templates/Checkpoints.js.

pragma solidity ^0.8.0;

import "./math/Math.sol";
import "./math/SafeCast.sol";

/**
 * @dev This library defines the `History` struct, for checkpointing values as they change at different points in
 * time, and later looking up past values by block number. See {Votes} as an example.
 *
 * To create a history of checkpoints define a variable type `Checkpoints.History` in your contract, and store a new
 * checkpoint for the current transaction block using the {push} function.
 *
 * _Available since v4.5._
 */
library Checkpoints {
    struct History {
        Checkpoint[] _checkpoints;
    }

    struct Checkpoint {
        uint32 _blockNumber;
        uint224 _value;
    }

    /**
     * @dev Returns the value at a given block number. If a checkpoint is not available at that block, the closest one
     * before it is returned, or zero otherwise. Because the number returned corresponds to that at the end of the
     * block, the requested block number must be in the past, excluding the current block.
     */
    function getAtBlock(History storage self, uint256 blockNumber) internal view returns (uint256) {
        require(blockNumber < block.number, "Checkpoints: block not yet mined");
        uint32 key = SafeCast.toUint32(blockNumber);

        uint256 len = self._checkpoints.length;
        uint256 pos = _upperBinaryLookup(self._checkpoints, key, 0, len);
        return pos == 0 ? 0 : _unsafeAccess(self._checkpoints, pos - 1)._value;
    }

    /**
     * @dev Returns the value at a given block number. If a checkpoint is not available at that block, the closest one
     * before it is returned, or zero otherwise. Similar to {upperLookup} but optimized for the case when the searched
     * checkpoint is probably "recent", defined as being among the last sqrt(N) checkpoints where N is the number of
     * checkpoints.
     */
    function getAtProbablyRecentBlock(History storage self, uint256 blockNumber) internal view returns (uint256) {
        require(blockNumber < block.number, "Checkpoints: block not yet mined");
        uint32 key = SafeCast.toUint32(blockNumber);

        uint256 len = self._checkpoints.length;

        uint256 low = 0;
        uint256 high = len;

        if (len > 5) {
            uint256 mid = len - Math.sqrt(len);
            if (key < _unsafeAccess(self._checkpoints, mid)._blockNumber) {
                high = mid;
            } else {
                low = mid + 1;
            }
        }

        uint256 pos = _upperBinaryLookup(self._checkpoints, key, low, high);

        return pos == 0 ? 0 : _unsafeAccess(self._checkpoints, pos - 1)._value;
    }

    /**
     * @dev Pushes a value onto a History so that it is stored as the checkpoint for the current block.
     *
     * Returns previous value and new value.
     */
    function push(History storage self, uint256 value) internal returns (uint256, uint256) {
        return _insert(self._checkpoints, SafeCast.toUint32(block.number), SafeCast.toUint224(value));
    }

    /**
     * @dev Pushes a value onto a History, by updating the latest value using binary operation `op`. The new value will
     * be set to `op(latest, delta)`.
     *
     * Returns previous value and new value.
     */
    function push(
        History storage self,
        function(uint256, uint256) view returns (uint256) op,
        uint256 delta
    ) internal returns (uint256, uint256) {
        return push(self, op(latest(self), delta));
    }

    /**
     * @dev Returns the value in the most recent checkpoint, or zero if there are no checkpoints.
     */
    function latest(History storage self) internal view returns (uint224) {
        uint256 pos = self._checkpoints.length;
        return pos == 0 ? 0 : _unsafeAccess(self._checkpoints, pos - 1)._value;
    }

    /**
     * @dev Returns whether there is a checkpoint in the structure (i.e. it is not empty), and if so the key and value
     * in the most recent checkpoint.
     */
    function latestCheckpoint(History storage self)
        internal
        view
        returns (
            bool exists,
            uint32 _blockNumber,
            uint224 _value
        )
    {
        uint256 pos = self._checkpoints.length;
        if (pos == 0) {
            return (false, 0, 0);
        } else {
            Checkpoint memory ckpt = _unsafeAccess(self._checkpoints, pos - 1);
            return (true, ckpt._blockNumber, ckpt._value);
        }
    }

    /**
     * @dev Returns the number of checkpoint.
     */
    function length(History storage self) internal view returns (uint256) {
        return self._checkpoints.length;
    }

    /**
     * @dev Pushes a (`key`, `value`) pair into an ordered list of checkpoints, either by inserting a new checkpoint,
     * or by updating the last one.
     */
    function _insert(
        Checkpoint[] storage self,
        uint32 key,
        uint224 value
    ) private returns (uint224, uint224) {
        uint256 pos = self.length;

        if (pos > 0) {
            // Copying to memory is important here.
            Checkpoint memory last = _unsafeAccess(self, pos - 1);

            // Checkpoints keys must be increasing.
            require(last._blockNumber <= key, "Checkpoint: invalid key");

            // Update or push new checkpoint
            if (last._blockNumber == key) {
                _unsafeAccess(self, pos - 1)._value = value;
            } else {
                self.push(Checkpoint({_blockNumber: key, _value: value}));
            }
            return (last._value, value);
        } else {
            self.push(Checkpoint({_blockNumber: key, _value: value}));
            return (0, value);
        }
    }

    /**
     * @dev Return the index of the oldest checkpoint whose key is greater than the search key, or `high` if there is none.
     * `low` and `high` define a section where to do the search, with inclusive `low` and exclusive `high`.
     *
     * WARNING: `high` should not be greater than the array's length.
     */
    function _upperBinaryLookup(
        Checkpoint[] storage self,
        uint32 key,
        uint256 low,
        uint256 high
    ) private view returns (uint256) {
        while (low < high) {
            uint256 mid = Math.average(low, high);
            if (_unsafeAccess(self, mid)._blockNumber > key) {
                high = mid;
            } else {
                low = mid + 1;
            }
        }
        return high;
    }

    /**
     * @dev Return the index of the oldest checkpoint whose key is greater or equal than the search key, or `high` if there is none.
     * `low` and `high` define a section where to do the search, with inclusive `low` and exclusive `high`.
     *
     * WARNING: `high` should not be greater than the array's length.
     */
    function _lowerBinaryLookup(
        Checkpoint[] storage self,
        uint32 key,
        uint256 low,
        uint256 high
    ) private view returns (uint256) {
        while (low < high) {
            uint256 mid = Math.average(low, high);
            if (_unsafeAccess(self, mid)._blockNumber < key) {
                low = mid + 1;
            } else {
                high = mid;
            }
        }
        return high;
    }

    /**
     * @dev Access an element of the array without performing bounds check. The position is assumed to be within bounds.
     */
    function _unsafeAccess(Checkpoint[] storage self, uint256 pos) private pure returns (Checkpoint storage result) {
        assembly {
            mstore(0, self.slot)
            result.slot := add(keccak256(0, 0x20), pos)
        }
    }

    struct Trace224 {
        Checkpoint224[] _checkpoints;
    }

    struct Checkpoint224 {
        uint32 _key;
        uint224 _value;
    }

    /**
     * @dev Pushes a (`key`, `value`) pair into a Trace224 so that it is stored as the checkpoint.
     *
     * Returns previous value and new value.
     */
    function push(
        Trace224 storage self,
        uint32 key,
        uint224 value
    ) internal returns (uint224, uint224) {
        return _insert(self._checkpoints, key, value);
    }

    /**
     * @dev Returns the value in the oldest checkpoint with key greater or equal than the search key, or zero if there is none.
     */
    function lowerLookup(Trace224 storage self, uint32 key) internal view returns (uint224) {
        uint256 len = self._checkpoints.length;
        uint256 pos = _lowerBinaryLookup(self._checkpoints, key, 0, len);
        return pos == len ? 0 : _unsafeAccess(self._checkpoints, pos)._value;
    }

    /**
     * @dev Returns the value in the most recent checkpoint with key lower or equal than the search key.
     */
    function upperLookup(Trace224 storage self, uint32 key) internal view returns (uint224) {
        uint256 len = self._checkpoints.length;
        uint256 pos = _upperBinaryLookup(self._checkpoints, key, 0, len);
        return pos == 0 ? 0 : _unsafeAccess(self._checkpoints, pos - 1)._value;
    }

    /**
     * @dev Returns the value in the most recent checkpoint, or zero if there are no checkpoints.
     */
    function latest(Trace224 storage self) internal view returns (uint224) {
        uint256 pos = self._checkpoints.length;
        return pos == 0 ? 0 : _unsafeAccess(self._checkpoints, pos - 1)._value;
    }

    /**
     * @dev Returns whether there is a checkpoint in the structure (i.e. it is not empty), and if so the key and value
     * in the most recent checkpoint.
     */
    function latestCheckpoint(Trace224 storage self)
        internal
        view
        returns (
            bool exists,
            uint32 _key,
            uint224 _value
        )
    {
        uint256 pos = self._checkpoints.length;
        if (pos == 0) {
            return (false, 0, 0);
        } else {
            Checkpoint224 memory ckpt = _unsafeAccess(self._checkpoints, pos - 1);
            return (true, ckpt._key, ckpt._value);
        }
    }

    /**
     * @dev Returns the number of checkpoint.
     */
    function length(Trace224 storage self) internal view returns (uint256) {
        return self._checkpoints.length;
    }

    /**
     * @dev Pushes a (`key`, `value`) pair into an ordered list of checkpoints, either by inserting a new checkpoint,
     * or by updating the last one.
     */
    function _insert(
        Checkpoint224[] storage self,
        uint32 key,
        uint224 value
    ) private returns (uint224, uint224) {
        uint256 pos = self.length;

        if (pos > 0) {
            // Copying to memory is important here.
            Checkpoint224 memory last = _unsafeAccess(self, pos - 1);

            // Checkpoints keys must be increasing.
            require(last._key <= key, "Checkpoint: invalid key");

            // Update or push new checkpoint
            if (last._key == key) {
                _unsafeAccess(self, pos - 1)._value = value;
            } else {
                self.push(Checkpoint224({_key: key, _value: value}));
            }
            return (last._value, value);
        } else {
            self.push(Checkpoint224({_key: key, _value: value}));
            return (0, value);
        }
    }

    /**
     * @dev Return the index of the oldest checkpoint whose key is greater than the search key, or `high` if there is none.
     * `low` and `high` define a section where to do the search, with inclusive `low` and exclusive `high`.
     *
     * WARNING: `high` should not be greater than the array's length.
     */
    function _upperBinaryLookup(
        Checkpoint224[] storage self,
        uint32 key,
        uint256 low,
        uint256 high
    ) private view returns (uint256) {
        while (low < high) {
            uint256 mid = Math.average(low, high);
            if (_unsafeAccess(self, mid)._key > key) {
                high = mid;
            } else {
                low = mid + 1;
            }
        }
        return high;
    }

    /**
     * @dev Return the index of the oldest checkpoint whose key is greater or equal than the search key, or `high` if there is none.
     * `low` and `high` define a section where to do the search, with inclusive `low` and exclusive `high`.
     *
     * WARNING: `high` should not be greater than the array's length.
     */
    function _lowerBinaryLookup(
        Checkpoint224[] storage self,
        uint32 key,
        uint256 low,
        uint256 high
    ) private view returns (uint256) {
        while (low < high) {
            uint256 mid = Math.average(low, high);
            if (_unsafeAccess(self, mid)._key < key) {
                low = mid + 1;
            } else {
                high = mid;
            }
        }
        return high;
    }

    /**
     * @dev Access an element of the array without performing bounds check. The position is assumed to be within bounds.
     */
    function _unsafeAccess(Checkpoint224[] storage self, uint256 pos)
        private
        pure
        returns (Checkpoint224 storage result)
    {
        assembly {
            mstore(0, self.slot)
            result.slot := add(keccak256(0, 0x20), pos)
        }
    }

    struct Trace160 {
        Checkpoint160[] _checkpoints;
    }

    struct Checkpoint160 {
        uint96 _key;
        uint160 _value;
    }

    /**
     * @dev Pushes a (`key`, `value`) pair into a Trace160 so that it is stored as the checkpoint.
     *
     * Returns previous value and new value.
     */
    function push(
        Trace160 storage self,
        uint96 key,
        uint160 value
    ) internal returns (uint160, uint160) {
        return _insert(self._checkpoints, key, value);
    }

    /**
     * @dev Returns the value in the oldest checkpoint with key greater or equal than the search key, or zero if there is none.
     */
    function lowerLookup(Trace160 storage self, uint96 key) internal view returns (uint160) {
        uint256 len = self._checkpoints.length;
        uint256 pos = _lowerBinaryLookup(self._checkpoints, key, 0, len);
        return pos == len ? 0 : _unsafeAccess(self._checkpoints, pos)._value;
    }

    /**
     * @dev Returns the value in the most recent checkpoint with key lower or equal than the search key.
     */
    function upperLookup(Trace160 storage self, uint96 key) internal view returns (uint160) {
        uint256 len = self._checkpoints.length;
        uint256 pos = _upperBinaryLookup(self._checkpoints, key, 0, len);
        return pos == 0 ? 0 : _unsafeAccess(self._checkpoints, pos - 1)._value;
    }

    /**
     * @dev Returns the value in the most recent checkpoint, or zero if there are no checkpoints.
     */
    function latest(Trace160 storage self) internal view returns (uint160) {
        uint256 pos = self._checkpoints.length;
        return pos == 0 ? 0 : _unsafeAccess(self._checkpoints, pos - 1)._value;
    }

    /**
     * @dev Returns whether there is a checkpoint in the structure (i.e. it is not empty), and if so the key and value
     * in the most recent checkpoint.
     */
    function latestCheckpoint(Trace160 storage self)
        internal
        view
        returns (
            bool exists,
            uint96 _key,
            uint160 _value
        )
    {
        uint256 pos = self._checkpoints.length;
        if (pos == 0) {
            return (false, 0, 0);
        } else {
            Checkpoint160 memory ckpt = _unsafeAccess(self._checkpoints, pos - 1);
            return (true, ckpt._key, ckpt._value);
        }
    }

    /**
     * @dev Returns the number of checkpoint.
     */
    function length(Trace160 storage self) internal view returns (uint256) {
        return self._checkpoints.length;
    }

    /**
     * @dev Pushes a (`key`, `value`) pair into an ordered list of checkpoints, either by inserting a new checkpoint,
     * or by updating the last one.
     */
    function _insert(
        Checkpoint160[] storage self,
        uint96 key,
        uint160 value
    ) private returns (uint160, uint160) {
        uint256 pos = self.length;

        if (pos > 0) {
            // Copying to memory is important here.
            Checkpoint160 memory last = _unsafeAccess(self, pos - 1);

            // Checkpoints keys must be increasing.
            require(last._key <= key, "Checkpoint: invalid key");

            // Update or push new checkpoint
            if (last._key == key) {
                _unsafeAccess(self, pos - 1)._value = value;
            } else {
                self.push(Checkpoint160({_key: key, _value: value}));
            }
            return (last._value, value);
        } else {
            self.push(Checkpoint160({_key: key, _value: value}));
            return (0, value);
        }
    }

    /**
     * @dev Return the index of the oldest checkpoint whose key is greater than the search key, or `high` if there is none.
     * `low` and `high` define a section where to do the search, with inclusive `low` and exclusive `high`.
     *
     * WARNING: `high` should not be greater than the array's length.
     */
    function _upperBinaryLookup(
        Checkpoint160[] storage self,
        uint96 key,
        uint256 low,
        uint256 high
    ) private view returns (uint256) {
        while (low < high) {
            uint256 mid = Math.average(low, high);
            if (_unsafeAccess(self, mid)._key > key) {
                high = mid;
            } else {
                low = mid + 1;
            }
        }
        return high;
    }

