// File: lib/openzeppelin-contracts/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: lib/openzeppelin-contracts/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: lib/openzeppelin-contracts/contracts/token/ERC20/IERC20.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.6.0) (token/ERC20/IERC20.sol)

pragma solidity ^0.8.0;

/**
 * @dev Interface of the ERC20 standard as defined in the EIP.
 */
interface IERC20 {
    /**
     * @dev Emitted when `value` tokens are moved from one account (`from`) to
     * another (`to`).
     *
     * Note that `value` may be zero.
     */
    event Transfer(address indexed from, address indexed to, uint256 value);

    /**
     * @dev Emitted when the allowance of a `spender` for an `owner` is set by
     * a call to {approve}. `value` is the new allowance.
     */
    event Approval(address indexed owner, address indexed spender, uint256 value);

    /**
     * @dev Returns the amount of tokens in existence.
     */
    function totalSupply() external view returns (uint256);

    /**
     * @dev Returns the amount of tokens owned by `account`.
     */
    function balanceOf(address account) external view returns (uint256);

    /**
     * @dev Moves `amount` tokens from the caller's account to `to`.
     *
     * Returns a boolean value indicating whether the operation succeeded.
     *
     * Emits a {Transfer} event.
     */
    function transfer(address to, uint256 amount) external returns (bool);

    /**
     * @dev Returns the remaining number of tokens that `spender` will be
     * allowed to spend on behalf of `owner` through {transferFrom}. This is
     * zero by default.
     *
     * This value changes when {approve} or {transferFrom} are called.
     */
    function allowance(address owner, address spender) external view returns (uint256);

    /**
     * @dev Sets `amount` as the allowance of `spender` over the caller's tokens.
     *
     * Returns a boolean value indicating whether the operation succeeded.
     *
     * IMPORTANT: Beware that changing an allowance with this method brings the risk
     * that someone may use both the old and the new allowance by unfortunate
     * transaction ordering. One possible solution to mitigate this race
     * condition is to first reduce the spender's allowance to 0 and set the
     * desired value afterwards:
     * https://github.com/ethereum/EIPs/issues/20#issuecomment-263524729
     *
     * Emits an {Approval} event.
     */
    function approve(address spender, uint256 amount) external returns (bool);

    /**
     * @dev Moves `amount` tokens from `from` to `to` using the
     * allowance mechanism. `amount` is then deducted from the caller's
     * allowance.
     *
     * Returns a boolean value indicating whether the operation succeeded.
     *
     * Emits a {Transfer} event.
     */
    function transferFrom(
        address from,
        address to,
        uint256 amount
    ) external returns (bool);
}

// File: lib/openzeppelin-contracts/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: lib/openzeppelin-contracts/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: lib/openzeppelin-contracts/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: lib/openzeppelin-contracts/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: lib/openzeppelin-contracts/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: lib/solmate/src/utils/FixedPointMathLib.sol



// SPDX-License-Identifier: MIT
pragma solidity >=0.8.0;

/// @notice Arithmetic library with operations for fixed-point numbers.
/// @author Solmate (https://github.com/Rari-Capital/solmate/blob/main/src/utils/FixedPointMathLib.sol)
library FixedPointMathLib {
    /*//////////////////////////////////////////////////////////////
                    SIMPLIFIED FIXED POINT OPERATIONS
    //////////////////////////////////////////////////////////////*/

    uint256 internal constant WAD = 1e18; // The scalar of ETH and most ERC20s.

    function mulWadDown(uint256 x, uint256 y) internal pure returns (uint256) {
        return mulDivDown(x, y, WAD); // Equivalent to (x * y) / WAD rounded down.
    }

    function mulWadUp(uint256 x, uint256 y) internal pure returns (uint256) {
        return mulDivUp(x, y, WAD); // Equivalent to (x * y) / WAD rounded up.
    }

    function divWadDown(uint256 x, uint256 y) internal pure returns (uint256) {
        return mulDivDown(x, WAD, y); // Equivalent to (x * WAD) / y rounded down.
    }

    function divWadUp(uint256 x, uint256 y) internal pure returns (uint256) {
        return mulDivUp(x, WAD, y); // Equivalent to (x * WAD) / y rounded up.
    }

    function powWad(int256 x, int256 y) internal pure returns (int256) {
        // Equivalent to x to the power of y because x ** y = (e ** ln(x)) ** y = e ** (ln(x) * y)
        return expWad((lnWad(x) * y) / int256(WAD)); // Using ln(x) means x must be greater than 0.
    }

    function expWad(int256 x) internal pure returns (int256 r) {
        unchecked {
            // When the result is < 0.5 we return zero. This happens when
            // x <= floor(log(0.5e18) * 1e18) ~ -42e18
            if (x <= -42139678854452767551) return 0;