    /**
     * @dev Return the index of the oldest checkpoint whose key is greater or equal than the search key, or `high` if there is none.
     * `low` and `high` define a section where to do the search, with inclusive `low` and exclusive `high`.
     *
     * WARNING: `high` should not be greater than the array's length.
     */
    function _lowerBinaryLookup(
        Checkpoint160[] storage self,
        uint96 key,
        uint256 low,
        uint256 high
    ) private view returns (uint256) {
        while (low < high) {
            uint256 mid = Math.average(low, high);
            if (_unsafeAccess(self, mid)._key < key) {
                low = mid + 1;
            } else {
                high = mid;
            }
        }
        return high;
    }

    /**
     * @dev Access an element of the array without performing bounds check. The position is assumed to be within bounds.
     */
    function _unsafeAccess(Checkpoint160[] storage self, uint256 pos)
        private
        pure
        returns (Checkpoint160 storage result)
    {
        assembly {
            mstore(0, self.slot)
            result.slot := add(keccak256(0, 0x20), pos)
        }
    }
}

// File: @openzeppelin/contracts/utils/Context.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (utils/Context.sol)

pragma solidity ^0.8.0;

/**
 * @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 Context {
    function _msgSender() internal view virtual returns (address) {
        return msg.sender;
    }

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

// File: @openzeppelin/contracts/utils/cryptography/ECDSA.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.8.0) (utils/cryptography/ECDSA.sol)

pragma solidity ^0.8.0;

import "../Strings.sol";

/**
 * @dev Elliptic Curve Digital Signature Algorithm (ECDSA) operations.
 *
 * These functions can be used to verify that a message was signed by the holder
 * of the private keys of a given address.
 */
library ECDSA {
    enum RecoverError {
        NoError,
        InvalidSignature,
        InvalidSignatureLength,
        InvalidSignatureS,
        InvalidSignatureV // Deprecated in v4.8
    }

    function _throwError(RecoverError error) private pure {
        if (error == RecoverError.NoError) {
            return; // no error: do nothing
        } else if (error == RecoverError.InvalidSignature) {
            revert("ECDSA: invalid signature");
        } else if (error == RecoverError.InvalidSignatureLength) {
            revert("ECDSA: invalid signature length");
        } else if (error == RecoverError.InvalidSignatureS) {
            revert("ECDSA: invalid signature 's' value");
        }
    }

    /**
     * @dev Returns the address that signed a hashed message (`hash`) with
     * `signature` or error string. This address can then be used for verification purposes.
     *
     * The `ecrecover` EVM opcode allows for malleable (non-unique) signatures:
     * this function rejects them by requiring the `s` value to be in the lower
     * half order, and the `v` value to be either 27 or 28.
     *
     * IMPORTANT: `hash` _must_ be the result of a hash operation for the
     * verification to be secure: it is possible to craft signatures that
     * recover to arbitrary addresses for non-hashed data. A safe way to ensure
     * this is by receiving a hash of the original message (which may otherwise
     * be too long), and then calling {toEthSignedMessageHash} on it.
     *
     * Documentation for signature generation:
     * - with https://web3js.readthedocs.io/en/v1.3.4/web3-eth-accounts.html#sign[Web3.js]
     * - with https://docs.ethers.io/v5/api/signer/#Signer-signMessage[ethers]
     *
     * _Available since v4.3._
     */
    function tryRecover(bytes32 hash, bytes memory signature) internal pure returns (address, RecoverError) {
        if (signature.length == 65) {
            bytes32 r;
            bytes32 s;
            uint8 v;
            // ecrecover takes the signature parameters, and the only way to get them
            // currently is to use assembly.
            /// @solidity memory-safe-assembly
            assembly {
                r := mload(add(signature, 0x20))
                s := mload(add(signature, 0x40))
                v := byte(0, mload(add(signature, 0x60)))
            }
            return tryRecover(hash, v, r, s);
        } else {
            return (address(0), RecoverError.InvalidSignatureLength);
        }
    }

    /**
     * @dev Returns the address that signed a hashed message (`hash`) with
     * `signature`. This address can then be used for verification purposes.
     *
     * The `ecrecover` EVM opcode allows for malleable (non-unique) signatures:
     * this function rejects them by requiring the `s` value to be in the lower
     * half order, and the `v` value to be either 27 or 28.
     *
     * IMPORTANT: `hash` _must_ be the result of a hash operation for the
     * verification to be secure: it is possible to craft signatures that
     * recover to arbitrary addresses for non-hashed data. A safe way to ensure
     * this is by receiving a hash of the original message (which may otherwise
     * be too long), and then calling {toEthSignedMessageHash} on it.
     */
    function recover(bytes32 hash, bytes memory signature) internal pure returns (address) {
        (address recovered, RecoverError error) = tryRecover(hash, signature);
        _throwError(error);
        return recovered;
    }

    /**
     * @dev Overload of {ECDSA-tryRecover} that receives the `r` and `vs` short-signature fields separately.
     *
     * See https://eips.ethereum.org/EIPS/eip-2098[EIP-2098 short signatures]
     *
     * _Available since v4.3._
     */
    function tryRecover(
        bytes32 hash,
        bytes32 r,
        bytes32 vs
    ) internal pure returns (address, RecoverError) {
        bytes32 s = vs & bytes32(0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff);
        uint8 v = uint8((uint256(vs) >> 255) + 27);
        return tryRecover(hash, v, r, s);
    }

    /**
     * @dev Overload of {ECDSA-recover} that receives the `r and `vs` short-signature fields separately.
     *
     * _Available since v4.2._
     */
    function recover(
        bytes32 hash,
        bytes32 r,
        bytes32 vs
    ) internal pure returns (address) {
        (address recovered, RecoverError error) = tryRecover(hash, r, vs);
        _throwError(error);
        return recovered;
    }

    /**
     * @dev Overload of {ECDSA-tryRecover} that receives the `v`,
     * `r` and `s` signature fields separately.
     *
     * _Available since v4.3._
     */
    function tryRecover(
        bytes32 hash,
        uint8 v,
        bytes32 r,
        bytes32 s
    ) internal pure returns (address, RecoverError) {
        // EIP-2 still allows signature malleability for ecrecover(). Remove this possibility and make the signature
        // unique. Appendix F in the Ethereum Yellow paper (https://ethereum.github.io/yellowpaper/paper.pdf), defines
        // the valid range for s in (301): 0 < s < secp256k1n ÷ 2 + 1, and for v in (302): v ∈ {27, 28}. Most
        // signatures from current libraries generate a unique signature with an s-value in the lower half order.
        //
        // If your library generates malleable signatures, such as s-values in the upper range, calculate a new s-value
        // with 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141 - s1 and flip v from 27 to 28 or
        // vice versa. If your library also generates signatures with 0/1 for v instead 27/28, add 27 to v to accept
        // these malleable signatures as well.
        if (uint256(s) > 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF5D576E7357A4501DDFE92F46681B20A0) {
            return (address(0), RecoverError.InvalidSignatureS);
        }

        // If the signature is valid (and not malleable), return the signer address
        address signer = ecrecover(hash, v, r, s);
        if (signer == address(0)) {
            return (address(0), RecoverError.InvalidSignature);
        }

        return (signer, RecoverError.NoError);
    }

    /**
     * @dev Overload of {ECDSA-recover} that receives the `v`,
     * `r` and `s` signature fields separately.
     */
    function recover(
        bytes32 hash,
        uint8 v,
        bytes32 r,
        bytes32 s
    ) internal pure returns (address) {
        (address recovered, RecoverError error) = tryRecover(hash, v, r, s);
        _throwError(error);
        return recovered;
    }

    /**
     * @dev Returns an Ethereum Signed Message, created from a `hash`. This
     * produces hash corresponding to the one signed with the
     * https://eth.wiki/json-rpc/API#eth_sign[`eth_sign`]
     * JSON-RPC method as part of EIP-191.
     *
     * See {recover}.
     */
    function toEthSignedMessageHash(bytes32 hash) internal pure returns (bytes32) {
        // 32 is the length in bytes of hash,
        // enforced by the type signature above
        return keccak256(abi.encodePacked("\x19Ethereum Signed Message:\n32", hash));
    }

    /**
     * @dev Returns an Ethereum Signed Message, created from `s`. This
     * produces hash corresponding to the one signed with the
     * https://eth.wiki/json-rpc/API#eth_sign[`eth_sign`]
     * JSON-RPC method as part of EIP-191.
     *
     * See {recover}.
     */
    function toEthSignedMessageHash(bytes memory s) internal pure returns (bytes32) {
        return keccak256(abi.encodePacked("\x19Ethereum Signed Message:\n", Strings.toString(s.length), s));
    }

    /**
     * @dev Returns an Ethereum Signed Typed Data, created from a
     * `domainSeparator` and a `structHash`. This produces hash corresponding
     * to the one signed with the
     * https://eips.ethereum.org/EIPS/eip-712[`eth_signTypedData`]
     * JSON-RPC method as part of EIP-712.
     *
     * See {recover}.
     */
    function toTypedDataHash(bytes32 domainSeparator, bytes32 structHash) internal pure returns (bytes32) {
        return keccak256(abi.encodePacked("\x19\x01", domainSeparator, structHash));
    }
}

// File: @openzeppelin/contracts/utils/cryptography/EIP712.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.8.0) (utils/cryptography/EIP712.sol)

pragma solidity ^0.8.0;

import "./ECDSA.sol";

/**
 * @dev https://eips.ethereum.org/EIPS/eip-712[EIP 712] is a standard for hashing and signing of typed structured data.
 *
 * The encoding specified in the EIP is very generic, and such a generic implementation in Solidity is not feasible,
 * thus this contract does not implement the encoding itself. Protocols need to implement the type-specific encoding
 * they need in their contracts using a combination of `abi.encode` and `keccak256`.
 *
 * This contract implements the EIP 712 domain separator ({_domainSeparatorV4}) that is used as part of the encoding
 * scheme, and the final step of the encoding to obtain the message digest that is then signed via ECDSA
 * ({_hashTypedDataV4}).
 *
 * The implementation of the domain separator was designed to be as efficient as possible while still properly updating
 * the chain id to protect against replay attacks on an eventual fork of the chain.
 *
 * NOTE: This contract implements the version of the encoding known as "v4", as implemented by the JSON RPC method
 * https://docs.metamask.io/guide/signing-data.html[`eth_signTypedDataV4` in MetaMask].
 *
 * _Available since v3.4._
 */
abstract contract EIP712 {
    /* solhint-disable var-name-mixedcase */
    // Cache the domain separator as an immutable value, but also store the chain id that it corresponds to, in order to
    // invalidate the cached domain separator if the chain id changes.
    bytes32 private immutable _CACHED_DOMAIN_SEPARATOR;
    uint256 private immutable _CACHED_CHAIN_ID;
    address private immutable _CACHED_THIS;

    bytes32 private immutable _HASHED_NAME;
    bytes32 private immutable _HASHED_VERSION;
    bytes32 private immutable _TYPE_HASH;

    /* solhint-enable var-name-mixedcase */

    /**
     * @dev Initializes the domain separator and parameter caches.
     *
     * The meaning of `name` and `version` is specified in
     * https://eips.ethereum.org/EIPS/eip-712#definition-of-domainseparator[EIP 712]:
     *
     * - `name`: the user readable name of the signing domain, i.e. the name of the DApp or the protocol.
     * - `version`: the current major version of the signing domain.
     *
     * NOTE: These parameters cannot be changed except through a xref:learn::upgrading-smart-contracts.adoc[smart
     * contract upgrade].
     */
    constructor(string memory name, string memory version) {
        bytes32 hashedName = keccak256(bytes(name));
        bytes32 hashedVersion = keccak256(bytes(version));
        bytes32 typeHash = keccak256(
            "EIP712Domain(string name,string version,uint256 chainId,address verifyingContract)"
        );
        _HASHED_NAME = hashedName;
        _HASHED_VERSION = hashedVersion;
        _CACHED_CHAIN_ID = block.chainid;
        _CACHED_DOMAIN_SEPARATOR = _buildDomainSeparator(typeHash, hashedName, hashedVersion);
        _CACHED_THIS = address(this);
        _TYPE_HASH = typeHash;
    }

    /**
     * @dev Returns the domain separator for the current chain.
     */
    function _domainSeparatorV4() internal view returns (bytes32) {
        if (address(this) == _CACHED_THIS && block.chainid == _CACHED_CHAIN_ID) {
            return _CACHED_DOMAIN_SEPARATOR;
        } else {
            return _buildDomainSeparator(_TYPE_HASH, _HASHED_NAME, _HASHED_VERSION);
        }
    }

    function _buildDomainSeparator(
        bytes32 typeHash,
        bytes32 nameHash,
        bytes32 versionHash
    ) private view returns (bytes32) {
        return keccak256(abi.encode(typeHash, nameHash, versionHash, block.chainid, address(this)));
    }

    /**
     * @dev Given an already https://eips.ethereum.org/EIPS/eip-712#definition-of-hashstruct[hashed struct], this
     * function returns the hash of the fully encoded EIP712 message for this domain.
     *
     * This hash can be used together with {ECDSA-recover} to obtain the signer of a message. For example:
     *
     * ```solidity
     * bytes32 digest = _hashTypedDataV4(keccak256(abi.encode(
     *     keccak256("Mail(address to,string contents)"),
     *     mailTo,
     *     keccak256(bytes(mailContents))
     * )));
     * address signer = ECDSA.recover(digest, signature);
     * ```
     */
    function _hashTypedDataV4(bytes32 structHash) internal view virtual returns (bytes32) {
        return ECDSA.toTypedDataHash(_domainSeparatorV4(), structHash);
    }
}

// File: @openzeppelin/contracts/utils/introspection/ERC165.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (utils/introspection/ERC165.sol)

pragma solidity ^0.8.0;

import "./IERC165.sol";

/**
 * @dev Implementation of the {IERC165} interface.
 *
 * Contracts that want to implement ERC165 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);
 * }
 * ```
 *
 * Alternatively, {ERC165Storage} provides an easier to use but more expensive implementation.
 */
abstract contract ERC165 is IERC165 {
    /**
     * @dev See {IERC165-supportsInterface}.
     */
    function supportsInterface(bytes4 interfaceId) public view virtual override returns (bool) {
        return interfaceId == type(IERC165).interfaceId;
    }
}

// File: @openzeppelin/contracts/utils/introspection/IERC165.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (utils/introspection/IERC165.sol)

pragma solidity ^0.8.0;

/**
 * @dev Interface of the ERC165 standard, as defined in the
 * https://eips.ethereum.org/EIPS/eip-165[EIP].
 *
 * 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[EIP 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);
}

// File: @openzeppelin/contracts/utils/math/Math.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.8.0) (utils/math/Math.sol)

pragma solidity ^0.8.0;

/**
 * @dev Standard math utilities missing in the Solidity language.
 */
library Math {
    enum Rounding {
        Down, // Toward negative infinity
        Up, // Toward infinity
        Zero // Toward zero
    }

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

    /**
     * @dev Returns the smallest of two numbers.
     */
    function min(uint256 a, uint256 b) internal pure returns (uint256) {
        return 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 up instead
     * of rounding down.
     */
    function ceilDiv(uint256 a, uint256 b) internal pure returns (uint256) {
        // (a + b - 1) / b can overflow on addition, so we distribute.
        return a == 0 ? 0 : (a - 1) / b + 1;
    }

    /**
     * @notice Calculates floor(x * y / denominator) with full precision. Throws if result overflows a uint256 or denominator == 0
     * @dev 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 2^256 and mod 2^256 - 1, then use
            // use the Chinese Remainder Theorem to reconstruct the 512 bit result. The result is stored in two 256
            // variables such that product = prod1 * 2^256 + prod0.
            uint256 prod0; // Least significant 256 bits of the product
            uint256 prod1; // Most significant 256 bits of the product
            assembly {
                let mm := mulmod(x, y, not(0))
                prod0 := mul(x, y)
                prod1 := sub(sub(mm, prod0), lt(mm, prod0))
            }

            // Handle non-overflow cases, 256 by 256 division.
            if (prod1 == 0) {
                return prod0 / denominator;
            }

            // Make sure the result is less than 2^256. Also prevents denominator == 0.
            require(denominator > prod1);

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

            // Make division exact by subtracting the remainder from [prod1 prod0].
            uint256 remainder;
            assembly {
                // 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.

            // Does not overflow because the denominator cannot be zero at this stage in the function.
            uint256 twos = denominator & (~denominator + 1);
            assembly {
                // Divide denominator by twos.
                denominator := div(denominator, twos)

                // Divide [prod1 prod0] by twos.
                prod0 := div(prod0, twos)

                // Flip twos such that it is 2^256 / 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 2^256. Now that denominator is an odd number, it has an inverse modulo 2^256 such
            // that denominator * inv = 1 mod 2^256. Compute the inverse by starting with a seed that is correct for
            // four bits. That is, denominator * inv = 1 mod 2^4.
            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 2^8
            inverse *= 2 - denominator * inverse; // inverse mod 2^16
            inverse *= 2 - denominator * inverse; // inverse mod 2^32
            inverse *= 2 - denominator * inverse; // inverse mod 2^64
            inverse *= 2 - denominator * inverse; // inverse mod 2^128
            inverse *= 2 - denominator * inverse; // inverse mod 2^256

            // 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 2^256. Since the preconditions guarantee that the outcome is
            // less than 2^256, 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;
        }
    }

    /**
     * @notice 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) {
        uint256 result = mulDiv(x, y, denominator);
        if (rounding == Rounding.Up && mulmod(x, y, denominator) > 0) {
            result += 1;
        }
        return result;
    }

    /**
     * @dev Returns the square root of a number. If the number is not a perfect square, the value is rounded down.
     *
     * Inspired by Henry S. Warren, Jr.'s "Hacker's Delight" (Chapter 11).
     */
    function sqrt(uint256 a) internal pure returns (uint256) {
        if (a == 0) {
            return 0;
        }

        // For our first guess, we get the biggest power of 2 which is smaller than the square root of the target.
        //
        // We know that the "msb" (most significant bit) of our target number `a` is a power of 2 such that we have
        // `msb(a) <= a < 2*msb(a)`. This value can be written `msb(a)=2**k` with `k=log2(a)`.
        //
        // This can be rewritten `2**log2(a) <= a < 2**(log2(a) + 1)`
        // → `sqrt(2**k) <= sqrt(a) < sqrt(2**(k+1))`
        // → `2**(k/2) <= sqrt(a) < 2**((k+1)/2) <= 2**(k/2 + 1)`
        //
        // Consequently, `2**(log2(a) / 2)` is a good first approximation of `sqrt(a)` with at least 1 correct bit.
        uint256 result = 1 << (log2(a) >> 1);

        // At this point `result` is an estimation with one bit of precision. We know the true value is a uint128,
        // since it is the square root of a uint256. Newton's method converges quadratically (precision doubles at
        // every iteration). We thus need at most 7 iteration to turn our partial result with one bit of precision
        // into the expected uint128 result.
        unchecked {
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            return min(result, a / result);
        }
    }

    /**
     * @notice 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 + (rounding == Rounding.Up && result * result < a ? 1 : 0);
        }
    }

    /**
     * @dev Return the log in base 2, rounded down, of a positive value.
     * Returns 0 if given 0.
     */
    function log2(uint256 value) internal pure returns (uint256) {
        uint256 result = 0;
        unchecked {
            if (value >> 128 > 0) {
                value >>= 128;
                result += 128;
            }
            if (value >> 64 > 0) {
                value >>= 64;
                result += 64;
            }
            if (value >> 32 > 0) {
                value >>= 32;
                result += 32;
            }
            if (value >> 16 > 0) {
                value >>= 16;
                result += 16;
            }
            if (value >> 8 > 0) {
                value >>= 8;
                result += 8;
            }
            if (value >> 4 > 0) {
                value >>= 4;
                result += 4;
            }
            if (value >> 2 > 0) {
                value >>= 2;
                result += 2;
            }
            if (value >> 1 > 0) {
                result += 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 + (rounding == Rounding.Up && 1 << result < value ? 1 : 0);
        }
    }

    /**
     * @dev Return the log in base 10, rounded down, of a positive value.
     * 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 + (rounding == Rounding.Up && 10**result < value ? 1 : 0);
        }
    }

    /**
     * @dev Return the log in base 256, rounded down, of a positive value.
     * 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;
        unchecked {
            if (value >> 128 > 0) {
                value >>= 128;
                result += 16;
            }
            if (value >> 64 > 0) {
                value >>= 64;
                result += 8;
            }
            if (value >> 32 > 0) {
                value >>= 32;
                result += 4;
            }
            if (value >> 16 > 0) {
                value >>= 16;
                result += 2;
            }
            if (value >> 8 > 0) {
                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 log256(uint256 value, Rounding rounding) internal pure returns (uint256) {
        unchecked {
            uint256 result = log256(value);
            return result + (rounding == Rounding.Up && 1 << (result * 8) < value ? 1 : 0);
        }
    }
}

// File: @openzeppelin/contracts/utils/math/SafeCast.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.8.0) (utils/math/SafeCast.sol)
// This file was procedurally generated from scripts/generate/templates/SafeCast.js.

pragma solidity ^0.8.0;

/**
 * @dev Wrappers over Solidity's uintXX/intXX 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.
 *
 * Can be combined with {SafeMath} and {SignedSafeMath} to extend it to smaller types, by performing
 * all math on `uint256` and `int256` and then downcasting.
 */
library SafeCast {
    /**
     * @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
     *
     * _Available since v4.7._
     */
    function toUint248(uint256 value) internal pure returns (uint248) {
        require(value <= type(uint248).max, "SafeCast: value doesn't fit in 248 bits");
        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
     *
     * _Available since v4.7._
     */
    function toUint240(uint256 value) internal pure returns (uint240) {
        require(value <= type(uint240).max, "SafeCast: value doesn't fit in 240 bits");
        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
     *
     * _Available since v4.7._
     */
    function toUint232(uint256 value) internal pure returns (uint232) {
        require(value <= type(uint232).max, "SafeCast: value doesn't fit in 232 bits");
        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
     *
     * _Available since v4.2._
     */
    function toUint224(uint256 value) internal pure returns (uint224) {
        require(value <= type(uint224).max, "SafeCast: value doesn't fit in 224 bits");
        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
     *
     * _Available since v4.7._
     */
    function toUint216(uint256 value) internal pure returns (uint216) {
        require(value <= type(uint216).max, "SafeCast: value doesn't fit in 216 bits");
        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
     *
     * _Available since v4.7._
     */
    function toUint208(uint256 value) internal pure returns (uint208) {
        require(value <= type(uint208).max, "SafeCast: value doesn't fit in 208 bits");
        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
     *
     * _Available since v4.7._
     */
    function toUint200(uint256 value) internal pure returns (uint200) {
        require(value <= type(uint200).max, "SafeCast: value doesn't fit in 200 bits");
        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
     *
     * _Available since v4.7._
     */
    function toUint192(uint256 value) internal pure returns (uint192) {
        require(value <= type(uint192).max, "SafeCast: value doesn't fit in 192 bits");
        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
     *
     * _Available since v4.7._
     */
    function toUint184(uint256 value) internal pure returns (uint184) {
        require(value <= type(uint184).max, "SafeCast: value doesn't fit in 184 bits");
        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
     *
     * _Available since v4.7._
     */
    function toUint176(uint256 value) internal pure returns (uint176) {
        require(value <= type(uint176).max, "SafeCast: value doesn't fit in 176 bits");
        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
     *
     * _Available since v4.7._
     */
    function toUint168(uint256 value) internal pure returns (uint168) {
        require(value <= type(uint168).max, "SafeCast: value doesn't fit in 168 bits");
        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
     *
     * _Available since v4.7._
     */
    function toUint160(uint256 value) internal pure returns (uint160) {
        require(value <= type(uint160).max, "SafeCast: value doesn't fit in 160 bits");
        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
     *
     * _Available since v4.7._
     */
    function toUint152(uint256 value) internal pure returns (uint152) {
        require(value <= type(uint152).max, "SafeCast: value doesn't fit in 152 bits");
        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
     *
     * _Available since v4.7._
     */
    function toUint144(uint256 value) internal pure returns (uint144) {
        require(value <= type(uint144).max, "SafeCast: value doesn't fit in 144 bits");
        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
     *
     * _Available since v4.7._
     */
    function toUint136(uint256 value) internal pure returns (uint136) {
        require(value <= type(uint136).max, "SafeCast: value doesn't fit in 136 bits");
        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
     *
     * _Available since v2.5._
     */
    function toUint128(uint256 value) internal pure returns (uint128) {
        require(value <= type(uint128).max, "SafeCast: value doesn't fit in 128 bits");
        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
     *
     * _Available since v4.7._
     */
    function toUint120(uint256 value) internal pure returns (uint120) {
        require(value <= type(uint120).max, "SafeCast: value doesn't fit in 120 bits");
        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
     *
     * _Available since v4.7._
     */
    function toUint112(uint256 value) internal pure returns (uint112) {
        require(value <= type(uint112).max, "SafeCast: value doesn't fit in 112 bits");
        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
     *
     * _Available since v4.7._
     */
    function toUint104(uint256 value) internal pure returns (uint104) {
        require(value <= type(uint104).max, "SafeCast: value doesn't fit in 104 bits");
        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
     *
     * _Available since v4.2._
     */
    function toUint96(uint256 value) internal pure returns (uint96) {
        require(value <= type(uint96).max, "SafeCast: value doesn't fit in 96 bits");
        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
     *
     * _Available since v4.7._
     */
    function toUint88(uint256 value) internal pure returns (uint88) {
        require(value <= type(uint88).max, "SafeCast: value doesn't fit in 88 bits");
        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
     *
     * _Available since v4.7._
     */
    function toUint80(uint256 value) internal pure returns (uint80) {
        require(value <= type(uint80).max, "SafeCast: value doesn't fit in 80 bits");
        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
     *
     * _Available since v4.7._
     */
    function toUint72(uint256 value) internal pure returns (uint72) {
        require(value <= type(uint72).max, "SafeCast: value doesn't fit in 72 bits");
        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
     *
     * _Available since v2.5._
     */
    function toUint64(uint256 value) internal pure returns (uint64) {
        require(value <= type(uint64).max, "SafeCast: value doesn't fit in 64 bits");
        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
     *
     * _Available since v4.7._
     */
    function toUint56(uint256 value) internal pure returns (uint56) {
        require(value <= type(uint56).max, "SafeCast: value doesn't fit in 56 bits");
        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
     *
     * _Available since v4.7._
     */
    function toUint48(uint256 value) internal pure returns (uint48) {
        require(value <= type(uint48).max, "SafeCast: value doesn't fit in 48 bits");
        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
     *
     * _Available since v4.7._
     */
    function toUint40(uint256 value) internal pure returns (uint40) {
        require(value <= type(uint40).max, "SafeCast: value doesn't fit in 40 bits");
        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
     *
     * _Available since v2.5._
     */
    function toUint32(uint256 value) internal pure returns (uint32) {
        require(value <= type(uint32).max, "SafeCast: value doesn't fit in 32 bits");
        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
     *
     * _Available since v4.7._
     */
    function toUint24(uint256 value) internal pure returns (uint24) {
        require(value <= type(uint24).max, "SafeCast: value doesn't fit in 24 bits");
        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
     *
     * _Available since v2.5._
     */
    function toUint16(uint256 value) internal pure returns (uint16) {
        require(value <= type(uint16).max, "SafeCast: value doesn't fit in 16 bits");
        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
     *
     * _Available since v2.5._
     */
    function toUint8(uint256 value) internal pure returns (uint8) {
        require(value <= type(uint8).max, "SafeCast: value doesn't fit in 8 bits");
        return uint8(value);
    }

    /**
     * @dev Converts a signed int256 into an unsigned uint256.