            // When the result is > (2**255 - 1) / 1e18 we can not represent it as an
            // int. This happens when x >= floor(log((2**255 - 1) / 1e18) * 1e18) ~ 135.
            if (x >= 135305999368893231589) revert("EXP_OVERFLOW");

            // x is now in the range (-42, 136) * 1e18. Convert to (-42, 136) * 2**96
            // for more intermediate precision and a binary basis. This base conversion
            // is a multiplication by 1e18 / 2**96 = 5**18 / 2**78.
            x = (x << 78) / 5**18;

            // Reduce range of x to (-½ ln 2, ½ ln 2) * 2**96 by factoring out powers
            // of two such that exp(x) = exp(x') * 2**k, where k is an integer.
            // Solving this gives k = round(x / log(2)) and x' = x - k * log(2).
            int256 k = ((x << 96) / 54916777467707473351141471128 + 2**95) >> 96;
            x = x - k * 54916777467707473351141471128;

            // k is in the range [-61, 195].

            // Evaluate using a (6, 7)-term rational approximation.
            // p is made monic, we'll multiply by a scale factor later.
            int256 y = x + 1346386616545796478920950773328;
            y = ((y * x) >> 96) + 57155421227552351082224309758442;
            int256 p = y + x - 94201549194550492254356042504812;
            p = ((p * y) >> 96) + 28719021644029726153956944680412240;
            p = p * x + (4385272521454847904659076985693276 << 96);

            // We leave p in 2**192 basis so we don't need to scale it back up for the division.
            int256 q = x - 2855989394907223263936484059900;
            q = ((q * x) >> 96) + 50020603652535783019961831881945;
            q = ((q * x) >> 96) - 533845033583426703283633433725380;
            q = ((q * x) >> 96) + 3604857256930695427073651918091429;
            q = ((q * x) >> 96) - 14423608567350463180887372962807573;
            q = ((q * x) >> 96) + 26449188498355588339934803723976023;

            assembly {
                // Div in assembly because solidity adds a zero check despite the unchecked.
                // The q polynomial won't have zeros in the domain as all its roots are complex.
                // No scaling is necessary because p is already 2**96 too large.
                r := sdiv(p, q)
            }

            // r should be in the range (0.09, 0.25) * 2**96.

            // We now need to multiply r by:
            // * the scale factor s = ~6.031367120.
            // * the 2**k factor from the range reduction.
            // * the 1e18 / 2**96 factor for base conversion.
            // We do this all at once, with an intermediate result in 2**213
            // basis, so the final right shift is always by a positive amount.
            r = int256((uint256(r) * 3822833074963236453042738258902158003155416615667) >> uint256(195 - k));
        }
    }

    function lnWad(int256 x) internal pure returns (int256 r) {
        unchecked {
            require(x > 0, "UNDEFINED");

            // We want to convert x from 10**18 fixed point to 2**96 fixed point.
            // We do this by multiplying by 2**96 / 10**18. But since
            // ln(x * C) = ln(x) + ln(C), we can simply do nothing here
            // and add ln(2**96 / 10**18) at the end.

            // Reduce range of x to (1, 2) * 2**96
            // ln(2^k * x) = k * ln(2) + ln(x)
            int256 k = int256(log2(uint256(x))) - 96;
            x <<= uint256(159 - k);
            x = int256(uint256(x) >> 159);

            // Evaluate using a (8, 8)-term rational approximation.
            // p is made monic, we will multiply by a scale factor later.
            int256 p = x + 3273285459638523848632254066296;
            p = ((p * x) >> 96) + 24828157081833163892658089445524;
            p = ((p * x) >> 96) + 43456485725739037958740375743393;
            p = ((p * x) >> 96) - 11111509109440967052023855526967;
            p = ((p * x) >> 96) - 45023709667254063763336534515857;
            p = ((p * x) >> 96) - 14706773417378608786704636184526;
            p = p * x - (795164235651350426258249787498 << 96);