     *
     * Requirements:
     *
     * - input must be greater than or equal to 0.
     *
     * _Available since v3.0._
     */
    function toUint256(int256 value) internal pure returns (uint256) {
        require(value >= 0, "SafeCast: value must be positive");
        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
     *
     * _Available since v4.7._
     */
    function toInt248(int256 value) internal pure returns (int248 downcasted) {
        downcasted = int248(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 248 bits");
    }

    /**
     * @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
     *
     * _Available since v4.7._
     */
    function toInt240(int256 value) internal pure returns (int240 downcasted) {
        downcasted = int240(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 240 bits");
    }

    /**
     * @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
     *
     * _Available since v4.7._
     */
    function toInt232(int256 value) internal pure returns (int232 downcasted) {
        downcasted = int232(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 232 bits");
    }

    /**
     * @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
     *
     * _Available since v4.7._
     */
    function toInt224(int256 value) internal pure returns (int224 downcasted) {
        downcasted = int224(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 224 bits");
    }

    /**
     * @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
     *
     * _Available since v4.7._
     */
    function toInt216(int256 value) internal pure returns (int216 downcasted) {
        downcasted = int216(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 216 bits");
    }

    /**
     * @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
     *
     * _Available since v4.7._
     */
    function toInt208(int256 value) internal pure returns (int208 downcasted) {
        downcasted = int208(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 208 bits");
    }

    /**
     * @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
     *
     * _Available since v4.7._
     */
    function toInt200(int256 value) internal pure returns (int200 downcasted) {
        downcasted = int200(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 200 bits");
    }

    /**
     * @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
     *
     * _Available since v4.7._
     */
    function toInt192(int256 value) internal pure returns (int192 downcasted) {
        downcasted = int192(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 192 bits");
    }

    /**
     * @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
     *
     * _Available since v4.7._
     */
    function toInt184(int256 value) internal pure returns (int184 downcasted) {
        downcasted = int184(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 184 bits");
    }

    /**
     * @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
     *
     * _Available since v4.7._
     */
    function toInt176(int256 value) internal pure returns (int176 downcasted) {
        downcasted = int176(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 176 bits");
    }

    /**
     * @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
     *
     * _Available since v4.7._
     */
    function toInt168(int256 value) internal pure returns (int168 downcasted) {
        downcasted = int168(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 168 bits");
    }

    /**
     * @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
     *
     * _Available since v4.7._
     */
    function toInt160(int256 value) internal pure returns (int160 downcasted) {
        downcasted = int160(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 160 bits");
    }

    /**
     * @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
     *
     * _Available since v4.7._
     */
    function toInt152(int256 value) internal pure returns (int152 downcasted) {
        downcasted = int152(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 152 bits");
    }

    /**
     * @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
     *
     * _Available since v4.7._
     */
    function toInt144(int256 value) internal pure returns (int144 downcasted) {
        downcasted = int144(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 144 bits");
    }

    /**
     * @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
     *
     * _Available since v4.7._
     */
    function toInt136(int256 value) internal pure returns (int136 downcasted) {
        downcasted = int136(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 136 bits");
    }

    /**
     * @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
     *
     * _Available since v3.1._
     */
    function toInt128(int256 value) internal pure returns (int128 downcasted) {
        downcasted = int128(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 128 bits");
    }

    /**
     * @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
     *
     * _Available since v4.7._
     */
    function toInt120(int256 value) internal pure returns (int120 downcasted) {
        downcasted = int120(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 120 bits");
    }

    /**
     * @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
     *
     * _Available since v4.7._
     */
    function toInt112(int256 value) internal pure returns (int112 downcasted) {
        downcasted = int112(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 112 bits");
    }

    /**
     * @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
     *
     * _Available since v4.7._
     */
    function toInt104(int256 value) internal pure returns (int104 downcasted) {
        downcasted = int104(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 104 bits");
    }

    /**
     * @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
     *
     * _Available since v4.7._
     */
    function toInt96(int256 value) internal pure returns (int96 downcasted) {
        downcasted = int96(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 96 bits");
    }

    /**
     * @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
     *
     * _Available since v4.7._
     */
    function toInt88(int256 value) internal pure returns (int88 downcasted) {
        downcasted = int88(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 88 bits");
    }

    /**
     * @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
     *
     * _Available since v4.7._
     */
    function toInt80(int256 value) internal pure returns (int80 downcasted) {
        downcasted = int80(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 80 bits");
    }

    /**
     * @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
     *
     * _Available since v4.7._
     */
    function toInt72(int256 value) internal pure returns (int72 downcasted) {
        downcasted = int72(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 72 bits");
    }

    /**
     * @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
     *
     * _Available since v3.1._
     */
    function toInt64(int256 value) internal pure returns (int64 downcasted) {
        downcasted = int64(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 64 bits");
    }

    /**
     * @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
     *
     * _Available since v4.7._
     */
    function toInt56(int256 value) internal pure returns (int56 downcasted) {
        downcasted = int56(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 56 bits");
    }

    /**
     * @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
     *
     * _Available since v4.7._
     */
    function toInt48(int256 value) internal pure returns (int48 downcasted) {
        downcasted = int48(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 48 bits");
    }

    /**
     * @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
     *
     * _Available since v4.7._
     */
    function toInt40(int256 value) internal pure returns (int40 downcasted) {
        downcasted = int40(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 40 bits");
    }

    /**
     * @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
     *
     * _Available since v3.1._
     */
    function toInt32(int256 value) internal pure returns (int32 downcasted) {
        downcasted = int32(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 32 bits");
    }

    /**
     * @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
     *
     * _Available since v4.7._
     */
    function toInt24(int256 value) internal pure returns (int24 downcasted) {
        downcasted = int24(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 24 bits");
    }

    /**
     * @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
     *
     * _Available since v3.1._
     */
    function toInt16(int256 value) internal pure returns (int16 downcasted) {
        downcasted = int16(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 16 bits");
    }

    /**
     * @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
     *
     * _Available since v3.1._
     */
    function toInt8(int256 value) internal pure returns (int8 downcasted) {
        downcasted = int8(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 8 bits");
    }

    /**
     * @dev Converts an unsigned uint256 into a signed int256.
     *
     * Requirements:
     *
     * - input must be less than or equal to maxInt256.
     *
     * _Available since v3.0._
     */
    function toInt256(uint256 value) internal pure returns (int256) {
        // Note: Unsafe cast below is okay because `type(int256).max` is guaranteed to be positive
        require(value <= uint256(type(int256).max), "SafeCast: value doesn't fit in an int256");
        return int256(value);
    }
}

// File: @openzeppelin/contracts/utils/Strings.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.8.0) (utils/Strings.sol)

pragma solidity ^0.8.0;

import "./math/Math.sol";

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

    /**
     * @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;
            /// @solidity memory-safe-assembly
            assembly {
                ptr := add(buffer, add(32, length))
            }
            while (true) {
                ptr--;
                /// @solidity memory-safe-assembly
                assembly {
                    mstore8(ptr, byte(mod(value, 10), _SYMBOLS))
                }
                value /= 10;
                if (value == 0) break;
            }
            return buffer;
        }
    }

    /**
     * @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) {
        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] = _SYMBOLS[value & 0xf];
            value >>= 4;
        }
        require(value == 0, "Strings: hex length insufficient");
        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);
    }
}

// File: contracts/v1/ERC721MultiCollection.sol



// SPDX-License-Identifier: MIT
pragma solidity 0.8.17;

import "@openzeppelin/contracts/token/ERC721/ERC721.sol";
import "./interfaces/IERC721MultiCollection.sol";

/// @title ERC721 Multi collection extension implementation - Part of the Particle Protocol V1.1
/// @author Particle Collection - valdi.eth
/// See {IERC721MultiCollection}.
/// @dev Based on OpenZeppelin's ERC721Enumerable.sol, extending it to allow for multiple collections.
abstract contract ERC721MultiCollection is ERC721, IERC721MultiCollection {
    uint256 public immutable MAX_COLLECTION_SIZE;

    // Mapping owner address to token count per collection
    // owner => collection id => balance
    mapping(address =>  mapping(uint256 => uint256)) private _collectionBalances;
    // Mapping from owner to list of owned token IDs per collection
    // owner => collection id => token index => token id
    mapping(address => mapping(uint256 => mapping(uint256 => uint256))) private _collectionOwnedTokens;
    // Mapping from token ID to index of the owner tokens list per collection
    // owner => collectionId => tokenId => index
    mapping(address => mapping(uint256 => mapping(uint256 => uint256))) private _collectionOwnedTokensIndex;
    // Mapping from collection id to number of tokens on that collection
    mapping(uint256 => uint256) private _tokensPerCollection;

    /// bool indicating if adding new collections is forbidden;
    /// default behavior is to allow new collections
    bool private _newCollectionsForbidden;

    /// next collection ID to be created
    uint256 private _nextCollectionId;

    modifier onlyValidCollectionId(uint256 _collectionId) {
        if (!collectionExists(_collectionId)) {
            revert InvalidCollectionId(_collectionId);
        }
        _;
    }

    constructor(uint256 maxCollectionSize) {
        MAX_COLLECTION_SIZE = maxCollectionSize;
    }

    /**  
    * @dev External function to determine if a collection exists.
    */
    function collectionExists(uint256 collectionId) public view override returns (bool) {
        return collectionId < _nextCollectionId;
    }

    /**  
    * @dev Determines if new collections can be added to this contract.
    */
    function _newCollectionsAllowed() internal view returns (bool) {
        return !_newCollectionsForbidden;
    }

    /**
     * @dev Determines if a collection size is valid.
     */
    function _validCollectionSize(uint256 collectionSize) internal view returns (bool) {
        return collectionSize > 0 && collectionSize <= MAX_COLLECTION_SIZE;
    }

    /**  
    * @dev Adds a new collection and returns the collection ID.
    */
    function _addCollection(uint256 collectionSize) internal returns (uint256){
        require(!_newCollectionsForbidden, "New collections forbidden");
        require(_validCollectionSize(collectionSize), "Number of particles must be > 0 && <= MAX_COLLECTION_SIZE");

        uint256 collectionId = _nextCollectionId;
        
        _nextCollectionId++;

        emit CollectionAdded(collectionId);
        return collectionId;
    }

    /**
     * @notice returns the total number of collections.
     */
    function numberOfCollections() public view returns (uint256) {
        return _nextCollectionId;
    }

    /**
     * @notice Balance for `owner` in `collectionId`
     */
    function balanceOf(address owner, uint256 collectionId) public view returns (uint256) {
        if (owner == address(0)) {
            revert InvalidOwnerAddress();
        }
        return _collectionBalances[owner][collectionId];
    }

    /**
     * @dev Returns the total amount of tokens stored by the contract for `collectionId`.
     */
    function tokenTotalSupply(uint256 collectionId) external view returns (uint256) {
        return _tokensPerCollection[collectionId];
    }

    /**
     * @dev Returns a token ID owned by `owner` at a given `index` of its token list on `collectionId`.
     * Use along with {balanceOf} to enumerate all of ``owner``'s tokens.
     */
    function tokenOfOwnerByIndex(address owner, uint256 index, uint256 collectionId) external view returns (uint256) {
        require(index < balanceOf(owner, collectionId), "ERC721MultiCollection: owner index out of bounds");
        return _collectionOwnedTokens[owner][collectionId][index];
    }

    /**
     * @notice Forever forbids new collections from being added to this contract.
     */
    function _forbidNewCollections()
        internal
    {
        require(!_newCollectionsForbidden, "Already forbidden");
        _newCollectionsForbidden = true;

        emit NewCollectionsForbidden();
    }

    /**
     * @notice Get the collection ID for a given token ID
     */
    function tokenIdToCollectionId(uint256 _tokenId) public view returns (uint256 collectionId) {
        return _tokenId / MAX_COLLECTION_SIZE;
    }

    /**
     * @notice Burns `tokensToBurn` tokens in a collection for user `owner`.
     * @notice It does not let the caller specify which tokens to burn.
     *
     * @dev does not check for approval or ownership of the caller.
     * Checking is left to the extended contract if needed according to it's own logic.
     */
    function _burn(address owner, uint256 collectionId, uint256 tokensToBurn) internal returns (uint256 tokensBurnt) {
        uint256 balance = _collectionBalances[owner][collectionId];

        if (balance < tokensToBurn) {
            revert InvalidBurnAmount(owner, collectionId, tokensToBurn, balance);
        }

        for (uint256 i = 0; i < tokensToBurn;) {
            uint256 tokenId = _collectionOwnedTokens[owner][collectionId][balance - 1 - i]; // Burn token at index balance - 1 - i, preventing swapping on each burn
            _burn(tokenId);

            unchecked { i++; }
        }

        return tokensToBurn;
    }

    /**
     * @notice Burns `tokens` array in a collection for user `owner`.
     * @notice It lets the caller specify which tokens to burn.
     *
     * @dev does not check for approval or ownership of the caller.
     * Checking is left to the extended contract if needed according to it's own logic.
     */
    function _burn(address owner, uint256 collectionId, uint256[] calldata tokens) internal returns (uint256 tokensBurnt) {
        uint256 nOfTokens = tokens.length;

        for (uint256 i = 0; i < nOfTokens;) {
            uint256 tokenId = tokens[i];

            if (ownerOf(tokenId) != owner) {
                revert InvalidBurnOwner(owner, tokenId);
            }
            if (tokenIdToCollectionId(tokenId) != collectionId) {
                revert InvalidCollectionId(collectionId);
            }

            _burn(tokenId);

            unchecked { i++; }
        }

        return nOfTokens;
    }

    /**
     * @dev Private function to add a token to this extension's ownership-tracking data structures.
     * @param to address representing the new owner of the given token ID
     * @param tokenId uint256 ID of the token to be added to the tokens list of the given address
     */
    function _addTokenToOwnerCollectionEnumeration(address to, uint256 tokenId, uint256 collectionId) private {
        uint256 length = _collectionBalances[to][collectionId];
        _collectionOwnedTokens[to][collectionId][length] = tokenId;
        _collectionOwnedTokensIndex[to][collectionId][tokenId] = length;

        _collectionBalances[to][collectionId] += 1;
    }

    /**
     * @dev Private function to remove a token from this extension's ownership-tracking data structures. Note that
     * while the token is not assigned a new owner, the `_collectionOwnedTokensIndex` mapping is _not_ updated: this allows for
     * gas optimizations e.g. when performing a transfer operation (avoiding double writes).
     * This has O(1) time complexity, but alters the order of the _collectionOwnedTokens array.
     * @param from address representing the previous owner of the given token ID
     * @param tokenId uint256 ID of the token to be removed from the tokens list of the given address
     */
    function _removeTokenFromOwnerCollectionEnumeration(address from, uint256 tokenId, uint256 collectionId) private {
        // To prevent a gap in from's tokens array, we store the last token in the index of the token to delete, and
        // then delete the last slot (swap and pop).

        uint256 lastTokenIndex = _collectionBalances[from][collectionId] - 1;
        uint256 tokenIndex = _collectionOwnedTokensIndex[from][collectionId][tokenId];

        // When the token to delete is the last token, the swap operation is unnecessary
        if (tokenIndex != lastTokenIndex) {
            uint256 lastTokenId = _collectionOwnedTokens[from][collectionId][lastTokenIndex];

            _collectionOwnedTokens[from][collectionId][tokenIndex] = lastTokenId; // Move the last token to the slot of the to-delete token
            _collectionOwnedTokensIndex[from][collectionId][lastTokenId] = tokenIndex; // Update the moved token's index
        }

        // This also deletes the contents at the last position of the array
        delete _collectionOwnedTokensIndex[from][collectionId][tokenId];
        delete _collectionOwnedTokens[from][collectionId][lastTokenIndex];

        _collectionBalances[from][collectionId] -= 1;
    }

    // The following functions are overrides required by Solidity.

    function _beforeTokenTransfer(
        address from,
        address to,
        uint256 tokenId,
        uint256 batchSize
    ) internal virtual override(ERC721) {
        super._beforeTokenTransfer(from, to, tokenId, batchSize);

        uint256 collectionId = tokenIdToCollectionId(tokenId);

        if (from != address(0)) {
            _removeTokenFromOwnerCollectionEnumeration(from, tokenId, collectionId);
        } else {
            _tokensPerCollection[collectionId] += 1;
        }
        if (to != address(0)) {
            _addTokenToOwnerCollectionEnumeration(to, tokenId, collectionId);
        } else {
            _tokensPerCollection[collectionId] -= 1;
        }
    }
}

// File: contracts/v1/governance/IPRTCLVotes.sol



// SPDX-License-Identifier: MIT
pragma solidity 0.8.17;

/// @title Interface for using {PRTCLCollections721V1} as voting tokens per collection.
/// @author Particle Collection - valdi.eth
/// @notice Manages base voting data
/// @dev Modified version of OpenZeppelin's {IVotes} to accommodate multiple collections.
interface IPRTCLVotes {
    /**
     * @dev Emitted when an account changes their delegate.
     */
    event DelegateChanged(address indexed delegator, address indexed fromDelegate, address indexed toDelegate, uint256 collectionId);

    /**
     * @dev Emitted when a token transfer or delegate change results in changes to a delegate's number of votes.
     */
    event DelegateVotesChanged(address indexed delegate, uint256 previousBalance, uint256 newBalance, uint256 collectionId);

    /**
     * @dev Returned when checking voting power for a block number that is not yet mined.
     */
    error BlockNotMined();

    /**
     * @dev Returns the current amount of votes that `account` has for collection `collectionId`.
     */
    function getVotes(address account, uint256 collectionId) external view returns (uint256);

    /**
     * @dev Returns the amount of votes that `account` had at the end of a past block (`blockNumber`)
     * for collection `collectionId`.
     */
    function getPastVotes(address account, uint256 blockNumber, uint256 collectionId) external view returns (uint256);

    /**
     * @dev Returns the total supply of votes available at the end of a past block (`blockNumber`),
     * for collection `collectionId`.
     *
     * NOTE: This value is the sum of all available votes, which is not necessarily the sum of all delegated votes.
     * Votes that have not been delegated are still part of total supply, even though they would not participate in a
     * vote.
     */
    function getPastTotalSupply(uint256 blockNumber, uint256 collectionId) external view returns (uint256);

    /**
     * @dev Returns the current total supply of votes for a given collection.
     */
    function getTotalSupply(uint256 collectionId) external view returns (uint256);

    /**
     * @dev Delegates `collectionId` collection votes from the sender to `delegatee`.
     */
    function delegate(address delegatee, uint256 collectionId) external;

    /**
     * @dev Returns the delegate that `account` has chosen for `collectionId` collection.
     */
    function delegates(address account, uint256 collectionId) external view returns (address);
}

// File: contracts/v1/governance/PRTCLCoreERC721Votes.sol



// SPDX-License-Identifier: MIT
pragma solidity 0.8.17;

import "@openzeppelin/contracts/utils/cryptography/ECDSA.sol";

import "../ERC721MultiCollection.sol";
import "./PRTCLVotes.sol";

/**
 * @dev Extension of ERC721MultiCollection to support voting and delegation as implemented by {PRTCLVotes}, where each individual NFT counts
 * as 1 vote unit within a collection.
 *
 * Tokens do not count as votes until they are delegated, because votes must be tracked which incurs an additional cost
 * on every transfer. Token holders can either delegate to a trusted representative who will decide how to make use of
 * the votes in governance decisions, or they can delegate to themselves to be their own representative.
 *
 * @author Particle Collection - valdi.eth
 */
abstract contract PRTCLCoreERC721Votes is ERC721MultiCollection, PRTCLVotes {
    using ECDSA for bytes32;

    /**
     * @notice Used to validate delegation addresses
     */
    address public delegateSigner;

    /**
     * @dev Emitted when the signer address is updated.
     */
    event SignerUpdated(address signer);

    /**
     * @dev Returned when a user tries to delegate with an invalid signature.
     */
    error InvalidSignature();

    /**
     * @dev Initializes the contract by setting a `delegateSigner`.
     */
    constructor(address _delegateSigner) {
        delegateSigner = _delegateSigner;
    }

    /**
     * @dev Update signer address.
     */
    function _setDelegationSigner(address _signer) internal {
        require(_signer != address(0), "Must input non-zero address");
        delegateSigner = _signer;

        emit SignerUpdated(_signer);
    }

    /**
     * @dev See {ERC721-_afterTokenTransfer}. Adjusts votes when tokens are transferred.
     *
     * Emits a {IPRTCLVotes-DelegateVotesChanged} event.
     */
    function _afterTokenTransfer(
        address from,
        address to,
        uint256 firstTokenId,
        uint256 batchSize
    ) internal virtual override {
        _transferVotingUnits(from, to, batchSize, tokenIdToCollectionId(firstTokenId));
        super._afterTokenTransfer(from, to, firstTokenId, batchSize);
    }

    /**
     * @dev Returns the balance of `account` for collection `collectionId`.
     * 1 vote per token.
     */
    function _getVotingUnits(address account, uint256 collectionId) internal view virtual override returns (uint256) {
        return balanceOf(account, collectionId);
    }

    /**
     * @dev Override regular delegation to disable it
     */
    function delegate(address /* delegatee */, uint256 /* collectionId */) public virtual override {
        revert("PRTCLCoreERC721Votes: regular delegation disabled. Please use delegation with signature.");
    }

    /**
     * @dev Delegation that only allows whitelisted addresses
     */
    function delegate(address delegatee, uint256 collectionId, bytes memory signature, uint256 expirationBlock) public {
        if (!verifyDelegation(signature, expirationBlock, msg.sender, delegatee, collectionId)) {
            revert InvalidSignature();
        }
        super.delegate(delegatee, collectionId);
    }

    /**
     * @dev Verify signature for delegation
     */
    function verifyDelegation(bytes memory _signature, uint256 _expirationBlock, address _delegate, address _delegatee, uint256 _collectionId) public 
    view returns (bool) {
        bytes32 messageHash = keccak256(abi.encodePacked(_delegate, _delegatee, _collectionId, _expirationBlock));
        return block.number < _expirationBlock && delegateSigner == messageHash.toEthSignedMessageHash().recover(_signature);
    }
}
// File: contracts/v1/governance/PRTCLVotes.sol



// SPDX-License-Identifier: MIT
pragma solidity 0.8.17;

import "@openzeppelin/contracts/utils/Context.sol";
import "@openzeppelin/contracts/utils/Checkpoints.sol";
import "./IPRTCLVotes.sol";

/**
 * @dev Modified version of OpenZeppelin's {Votes} to accommodate multiple collections.
 *
 * @author Particle Collection - valdi.eth
 */
abstract contract PRTCLVotes is IPRTCLVotes, Context {
    using Checkpoints for Checkpoints.History;

    mapping(uint256 => mapping(address => address)) private _collectionDelegation;
    mapping(uint256 => mapping(address => Checkpoints.History)) private _collectionDelegateCheckpoints;
    mapping(uint256 => Checkpoints.History) private _collectionTotalCheckpoints;

    /**
     * @dev Returns the current amount of votes that `account` has for a given collection.
     */
    function getVotes(address account, uint256 collectionId) public view virtual override returns (uint256) {
        return _collectionDelegateCheckpoints[collectionId][account].latest();
    }

    /**
     * @dev Returns the amount of votes that `account` had at the end of a past block (`blockNumber`) for a given collection.
     *
     * Requirements:
     *
     * - `blockNumber` must have been already mined
     */
    function getPastVotes(address account, uint256 blockNumber, uint256 collectionId) public view virtual override returns (uint256) {
        if (blockNumber >= block.number) {
            revert BlockNotMined();
        }
        return _collectionDelegateCheckpoints[collectionId][account].getAtProbablyRecentBlock(blockNumber);
    }

    /**
     * @dev Returns the total supply of votes available at the end of a past block (`blockNumber`) for a given collection.
     *
     * NOTE: This value is the sum of all available votes, which is not necessarily the sum of all delegated votes.
     * Votes that have not been delegated are still part of total supply, even though they would not participate in a
     * vote.
     *
     * Requirements:
     *
     * - `blockNumber` must have been already mined
     */
    function getPastTotalSupply(uint256 blockNumber, uint256 collectionId) public view virtual override returns (uint256) {
        if (blockNumber >= block.number) {
            revert BlockNotMined();
        }
        return _collectionTotalCheckpoints[collectionId].getAtProbablyRecentBlock(blockNumber);
    }

    /**
     * @dev Returns the current total supply of votes for a given collection.
     */
    function getTotalSupply(uint256 collectionId) public view virtual override returns (uint256) {
        return _collectionTotalCheckpoints[collectionId].latest();
    }

    /**
     * @dev Returns the delegate that `account` has chosen for a given collection.
     */
    function delegates(address account, uint256 collectionId) public view virtual override returns (address) {
        return _collectionDelegation[collectionId][account];
    }

    /**
     * @dev Delegates votes from the sender to `delegatee` for a given collection.
     */
    function delegate(address delegatee, uint256 collectionId) public virtual override {
        address account = _msgSender();
        address oldDelegate = delegates(account, collectionId);
        _collectionDelegation[collectionId][account] = delegatee;

        emit DelegateChanged(account, oldDelegate, delegatee, collectionId);
        _moveDelegateVotes(oldDelegate, delegatee, _getVotingUnits(account, collectionId), collectionId);
    }

    /**
     * @dev Transfers, mints, or burns voting units. To register a mint, `from` should be zero. To register a burn, `to`
     * should be zero. Total supply of voting units will be adjusted with mints and burns.
     */
    function _transferVotingUnits(
        address from,
        address to,
        uint256 amount,
        uint256 collectionId
    ) internal virtual {
        if (from == address(0)) {
            _collectionTotalCheckpoints[collectionId].push(_add, amount);
        }
        if (to == address(0)) {
            _collectionTotalCheckpoints[collectionId].push(_subtract, amount);
        }
        _moveDelegateVotes(delegates(from, collectionId), delegates(to, collectionId), amount, collectionId);
    }

    /**
     * @dev Moves delegated votes from one delegate to another for a given collection.
     */
    function _moveDelegateVotes(
        address from,
        address to,
        uint256 amount,
        uint256 collectionId
    ) private {
        if (from != to && amount > 0) {
            if (from != address(0)) {
                (uint256 oldValue, uint256 newValue) = _collectionDelegateCheckpoints[collectionId][from].push(_subtract, amount);
                emit DelegateVotesChanged(from, oldValue, newValue, collectionId);
            }
            if (to != address(0)) {
                (uint256 oldValue, uint256 newValue) = _collectionDelegateCheckpoints[collectionId][to].push(_add, amount);
                emit DelegateVotesChanged(to, oldValue, newValue, collectionId);
            }
        }
    }

    function _add(uint256 a, uint256 b) private pure returns (uint256) {
        return a + b;
    }

    function _subtract(uint256 a, uint256 b) private pure returns (uint256) {
        return a - b;
    }

    /**
     * @dev Must return the voting units held by an account for a given collection.
     */
    function _getVotingUnits(address owner, uint256 collectionId) internal view virtual returns (uint256);
}

// File: contracts/v1/interfaces/IERC721MultiCollection.sol



// SPDX-License-Identifier: MIT
pragma solidity 0.8.17;

import "@openzeppelin/contracts/token/ERC721/IERC721.sol";

/// @title ERC721Multi collection interface
/// @author Particle Collection - valdi.eth
/// @notice Adds public facing and multi collection balanceOf and collectionId to tokenId functions
/// @dev This implements an optional extension of {ERC721} that adds
/// support for multiple collections and enumerability of all the
/// token ids in the contract as well as all token ids owned by each account per collection.
interface IERC721MultiCollection is IERC721 {
    /// @notice Collection ID `_collectionId` added
    event CollectionAdded(uint256 indexed collectionId);

    /// @notice New collections forbidden
    event NewCollectionsForbidden();

    /// @dev Returned when trying to interact with a non existent collection, or redeeming funds for a sale with a token from a different collection.
    error InvalidCollectionId(uint256 collectionId);

    /// @dev Returned when trying to check balance of the zero address.
    error InvalidOwnerAddress();

    /// @dev Returned when trying to burn more than the balance for the owner in the given collection.
    error InvalidBurnAmount(address owner, uint256 collectionId, uint256 tokensToBurn, uint256 balance);

    /// @dev Returned when trying to burn a token that is not owned by owner in the given collection.
    error InvalidBurnOwner(address owner, uint256 tokenId);

    /// @dev Determine if a collection exists.
    function collectionExists(uint256 collectionId) external view returns (bool);

    /// @notice Balance for `owner` in `collectionId`
    function balanceOf(address owner, uint256 collectionId) external view returns (uint256);

    /// @notice Get the collection ID for a given token ID
    function tokenIdToCollectionId(uint256 tokenId) external view returns (uint256 collectionId);

    /// @notice returns the total number of collections.
    function numberOfCollections() external view returns (uint256);

    /// @dev Returns the total amount of tokens stored by the contract for `collectionId`.
    function tokenTotalSupply(uint256 collectionId) external view returns (uint256);

    /// @dev Returns a token ID owned by `owner` at a given `index` of its token list on `collectionId`.
    /// Use along with {balanceOf} to enumerate all of ``owner``'s tokens.
    function tokenOfOwnerByIndex(address owner, uint256 index, uint256 collectionId) external view returns (uint256);

    /// @notice returns maximum size for collections.
    function MAX_COLLECTION_SIZE() external view returns (uint256);
}

// File: contracts/v1/interfaces/IManifold.sol



// SPDX-License-Identifier: MIT

pragma solidity 0.8.17;

/// @author: manifold.xyz

/**
 * @dev Royalty interface for creator core classes
 */
interface IManifold {

    /**
     * @dev Get royalites of a token.  Returns list of receivers and basisPoints
     *
     *  bytes4(keccak256('getRoyalties(uint256)')) == 0xbb3bafd6
     *
     *  => 0xbb3bafd6 = 0xbb3bafd6
     */
    function getRoyalties(uint256 tokenId) external view returns (address payable[] memory, uint256[] memory);
}
// File: contracts/v1/interfaces/IPRTCLCollections721V1.sol



// SPDX-License-Identifier: MIT
pragma solidity 0.8.17;

/// use the Royalty Registry's IManifold interface for token royalties
import "./IManifold.sol";
import "./IERC721MultiCollection.sol";

/// @title Interface for Core ERC721 contract for multiple collections
/// @author Particle Collection - valdi.eth
/// @notice Manages all collections tokens
/// @dev Exposes all public functions and events needed by the Particle Collection's smart contracts
/// @dev Adheres to the ERC721 standard, ERC721MultiCollection extension and Manifold for secondary royalties
interface IPRTCLCollections721V1 is IERC721, IERC721MultiCollection, IManifold {
    /// @notice Collection ID `_collectionId` updated
    event CollectionDataUpdated(uint256 indexed _collectionId);

    /// @notice Collection ID `_collectionId` size updated
    event CollectionSizeUpdated(uint256 indexed _collectionId, uint256 _size);

    /// @notice Collection ID `_collectionId` sold through governance
    event CollectionSold(uint256 indexed _collectionId, address _buyer);

    /// @notice Collection ID `_collectionId` active
    event CollectionActive(uint256 indexed _collectionId);

    /// @notice Collection ID `_collectionId` not active
    event CollectionInactive(uint256 indexed _collectionId);

    /// @notice Collection ID `_collectionId` royalties updated
    event CollectionRoyaltiesUpdated(uint256 indexed _collectionId);

    /// @notice Collection ID `_collectionId` primary split updated
    event CollectionPrimarySplitUpdated(uint256 indexed _collectionId);

    /// @notice Collection ID `_collectionId` fully minted
    event CollectionFullyMinted(uint256 indexed _collectionId);

    /// @notice Updated base uri
    event BaseURIUpdated(string _baseURI);

    /// @notice Royalties addresses updated
    event RoyaltiesAddressesUpdated(address _FJMAddress, address _DAOAddress);

    /// @notice Randomizer contract updated
    event RandomizerUpdated(address _randomizer);

    /// @notice Collection seeds set
    event CollectionSeedsSet(uint256 _collectionId, uint24 _seed1, uint24 _seed2);

    /// @notice Returned when a collection cannot be sold, as it was already sold
    error AlreadySold();

    /// @notice Returned when querying a non-existent token id
    error InvalidTokenId(uint256 tokenId);

    /// @notice Returned when querying coordinates for a token in a collection that is not revealed yet
    error CollectionNotRevealed(uint256 collectionId);

    /// @notice Returned when trying to mint an invalid amount of tokens (0 or more than allowed)
    error InvalidMintAmount(uint256 amount);

    /// @notice Returned when trying to mint a token for a collection that is not yet active
    error CollectionNotActive(uint256 collectionId);

    /// @notice Returned when trying to call a function without the required role
    error NotAllowed();

    ///
    /// Collection data
    ///

    /// @notice Artist address for collection ID `_collectionId`
    function collectionIdToArtistAddress(uint256 _collectionId) external view returns (address payable);

    /// @notice Get the primary revenue splits for a given collection ID and sale price
    /// @dev Used by minter contract
    function getPrimaryRevenueSplits(uint256 _collectionId, uint256 _price) external view
        returns (
            uint256 FJMRevenue_,
            address payable FJMAddress_,
            uint256 DAORevenue_,
            address payable DAOAddress_,
            uint256 artistRevenue_,
            address payable artistAddress_
        );

    /// @notice Main collection data
    function collectionData(uint256 _collectionId) external view returns (
        uint256 nParticles,
        uint256 maxParticles,
        bool active,
        string memory collectionName,
        bool sold,
        uint24[] memory seeds,
        uint256 setSeedsAfterBlock
    );

    /// @notice Check if the collection can be sold
    /// @dev Used by governance contract
    function collectionCanBeSold(uint256 _collectionId) external view returns (bool);

    /// @notice Get the proceeds for a given collection ID, sale price, sale comission and number of tokens
    /// @dev Used by governance contract
    function proceeds(uint256 _collectionId, uint256 _salePrice, uint256 _commission, uint256 _tokens) external view returns (uint256);

    /// @notice Get coordinates within an artwork for a given token ID
    function getCoordinate(uint256 _tokenId) external view returns (uint256);

    ///
    /// Collection interactions
    ///

    /// @notice Mark a collection as sold
    /// @dev Only callable by the governance role
    function markCollectionSold(uint256 _collectionId, address _buyer) external;
    
    /// @notice Mint a new token.
    /// Used by minter contract and BE infrastructure when handling fiat payments
    /// @dev Only callable by the minter role
    function mint(address _to, uint256 _collectionId, uint24 _amount) external returns (uint256 tokenId);

    /// @notice Burn tokensToRedeem tokens owned by `owner` in collection `_collectionId`
    /// Used when redeeming tokens for sale proceeds
    /// @dev Only callable by the governance role
    function burn(address owner, uint256 collectionId, uint256 tokensToRedeem) external returns (uint256 tokensBurnt);

    /// @notice Burn `tokens` owned by `owner`
    /// Used when redeeming tokens for sale proceeds
    /// @dev Only callable by the governance role
    function burn(address tokensOwner, uint256 collectionId, uint256[] calldata tokens) external returns (uint256 tokensBurnt);

    /// @notice Set the random prime seeds for a given collection ID, used to calculate token coordinates
    /// @dev Only callable by the Randomizer contract
    function setCollectionSeeds(uint256 _collectionId, uint24[2] calldata _seeds) external;
}

// File: contracts/v1/interfaces/IRandomizerV1.sol



// SPDX-License-Identifier: MIT
pragma solidity 0.8.17;

/// @title Interface for the Randomizer contract version 1
/// @author Particle Collection - valdi.eth
/// @notice Sets the random prime seeds for the collection on the core ERC721 contract
interface IRandomizerV1 {
    /// @notice Sets random prime seeds for the collection
    /// @dev Only callable by the core ERC721 contract
    function setCollectionSeeds(uint256 _collectionId) external;
}

// File: contracts/v1/PRTCLCollections721V1.sol



// SPDX-License-Identifier: LGPL-3.0-only
pragma solidity 0.8.17;

import "@openzeppelin/contracts/access/AccessControl.sol";
import "@openzeppelin/contracts/security/ReentrancyGuard.sol";
import "@openzeppelin/contracts/utils/cryptography/EIP712.sol";
import "operator-filter-registry/src/RevokableDefaultOperatorFilterer.sol";
import "./interfaces/IPRTCLCollections721V1.sol";
import "./interfaces/IRandomizerV1.sol";
import "./governance/PRTCLCoreERC721Votes.sol";

/// @title Core ERC721 contract for multiple collections - Part of the Particle Protocol V1.1
/// @author Particle Collection - valdi.eth
/// @notice Manages all collections tokens and voting rights
/// @dev Exposes all public functions and events needed by the Particle Collection's smart contract suite version 1
/// @dev Adheres to the ERC721 standard, ERC721MultiCollection extension and Manifold for secondary royalties
/// @dev Integrates with the OpenSea's Operator Filter Registry to allow for filtering of token transfers: https://github.com/ProjectOpenSea/operator-filter-registry
/// @dev Based on Artblock's GenArt721CoreV3 contract design: https://github.com/ArtBlocks/artblocks-contracts/blob/main/contracts/GenArt721CoreV3.sol
/// Modifications to the original design:
/// - AccessControl extension from OZ
/// - Voting power extension modified from OZ's Votes contract
/// - MultiCollection support
/// - Collection state management modified to accomodate sales
/// - Added coordinate system by modyifing the Randomization design
/// - Added per collection, multi token burning
/// @dev The PRTCLCollections721V1 contract contains the following privileged access for the following functions:
/// - The MINTER_ROLE can mint a new token for any collection using mint().
/// - The GOVERNOR_ROLE can mark a collection as sold using markCollectionSold().
/// - The GOVERNOR_ROLE can burn all tokens of any owner for a specific collectionId using burn().
/// - The DEFAULT_ADMIN_ROLE can update the base URI using updateBaseURI().
/// - The DEFAULT_ADMIN_ROLE can disable new collections from being added using forbidNewCollections().
/// - The DEFAULT_ADMIN_ROLE can add a new collection using addCollection().
/// - The DEFAULT_ADMIN_ROLE can change whether a collection is active using toggleCollectionIsActive().
/// - The DEFAULT_ADMIN_ROLE can update the collection data using updateCollectionData().
/// - The DEFAULT_ADMIN_ROLE can update the collection financials using updateCollectionRoyalties(), updateCollectionPrimarySplit(), or updateRoyaltiesAddresses().
/// - The DEFAULT_ADMIN_ROLE can request collection seed after the time criteria have passed using requestCollectionSeeds().
/// - The DEFAULT_ADMIN_ROLE can update the randomizer contract using updateRandomizer().
/// - The DEFAULT_ADMIN_ROLE can mint a new token for any collection using mint() regardless of the collection status as long as the particle does not exceed the maximum.
/// - The DEFAULT_ADMIN_ROLE can update the operator filter registry admin using updateOperatorFilterRegistryAdmin().
/// @custom:security-contact nacho@particlecollection.com
contract PRTCLCollections721V1 is
    AccessControl,
    EIP712,
    PRTCLCoreERC721Votes,
    IPRTCLCollections721V1,
    RevokableDefaultOperatorFilterer,
    ReentrancyGuard
{
    bytes32 public constant MINTER_ROLE = keccak256("MINTER_ROLE");
    bytes32 public constant GOVERNOR_ROLE = keccak256("GOVERNOR_ROLE");

    uint256 constant MAX_BPS = 10000; // 10_000 BPS = 100%

    uint256 constant DEFAULT_ARTIST_ROYALTY_BPS = 500; // 5%
    uint256 constant DEFAULT_FJM_ROYALTY_BPS = 250; // 2,5%
    uint256 constant DEFAULT_DAO_ROYALTY_BPS = 250; // 2,5%

    uint256 constant DEFAULT_ARTIST_PRIMARY_BPS = 0; // 0%
    uint256 constant DEFAULT_FJM_PRIMARY_BPS = 10000; // 10_000 BPS = 100%
    uint256 constant DEFAULT_DAO_PRIMARY_BPS = 0; // 0%

    /// 4JM wallet address
    address payable public FJMAddress;
    /// Particle Collection DAO wallet address
    address payable public DAOAddress;
    /// Current randomizer contract
    IRandomizerV1 public randomizerContract;

    string public baseURI;

    struct Collection {
        // Number of particles in the collection
        uint24 nParticles;
        // Max number of particles in the collection
        uint24 maxParticles;
        bool active;
        // The original artwork has been sold through an accepted bid by the collection owners
        // Only editable by the governor contract, thus by a governance vote
        bool sold;
        string name;
        // Seeds to randomize token coordinates. Seeds are set after minting,
        // potentially altering the coordinate assignment of all tokens.
        // Only Randomizer contract can assign seeds.
        // E.g. Token id 1 could map to coordinate 4321
        uint24[] seeds;
        // Timestamp after which setting seeds (and thus revealing metadata) is allowed.
        // Block number, set to 256 blocks after last particle mint, to prevent speculation when setting seeds (look-ahead period of 8 epochs)
        uint256 setSeedsAfterBlock;
    }

    mapping(uint256 => Collection) collections;

    /// struct containing collection financial information
    struct CollectionFinance {
        address payable artistAddress;
        uint256 artistRoyaltyBPS;
        uint256 FJMRoyaltyBPS;
        uint256 DAORoyaltyBPS;
        uint256 artistPrimaryBPS;
        uint256 FJMPrimaryBPS;
        uint256 DAOPrimaryBPS;
    }

    // Collection financials mapping
    mapping(uint256 => CollectionFinance) collectionIdToFinancials;

    // Address that can modify the operator filter registry
    address public operatorFilterRegistryAdmin;

    modifier onlyNonZeroAddress(address _address) {
        require(_address != address(0), "Must input non-zero address");
        _;
    }

    modifier onlyNonEmptyString(string memory _string) {
        require(bytes(_string).length != 0, "Must input non-empty string");
        _;
    }

    constructor(
        string memory _bURI,
        address _delegationSigner,
        address payable _FJMAddress,
        address payable _DAOAddress
    )   onlyNonEmptyString(_bURI)
        onlyNonZeroAddress(_delegationSigner)
        ERC721MultiCollection(1_000_000)
        ERC721("Particle", "PRTCL")
        EIP712("Particle", "1")
        PRTCLCoreERC721Votes(_delegationSigner)
        ReentrancyGuard()
    {
        _grantRole(DEFAULT_ADMIN_ROLE, msg.sender);
        operatorFilterRegistryAdmin = msg.sender;
        baseURI = _bURI;

        updateRoyaltiesAddresses(_FJMAddress, _DAOAddress);
    }

    /**
     * @notice Updates base URI to `_newBaseURI`.
     * @param _newBaseURI New base URI.
     */
    function updateBaseURI(string memory _newBaseURI)
        external
        onlyRole(DEFAULT_ADMIN_ROLE)
        onlyNonEmptyString(_newBaseURI)
    {
        baseURI = _newBaseURI;

        emit BaseURIUpdated(_newBaseURI);
    }

    /**
     * @notice Returns the base URI for all tokens. Used in tokenURI().
     */
    function _baseURI() internal view override returns (string memory) {
        return baseURI;
    }

    /**
     * @notice Updates delegation signer to `_newDelegationSigner`.
     * @param _newDelegationSigner New delegation signer.
     */
    function updateDelegationSigner(address _newDelegationSigner)
        external
        onlyRole(DEFAULT_ADMIN_ROLE) {
        // Checks for non zero address
        _setDelegationSigner(_newDelegationSigner);
    }

    /**
     * @dev Updates the operator filter registry admin
     */
    function updateOperatorFilterRegistryAdmin(address _newAdmin)
        external
        onlyRole(DEFAULT_ADMIN_ROLE)
        onlyNonZeroAddress(_newAdmin)
    {
        operatorFilterRegistryAdmin = _newAdmin;
    }

    /**
     * @dev Returns the address that can modify the operator filter registry.
     * Used by RevokableDefaultOperatorFilterer to allow modifications or revoking of filtering.
     */
    function owner() public view override returns (address) {
        return operatorFilterRegistryAdmin;
    }

    /**
     * @notice Forever forbids new collections from being added to this contract.
     * Only callable by DEFAULT_ADMIN_ROLE.
     * Should only be used after a new version of this contract has been deployed.
     * Emits NewCollectionsForbidden event.
     */
    function forbidNewCollections()
        external
        onlyRole(DEFAULT_ADMIN_ROLE)
    {
        _forbidNewCollections();
    }

    /**
     * @notice Check if adding new collections is allowed on this contract.
     */
    function newCollectionsAllowed() public view returns (bool) {
        return _newCollectionsAllowed();
    }

    /**
     * @notice The collection can be sold if it has not been sold and is fully minted.
     */
    function collectionCanBeSold(uint256 _collectionId) onlyValidCollectionId(_collectionId) external view returns (bool) {
        Collection memory collection = collections[_collectionId];
        return !collection.sold && collection.nParticles == collection.maxParticles;
    }

    /**
     * @notice Proceeds for _tokens for a sale of `_salePrice`.
     */
    function proceeds(uint256 _collectionId, uint256 _salePrice, uint256 _commission, uint256 _tokens) onlyValidCollectionId(_collectionId) external view returns (uint256) {
        // Multiply first to avoid rounding errors as much as possible
        return (_salePrice - _salePrice * _commission / 100) * _tokens / collections[_collectionId].maxParticles;
    }

    /**
     * @notice Mark collection as sold.
     * Only callable by GOVERNOR_ROLE, thus by a completed and accepted governance
     * proposal being executed.
     */
    function markCollectionSold(uint256 _collectionId, address _buyer)
        external
        onlyRole(GOVERNOR_ROLE)
        onlyValidCollectionId(_collectionId)
    {
        Collection storage collection = collections[_collectionId];

        if (collection.sold) {
            revert AlreadySold();
        }

        collection.sold = true;

        emit CollectionSold(_collectionId, _buyer);
    }

    /**
     * @notice Gets royalty Basis Points (BPS) for tokens in collection ID `collectionId`.
     * @param collectionId Collection ID to be queried.
     * @return recipients Array of royalty payment recipients
     * @return bps Array of Basis Points (BPS) allocated to each recipient,
     * aligned by index.
     * @dev only returns recipients that have a non-zero BPS allocation
     */
    function getRoyaltiesForCollection(
        uint256 collectionId
    )
        public
        view
        onlyValidCollectionId(collectionId)
        returns (address payable[] memory recipients, uint256[] memory bps)
    {
        recipients = new address payable[](3);
        bps = new uint256[](3);

        CollectionFinance memory financials = collectionIdToFinancials[collectionId];

        // calculate BPS = percentage * 100
        uint256 artistBPS = financials.artistRoyaltyBPS;
        uint256 daoBPS = financials.DAORoyaltyBPS;
        uint256 fjmBPS = financials.FJMRoyaltyBPS;
        // populate arrays
        uint256 payeeCount;
        if (artistBPS > 0) {
            recipients[payeeCount] = financials.artistAddress;
            bps[payeeCount++] = artistBPS;
        }
        if (daoBPS > 0) {
            recipients[payeeCount] = DAOAddress;
            bps[payeeCount++] = daoBPS;
        }
        if (fjmBPS > 0) {
            recipients[payeeCount] = FJMAddress;
            bps[payeeCount++] = fjmBPS;
        }
        // trim arrays if necessary
        if (3 > payeeCount) {
            assembly {
                let decrease := sub(3, payeeCount)
                mstore(recipients, sub(mload(recipients), decrease))
                mstore(bps, sub(mload(bps), decrease))
            }
        }
        return (recipients, bps);
    }

    /**
     * @notice Gets royalty Basis Points (BPS) for token ID `tokenId`.
     * This conforms to the IManifold interface designated in the Royalty
     * Registry's RoyaltyEngineV1.sol contract.
     * ref: https://github.com/manifoldxyz/royalty-registry-solidity
     * @param tokenId Token ID to be queried.
     * @return recipients Array of royalty payment recipients
     * @return bps Array of Basis Points (BPS) allocated to each recipient,
     * aligned by index.
     * @dev only returns recipients that have a non-zero BPS allocation
     */
    function getRoyalties(
        uint256 tokenId
    )
        external
        view
        returns (address payable[] memory recipients, uint256[] memory bps)
    {
        if (!_exists(tokenId)) {
            revert InvalidTokenId(tokenId);
        }
        return getRoyaltiesForCollection(tokenIdToCollectionId(tokenId));
    }

    /**
     * @notice Returns the address of the artist for a given collection ID.
     */
    function collectionIdToArtistAddress(
        uint256 _collectionId
    ) external view onlyValidCollectionId(_collectionId) returns (address payable) {
        return collectionIdToFinancials[_collectionId].artistAddress;
    }

    /**
     * @notice Returns revenue split for primary sale of `_price` for collection `_collectionId`.
     * @dev Used by minter contract to determine how much to pay to each party.
     */
    function getPrimaryRevenueSplits(
        uint256 _collectionId,
        uint256 _price
    )
        external
        view
        onlyValidCollectionId(_collectionId)
        returns (
            uint256 FJMRevenue_,
            address payable FJMAddress_,
            uint256 DAORevenue_,
            address payable DAOAddress_,
            uint256 artistRevenue_,
            address payable artistAddress_
        )
    {
        CollectionFinance memory financials = collectionIdToFinancials[
            _collectionId
        ];
        // BPS should first be divided by 100 to get the percentage, then by 100 to get the value in the corresponding currency
        FJMRevenue_ =
            (_price * financials.FJMPrimaryBPS) /
            MAX_BPS;
        artistRevenue_ =
            (_price * financials.artistPrimaryBPS) /
            MAX_BPS;
        DAORevenue_ =
            (_price * financials.DAOPrimaryBPS) /
            MAX_BPS;

        FJMAddress_ = FJMAddress;
        artistAddress_ = financials.artistAddress;
        DAOAddress_ = DAOAddress;
    }

    /**
     * @notice Returns collection data for collection `_collectionId`.
     */
    function collectionData(uint256 _collectionId)
        external
        view
        onlyValidCollectionId(_collectionId)
        returns (
            uint256 nParticles,
            uint256 maxParticles,
            bool active,
            string memory collectionName,
            bool sold,
            uint24[] memory seeds,
            uint256 setSeedsAfterBlock
        )
    {
        Collection memory collection = collections[_collectionId];

        nParticles = collection.nParticles;
        maxParticles = collection.maxParticles;
        active = collection.active;
        collectionName = collection.name;
        sold = collection.sold;
        seeds = collection.seeds;
        setSeedsAfterBlock = collection.setSeedsAfterBlock;
    }

    /**
     * @notice Returns the coordinate within the collection artwork for a given token ID.
     * @dev The coordinate is calculated based on the collection's seeds (set by the randomizer contract), and the token ID.
     */
    function getCoordinate(uint256 _tokenId) external view returns (uint256) {
        // Get collection id, check if seeds have been set, calculate coordinate based on seeds
        Collection memory collection = collections[
            tokenIdToCollectionId(_tokenId)
        ];

        if (collection.seeds.length == 0) {
            revert CollectionNotRevealed(tokenIdToCollectionId(_tokenId));
        }

        // p1 and p2 are primes above 1M, guaranteeing no collisions
        // Using another prime to shift, to avoid 0 or last token id always being the first element
        uint32 p1 = collection.seeds[0];
        uint32 p2 = collection.seeds[1];
        uint256 maxParticles = collection.maxParticles;

        return (_tokenId * p1 + p2) % maxParticles;
    }

    /**
     * @notice Adds new collection `_collectionName` by `_artistAddress`.
     * @param _collectionName Artwork (ERC-721 collection) name.
     * @param _numberOfParticles Artwork will be divided in these many particles.
     * @param _artistAddress Artist's address.
     * @dev token price stored on minter contract. Emits CollectionAdded event from ERC721MultiCollection.
     */
    function addCollection(
        string memory _collectionName,
        uint24 _numberOfParticles,
        address payable _artistAddress
    )
        external
        onlyRole(DEFAULT_ADMIN_ROLE)
        onlyNonZeroAddress(_artistAddress)
        onlyNonEmptyString(_collectionName)
        returns (uint256)
    {
        uint256 collectionId = _addCollection(_numberOfParticles);

        require(collectionId <= type(uint232).max, "Collection id > 232 bits");

        collectionIdToFinancials[collectionId].artistAddress = _artistAddress;
        collectionIdToFinancials[collectionId].artistRoyaltyBPS = DEFAULT_ARTIST_ROYALTY_BPS;
        collectionIdToFinancials[collectionId].FJMRoyaltyBPS = DEFAULT_FJM_ROYALTY_BPS;
        collectionIdToFinancials[collectionId].DAORoyaltyBPS = DEFAULT_DAO_ROYALTY_BPS;

        // Primary sales revenue split
        collectionIdToFinancials[collectionId].artistPrimaryBPS = DEFAULT_ARTIST_PRIMARY_BPS;
        collectionIdToFinancials[collectionId].FJMPrimaryBPS = DEFAULT_FJM_PRIMARY_BPS;
        collectionIdToFinancials[collectionId].DAOPrimaryBPS = DEFAULT_DAO_PRIMARY_BPS;

        collections[collectionId].name = _collectionName;
        collections[collectionId].maxParticles = _numberOfParticles;

        return collectionId;
    }

    /**
     * @notice Toggles collection `_collectionId` as active/inactive.
     * @param _collectionId Collection ID to be toggled.
     */
    function toggleCollectionIsActive(uint256 _collectionId)
        external
        onlyRole(DEFAULT_ADMIN_ROLE)
        onlyValidCollectionId(_collectionId)
    {
        collections[_collectionId].active = !collections[_collectionId].active;
        
        if (collections[_collectionId].active) {
            emit CollectionActive(_collectionId);
        } else {
            emit CollectionInactive(_collectionId);
        }
    }

    /**
     * @notice Updates a collection's data.
     * @param _collectionId Collection ID.
     * @param _artistAddress New artist address.
     * @param _collectionName New collection name.
     */
    function updateCollectionData(
        uint256 _collectionId,
        address payable _artistAddress,
        string memory _collectionName
    )
        external
        onlyValidCollectionId(_collectionId)
        onlyRole(DEFAULT_ADMIN_ROLE)
        onlyNonZeroAddress(_artistAddress)
        onlyNonEmptyString(_collectionName)
    {
        collections[_collectionId].name = _collectionName;
        collectionIdToFinancials[_collectionId].artistAddress = _artistAddress;
        emit CollectionDataUpdated(_collectionId);
    }

    /**
     * @notice Updates a collection's max particles.
     * @param _collectionId Collection ID.
     * @param _maxParticles New number of particles for collection.
     */
    function updateCollectionMaxParticles(
        uint256 _collectionId,
        uint24 _maxParticles
    )
        external
        onlyValidCollectionId(_collectionId)
        onlyRole(DEFAULT_ADMIN_ROLE)
    {
        require(_validCollectionSize(_maxParticles), "maxParticles has to be > 0 and <= 1M");
        require(collections[_collectionId].nParticles == 0, "maxParticles can only be updated if no particles have been minted");
        collections[_collectionId].maxParticles = _maxParticles;
        emit CollectionSizeUpdated(_collectionId, _maxParticles);
    }

    /**
     * @notice Updates collection's financials.
     * @param _collectionId Collection ID.
     * @param _artistRoyaltyBPS New artist fee percentage.
     * @param _FJMRoyaltyBPS New 4JM fee percentage.
     * @param _DAORoyaltyBPS New DAO fee percentage.
     */
    function updateCollectionRoyalties(
        uint256 _collectionId,
        uint256 _artistRoyaltyBPS,
        uint256 _FJMRoyaltyBPS,
        uint256 _DAORoyaltyBPS
    )
        external
        onlyValidCollectionId(_collectionId)
        onlyRole(DEFAULT_ADMIN_ROLE)
    {
        // 10_000 BPS = 100%
        // require the sum of all royalties to be less than or equal to MAX_BPS
        require(_artistRoyaltyBPS + _FJMRoyaltyBPS + _DAORoyaltyBPS <= MAX_BPS, "Royalties > 100%");
        collectionIdToFinancials[_collectionId].artistRoyaltyBPS = _artistRoyaltyBPS;
        collectionIdToFinancials[_collectionId].FJMRoyaltyBPS = _FJMRoyaltyBPS;
        collectionIdToFinancials[_collectionId].DAORoyaltyBPS = _DAORoyaltyBPS;
        emit CollectionRoyaltiesUpdated(_collectionId);
    }

    /**
     * @notice Updates collection's financials.
     * @param _collectionId Collection ID.
     * @param _artistPrimaryBPS New artist fee percentage.
     * @param _FJMPrimaryBPS New 4JM fee percentage.
     * @param _DAOPrimaryBPS New DAO fee percentage.
     */
    function updateCollectionPrimarySplit(
        uint256 _collectionId,
        uint256 _artistPrimaryBPS,
        uint256 _FJMPrimaryBPS,
        uint256 _DAOPrimaryBPS
    )
        external
        onlyValidCollectionId(_collectionId)
        onlyRole(DEFAULT_ADMIN_ROLE)
    {
        // 10_000 BPS = 100%
        // require the sum of all primary splits to be exactly MAX_BPS
        require(_artistPrimaryBPS + _FJMPrimaryBPS + _DAOPrimaryBPS == MAX_BPS, "Primary split != 100%");
        collectionIdToFinancials[_collectionId].artistPrimaryBPS = _artistPrimaryBPS;
        collectionIdToFinancials[_collectionId].FJMPrimaryBPS = _FJMPrimaryBPS;
        collectionIdToFinancials[_collectionId].DAOPrimaryBPS = _DAOPrimaryBPS;
        emit CollectionPrimarySplitUpdated(_collectionId);
    }

    /**
     * @notice Updates collection's seeds.
     * @param _collectionId Collection ID.
     * @param _seeds Seeds to be set for collection `_collectionId`.
     * @dev Only callable by Randomizer contract.
     */
    function setCollectionSeeds(
        uint256 _collectionId,
        uint24[2] calldata _seeds
    ) external onlyValidCollectionId(_collectionId) {
        require(
            msg.sender == address(randomizerContract),
            "Only randomizer may set"
        );

        Collection storage collection = collections[_collectionId];

        require(collection.seeds.length == 0, "Seeds already set");
        require(_seeds.length == 2, "Seeds must be length 2");

        collection.seeds = _seeds;

        emit CollectionSeedsSet(_collectionId, _seeds[0], _seeds[1]);
    }

    /**
     * @notice Requests an update to the collection's seeds from the Randomizer contract.
     * @param _collectionId Collection ID.
     * @dev Only callable by Admin after the setSeedsAfterBlock block number.
     */
    function requestCollectionSeeds(
        uint256 _collectionId
    ) external onlyValidCollectionId(_collectionId) onlyRole(DEFAULT_ADMIN_ROLE) {
        uint allowedBlock = collections[_collectionId].setSeedsAfterBlock;
        require(allowedBlock > 0 && block.number > allowedBlock, "Too early to set seeds");

        randomizerContract.setCollectionSeeds(_collectionId);
    }

    /**
     * @notice Updates 4JM and DAO addresses.
     * @param _FJMAddress 4JM address.
     * @param _DAOAddress DAO address.
     * Registry.
     */
    function updateRoyaltiesAddresses(
        address payable _FJMAddress,
        address payable _DAOAddress
    )
        public
        onlyRole(DEFAULT_ADMIN_ROLE)
        onlyNonZeroAddress(_FJMAddress)
        onlyNonZeroAddress(_DAOAddress)
    {
        FJMAddress = _FJMAddress;
        DAOAddress = _DAOAddress;

        emit RoyaltiesAddressesUpdated(_FJMAddress, _DAOAddress);
    }

    /**
     * @notice Updates randomizer to `_randomizerAddress`.
     * @param _randomizerAddress Address of new randomizer.
     */
    function updateRandomizer(
        address _randomizerAddress
    )
        external
        onlyRole(DEFAULT_ADMIN_ROLE)
        onlyNonZeroAddress(_randomizerAddress)
    {
        randomizerContract = IRandomizerV1(_randomizerAddress);

        emit RandomizerUpdated(_randomizerAddress);
    }

    /**
     * @notice Mints a new token for collection `_collectionId`.
     * @param _to Receiver of the new token.
     * @param _collectionId Collection ID.
     * @param _amount Number of tokens to mint.
     * @dev Mints ids in incremental order, coordinates are determined at random on last mint 
     * (requires minting all collection ids to generate seeds). Only callable by minter role 
     * (minter contract and admin account handling fiat sales).
     */
    function mint(
        address _to,
        uint256 _collectionId,
        uint24 _amount
    ) external onlyValidCollectionId(_collectionId) nonReentrant returns (uint256 tokenId) {
        if (!hasRole(DEFAULT_ADMIN_ROLE, msg.sender) && !hasRole(MINTER_ROLE, msg.sender)) {
            revert NotAllowed();
        }

        if (_amount == 0) {
            revert InvalidMintAmount(_amount);
        }

        Collection storage collection = collections[_collectionId];
        uint24 oldNParticles = collection.nParticles;
        uint24 maxParticles = collection.maxParticles;

        uint24 newNParticles = oldNParticles + _amount;

        if (newNParticles > maxParticles) {
            revert InvalidMintAmount(_amount);
        }

        if (!collection.active && !hasRole(DEFAULT_ADMIN_ROLE, msg.sender)) {
            revert CollectionNotActive(_collectionId);
        }

        collection.nParticles = newNParticles;

        uint256 newTokenId;

        unchecked {
            // oldNParticles is uint24 << max uint256. In production use,
            // _collectionId * ONE_MILLION must be << max uint256, otherwise
            // tokenIdToCollectionId function becomes invalid.
            // Therefore, no risk of overflow
            newTokenId = (_collectionId * MAX_COLLECTION_SIZE) + oldNParticles;
        }

        if (newNParticles == maxParticles) {
            // Allow setCollectionSeeds to be called 256 blocks (8 epochs) after the last mint, 
            // by a contract Admin (essentially revealing the final coordinates and metadata for each token)
            collection.setSeedsAfterBlock = block.number + 256;
            collection.active = false;

            emit CollectionFullyMinted(_collectionId);
        }

        for (uint256 i; i < _amount;) {
            _safeMint(_to, newTokenId + i);
            unchecked { i++; }
        }

        return newTokenId;
    }

    /**
     * @notice Burns tokensToRedeem tokens in a collection for user `tokensOwner`.
     * Used when redeeming proceeds from a sale.
     *
     * @dev The caller must be the governor contract.
     * Approval to burn is checked on the governor contract.
     */
    function burn(address tokensOwner, uint256 collectionId, uint256 tokensToRedeem)
        external
        onlyRole(GOVERNOR_ROLE)
        onlyValidCollectionId(collectionId)
        returns (uint256 tokensBurnt)
    {
        return _burn(tokensOwner, collectionId, tokensToRedeem);
    }

    /**
     * @notice Burns `tokens` array in a collection for user `tokensOwner`.
     * Used when redeeming proceeds from a sale.
     *
     * @dev The caller must be the governor contract.
     * Approval to burn is checked on the governor contract.
     */
    function burn(address tokensOwner, uint256 collectionId, uint256[] calldata tokens)
        external
        onlyRole(GOVERNOR_ROLE)
        returns (uint256 tokensBurnt)
    {
        return _burn(tokensOwner, collectionId, tokens);
    }

    /// @dev Override transfer and approval functions to use the operator filter registry

    /**
     * @dev See {IERC721-setApprovalForAll}.
     *      The added modifier ensures that the operator is allowed by the OperatorFilterRegistry.
     */
    function setApprovalForAll(address operator, bool approved) public override(IERC721, ERC721) onlyAllowedOperatorApproval(operator) {
        super.setApprovalForAll(operator, approved);
    }

    /**
     * @dev See {IERC721-approve}.
     *      The added modifier ensures that the operator is allowed by the OperatorFilterRegistry.
     */
    function approve(address operator, uint256 tokenId) public override(IERC721, ERC721) onlyAllowedOperatorApproval(operator) {
        super.approve(operator, tokenId);
    }

    /**
     * @dev See {IERC721-transferFrom}.
     *      The added modifier ensures that the operator is allowed by the OperatorFilterRegistry.
     */
    function transferFrom(address from, address to, uint256 tokenId) public override(IERC721, ERC721) onlyAllowedOperator(from) {
        super.transferFrom(from, to, tokenId);
    }

    /**
     * @dev See {IERC721-safeTransferFrom}.
     *      The added modifier ensures that the operator is allowed by the OperatorFilterRegistry.
     */
    function safeTransferFrom(address from, address to, uint256 tokenId) public override(IERC721, ERC721) onlyAllowedOperator(from) {
        super.safeTransferFrom(from, to, tokenId);
    }

    /**
     * @dev See {IERC721-safeTransferFrom}.
     *      The added modifier ensures that the operator is allowed by the OperatorFilterRegistry.
     */
    function safeTransferFrom(address from, address to, uint256 tokenId, bytes memory data)
        public
        override(IERC721, ERC721)
        onlyAllowedOperator(from)
    {
        super.safeTransferFrom(from, to, tokenId, data);
    }

    // The following functions are overrides required by Solidity.

    function _beforeTokenTransfer(
        address from,
        address to,
        uint256 tokenId,
        uint256 batchSize
    ) internal override(ERC721MultiCollection) {
        super._beforeTokenTransfer(from, to, tokenId, batchSize);
    }

    function _afterTokenTransfer(
        address from,
        address to,
        uint256 tokenId,
        uint256 batchSize
    ) internal override(PRTCLCoreERC721Votes) {
        super._afterTokenTransfer(from, to, tokenId, batchSize);
    }

    function supportsInterface(
        bytes4 interfaceId
    )
        public
        view
        override(ERC721, AccessControl, IERC165)
        returns (bool)
    {
        return super.supportsInterface(interfaceId);
    }
}

// File: operator-filter-registry/src/IOperatorFilterRegistry.sol



// SPDX-License-Identifier: MIT
pragma solidity ^0.8.13;

interface IOperatorFilterRegistry {
    /**
     * @notice Returns true if operator is not filtered for a given token, either by address or codeHash. Also returns
     *         true if supplied registrant address is not registered.
     */
    function isOperatorAllowed(address registrant, address operator) external view returns (bool);

    /**
     * @notice Registers an address with the registry. May be called by address itself or by EIP-173 owner.
     */
    function register(address registrant) external;

    /**
     * @notice Registers an address with the registry and "subscribes" to another address's filtered operators and codeHashes.
     */
    function registerAndSubscribe(address registrant, address subscription) external;

    /**
     * @notice Registers an address with the registry and copies the filtered operators and codeHashes from another
     *         address without subscribing.
     */
    function registerAndCopyEntries(address registrant, address registrantToCopy) external;

    /**
     * @notice Unregisters an address with the registry and removes its subscription. May be called by address itself or by EIP-173 owner.
     *         Note that this does not remove any filtered addresses or codeHashes.
     *         Also note that any subscriptions to this registrant will still be active and follow the existing filtered addresses and codehashes.
     */
    function unregister(address addr) external;

    /**
     * @notice Update an operator address for a registered address - when filtered is true, the operator is filtered.
     */
    function updateOperator(address registrant, address operator, bool filtered) external;

    /**
     * @notice Update multiple operators for a registered address - when filtered is true, the operators will be filtered. Reverts on duplicates.
     */
    function updateOperators(address registrant, address[] calldata operators, bool filtered) external;

    /**
     * @notice Update a codeHash for a registered address - when filtered is true, the codeHash is filtered.
     */
    function updateCodeHash(address registrant, bytes32 codehash, bool filtered) external;

    /**
     * @notice Update multiple codeHashes for a registered address - when filtered is true, the codeHashes will be filtered. Reverts on duplicates.
     */
    function updateCodeHashes(address registrant, bytes32[] calldata codeHashes, bool filtered) external;

    /**
     * @notice Subscribe an address to another registrant's filtered operators and codeHashes. Will remove previous
     *         subscription if present.
     *         Note that accounts with subscriptions may go on to subscribe to other accounts - in this case,
     *         subscriptions will not be forwarded. Instead the former subscription's existing entries will still be
     *         used.
     */
    function subscribe(address registrant, address registrantToSubscribe) external;

    /**
     * @notice Unsubscribe an address from its current subscribed registrant, and optionally copy its filtered operators and codeHashes.
     */
    function unsubscribe(address registrant, bool copyExistingEntries) external;

    /**
     * @notice Get the subscription address of a given registrant, if any.
     */
    function subscriptionOf(address addr) external returns (address registrant);

    /**
     * @notice Get the set of addresses subscribed to a given registrant.
     *         Note that order is not guaranteed as updates are made.
     */
    function subscribers(address registrant) external returns (address[] memory);

    /**
     * @notice Get the subscriber at a given index in the set of addresses subscribed to a given registrant.
     *         Note that order is not guaranteed as updates are made.
     */
    function subscriberAt(address registrant, uint256 index) external returns (address);

    /**
     * @notice Copy filtered operators and codeHashes from a different registrantToCopy to addr.
     */
    function copyEntriesOf(address registrant, address registrantToCopy) external;

    /**
     * @notice Returns true if operator is filtered by a given address or its subscription.
     */
    function isOperatorFiltered(address registrant, address operator) external returns (bool);

    /**
     * @notice Returns true if the hash of an address's code is filtered by a given address or its subscription.
     */
    function isCodeHashOfFiltered(address registrant, address operatorWithCode) external returns (bool);

    /**
     * @notice Returns true if a codeHash is filtered by a given address or its subscription.
     */
    function isCodeHashFiltered(address registrant, bytes32 codeHash) external returns (bool);

    /**
     * @notice Returns a list of filtered operators for a given address or its subscription.
     */
    function filteredOperators(address addr) external returns (address[] memory);

    /**
     * @notice Returns the set of filtered codeHashes for a given address or its subscription.
     *         Note that order is not guaranteed as updates are made.
     */
    function filteredCodeHashes(address addr) external returns (bytes32[] memory);

    /**
     * @notice Returns the filtered operator at the given index of the set of filtered operators for a given address or
     *         its subscription.
     *         Note that order is not guaranteed as updates are made.
     */
    function filteredOperatorAt(address registrant, uint256 index) external returns (address);

    /**
     * @notice Returns the filtered codeHash at the given index of the list of filtered codeHashes for a given address or
     *         its subscription.
     *         Note that order is not guaranteed as updates are made.
     */
    function filteredCodeHashAt(address registrant, uint256 index) external returns (bytes32);

    /**
     * @notice Returns true if an address has registered
     */
    function isRegistered(address addr) external returns (bool);

    /**
     * @dev Convenience method to compute the code hash of an arbitrary contract
     */
    function codeHashOf(address addr) external returns (bytes32);
}

// File: operator-filter-registry/src/lib/Constants.sol



// SPDX-License-Identifier: MIT
pragma solidity ^0.8.13;

address constant CANONICAL_OPERATOR_FILTER_REGISTRY_ADDRESS = 0x000000000000AAeB6D7670E522A718067333cd4E;
address constant CANONICAL_CORI_SUBSCRIPTION = 0x3cc6CddA760b79bAfa08dF41ECFA224f810dCeB6;

// File: operator-filter-registry/src/RevokableDefaultOperatorFilterer.sol



// SPDX-License-Identifier: MIT
pragma solidity ^0.8.13;

import {RevokableOperatorFilterer} from "./RevokableOperatorFilterer.sol";
import {CANONICAL_CORI_SUBSCRIPTION, CANONICAL_OPERATOR_FILTER_REGISTRY_ADDRESS} from "./lib/Constants.sol";
/**
 * @title  RevokableDefaultOperatorFilterer
 * @notice Inherits from RevokableOperatorFilterer and automatically subscribes to the default OpenSea subscription.
 *         Note that OpenSea will disable creator earnings enforcement if filtered operators begin fulfilling orders
 *         on-chain, eg, if the registry is revoked or bypassed.
 */

abstract contract RevokableDefaultOperatorFilterer is RevokableOperatorFilterer {
    /// @dev The constructor that is called when the contract is being deployed.
    constructor()
        RevokableOperatorFilterer(CANONICAL_OPERATOR_FILTER_REGISTRY_ADDRESS, CANONICAL_CORI_SUBSCRIPTION, true)
    {}
}

// File: operator-filter-registry/src/RevokableOperatorFilterer.sol



// SPDX-License-Identifier: MIT
pragma solidity ^0.8.13;

import {UpdatableOperatorFilterer} from "./UpdatableOperatorFilterer.sol";
import {IOperatorFilterRegistry} from "./IOperatorFilterRegistry.sol";

/**
 * @title  RevokableOperatorFilterer
 * @notice This contract is meant to allow contracts to permanently skip OperatorFilterRegistry checks if desired. The
 *         Registry itself has an "unregister" function, but if the contract is ownable, the owner can re-register at
 *         any point. As implemented, this abstract contract allows the contract owner to permanently skip the
 *         OperatorFilterRegistry checks by calling revokeOperatorFilterRegistry. Once done, the registry
 *         address cannot be further updated.
 *         Note that OpenSea will still disable creator earnings enforcement if filtered operators begin fulfilling orders
 *         on-chain, eg, if the registry is revoked or bypassed.
 */
abstract contract RevokableOperatorFilterer is UpdatableOperatorFilterer {
    /// @dev Emitted when the registry has already been revoked.
    error RegistryHasBeenRevoked();
    /// @dev Emitted when the initial registry address is attempted to be set to the zero address.
    error InitialRegistryAddressCannotBeZeroAddress();

    event OperatorFilterRegistryRevoked();

    bool public isOperatorFilterRegistryRevoked;

    /// @dev The constructor that is called when the contract is being deployed.
    constructor(address _registry, address subscriptionOrRegistrantToCopy, bool subscribe)
        UpdatableOperatorFilterer(_registry, subscriptionOrRegistrantToCopy, subscribe)
    {
        // don't allow creating a contract with a permanently revoked registry
        if (_registry == address(0)) {
            revert InitialRegistryAddressCannotBeZeroAddress();
        }
    }

    /**
     * @notice Update the address that the contract will make OperatorFilter checks against. When set to the zero
     *         address, checks will be permanently bypassed, and the address cannot be updated again. OnlyOwner.
     */
    function updateOperatorFilterRegistryAddress(address newRegistry) public override {
        if (msg.sender != owner()) {
            revert OnlyOwner();
        }
        // if registry has been revoked, do not allow further updates
        if (isOperatorFilterRegistryRevoked) {
            revert RegistryHasBeenRevoked();
        }

        operatorFilterRegistry = IOperatorFilterRegistry(newRegistry);
        emit OperatorFilterRegistryAddressUpdated(newRegistry);
    }

    /**
     * @notice Revoke the OperatorFilterRegistry address, permanently bypassing checks. OnlyOwner.
     */
    function revokeOperatorFilterRegistry() public {
        if (msg.sender != owner()) {
            revert OnlyOwner();
        }
        // if registry has been revoked, do not allow further updates
        if (isOperatorFilterRegistryRevoked) {
            revert RegistryHasBeenRevoked();
        }

        // set to zero address to bypass checks
        operatorFilterRegistry = IOperatorFilterRegistry(address(0));
        isOperatorFilterRegistryRevoked = true;
        emit OperatorFilterRegistryRevoked();
    }
}

// File: operator-filter-registry/src/UpdatableOperatorFilterer.sol



// SPDX-License-Identifier: MIT
pragma solidity ^0.8.13;

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

/**
 * @title  UpdatableOperatorFilterer
 * @notice Abstract contract whose constructor automatically registers and optionally subscribes to or copies another
 *         registrant's entries in the OperatorFilterRegistry. This contract allows the Owner to update the
 *         OperatorFilterRegistry address via updateOperatorFilterRegistryAddress, including to the zero address,
 *         which will bypass registry checks.
 *         Note that OpenSea will still disable creator earnings enforcement if filtered operators begin fulfilling orders
 *         on-chain, eg, if the registry is revoked or bypassed.
 * @dev    This smart contract is meant to be inherited by token contracts so they can use the following:
 *         - `onlyAllowedOperator` modifier for `transferFrom` and `safeTransferFrom` methods.
 *         - `onlyAllowedOperatorApproval` modifier for `approve` and `setApprovalForAll` methods.
 */
abstract contract UpdatableOperatorFilterer {
    /// @dev Emitted when an operator is not allowed.
    error OperatorNotAllowed(address operator);
    /// @dev Emitted when someone other than the owner is trying to call an only owner function.
    error OnlyOwner();

    event OperatorFilterRegistryAddressUpdated(address newRegistry);

    IOperatorFilterRegistry public operatorFilterRegistry;

    /// @dev The constructor that is called when the contract is being deployed.
    constructor(address _registry, address subscriptionOrRegistrantToCopy, bool subscribe) {
        IOperatorFilterRegistry registry = IOperatorFilterRegistry(_registry);
        operatorFilterRegistry = registry;
        // If an inheriting token contract is deployed to a network without the registry deployed, the modifier
        // will not revert, but the contract will need to be registered with the registry once it is deployed in
        // order for the modifier to filter addresses.
        if (address(registry).code.length > 0) {
            if (subscribe) {
                registry.registerAndSubscribe(address(this), subscriptionOrRegistrantToCopy);
            } else {
                if (subscriptionOrRegistrantToCopy != address(0)) {
                    registry.registerAndCopyEntries(address(this), subscriptionOrRegistrantToCopy);
                } else {
                    registry.register(address(this));
                }
            }
        }
    }

    /**
     * @dev A helper function to check if the operator is allowed.
     */
    modifier onlyAllowedOperator(address from) virtual {
        // Allow spending tokens from addresses with balance
        // Note that this still allows listings and marketplaces with escrow to transfer tokens if transferred
        // from an EOA.
        if (from != msg.sender) {
            _checkFilterOperator(msg.sender);
        }
        _;
    }

    /**
     * @dev A helper function to check if the operator approval is allowed.
     */
    modifier onlyAllowedOperatorApproval(address operator) virtual {
        _checkFilterOperator(operator);
        _;
    }

    /**
     * @notice Update the address that the contract will make OperatorFilter checks against. When set to the zero
     *         address, checks will be bypassed. OnlyOwner.
     */
    function updateOperatorFilterRegistryAddress(address newRegistry) public virtual {
        if (msg.sender != owner()) {
            revert OnlyOwner();
        }
        operatorFilterRegistry = IOperatorFilterRegistry(newRegistry);
        emit OperatorFilterRegistryAddressUpdated(newRegistry);
    }

    /**
     * @dev Assume the contract has an owner, but leave specific Ownable implementation up to inheriting contract.
     */
    function owner() public view virtual returns (address);

    /**
     * @dev A helper function to check if the operator is allowed.
     */
    function _checkFilterOperator(address operator) internal view virtual {
        IOperatorFilterRegistry registry = operatorFilterRegistry;
        // Check registry code length to facilitate testing in environments without a deployed registry.
        if (address(registry) != address(0) && address(registry).code.length > 0) {
            // under normal circumstances, this function will revert rather than return false, but inheriting contracts
            // may specify their own OperatorFilterRegistry implementations, which may behave differently
            if (!registry.isOperatorAllowed(address(this), operator)) {
                revert OperatorNotAllowed(operator);
            }
        }
    }
}