            // We leave p in 2**192 basis so we don't need to scale it back up for the division.
            // q is monic by convention.
            int256 q = x + 5573035233440673466300451813936;
            q = ((q * x) >> 96) + 71694874799317883764090561454958;
            q = ((q * x) >> 96) + 283447036172924575727196451306956;
            q = ((q * x) >> 96) + 401686690394027663651624208769553;
            q = ((q * x) >> 96) + 204048457590392012362485061816622;
            q = ((q * x) >> 96) + 31853899698501571402653359427138;
            q = ((q * x) >> 96) + 909429971244387300277376558375;
            assembly {
                // Div in assembly because solidity adds a zero check despite the unchecked.
                // The q polynomial is known not to have zeros in the domain.
                // No scaling required because p is already 2**96 too large.
                r := sdiv(p, q)
            }

            // r is in the range (0, 0.125) * 2**96

            // Finalization, we need to:
            // * multiply by the scale factor s = 5.549…
            // * add ln(2**96 / 10**18)
            // * add k * ln(2)
            // * multiply by 10**18 / 2**96 = 5**18 >> 78

            // mul s * 5e18 * 2**96, base is now 5**18 * 2**192
            r *= 1677202110996718588342820967067443963516166;
            // add ln(2) * k * 5e18 * 2**192
            r += 16597577552685614221487285958193947469193820559219878177908093499208371 * k;
            // add ln(2**96 / 10**18) * 5e18 * 2**192
            r += 600920179829731861736702779321621459595472258049074101567377883020018308;
            // base conversion: mul 2**18 / 2**192
            r >>= 174;
        }
    }

    /*//////////////////////////////////////////////////////////////
                    LOW LEVEL FIXED POINT OPERATIONS
    //////////////////////////////////////////////////////////////*/

    function mulDivDown(
        uint256 x,
        uint256 y,
        uint256 denominator
    ) internal pure returns (uint256 z) {
        assembly {
            // Store x * y in z for now.
            z := mul(x, y)

            // Equivalent to require(denominator != 0 && (x == 0 || (x * y) / x == y))
            if iszero(and(iszero(iszero(denominator)), or(iszero(x), eq(div(z, x), y)))) {
                revert(0, 0)
            }

            // Divide z by the denominator.
            z := div(z, denominator)
        }
    }

    function mulDivUp(
        uint256 x,
        uint256 y,
        uint256 denominator
    ) internal pure returns (uint256 z) {
        assembly {
            // Store x * y in z for now.
            z := mul(x, y)

            // Equivalent to require(denominator != 0 && (x == 0 || (x * y) / x == y))
            if iszero(and(iszero(iszero(denominator)), or(iszero(x), eq(div(z, x), y)))) {
                revert(0, 0)
            }

            // First, divide z - 1 by the denominator and add 1.
            // We allow z - 1 to underflow if z is 0, because we multiply the
            // end result by 0 if z is zero, ensuring we return 0 if z is zero.
            z := mul(iszero(iszero(z)), add(div(sub(z, 1), denominator), 1))
        }
    }

    function rpow(
        uint256 x,
        uint256 n,
        uint256 scalar
    ) internal pure returns (uint256 z) {
        assembly {
            switch x
            case 0 {
                switch n
                case 0 {
                    // 0 ** 0 = 1
                    z := scalar
                }
                default {
                    // 0 ** n = 0
                    z := 0
                }
            }
            default {
                switch mod(n, 2)
                case 0 {
                    // If n is even, store scalar in z for now.
                    z := scalar
                }
                default {
                    // If n is odd, store x in z for now.
                    z := x
                }

                // Shifting right by 1 is like dividing by 2.
                let half := shr(1, scalar)

                for {
                    // Shift n right by 1 before looping to halve it.
                    n := shr(1, n)
                } n {
                    // Shift n right by 1 each iteration to halve it.
                    n := shr(1, n)
                } {
                    // Revert immediately if x ** 2 would overflow.
                    // Equivalent to iszero(eq(div(xx, x), x)) here.
                    if shr(128, x) {
                        revert(0, 0)
                    }

                    // Store x squared.
                    let xx := mul(x, x)

                    // Round to the nearest number.
                    let xxRound := add(xx, half)

                    // Revert if xx + half overflowed.
                    if lt(xxRound, xx) {
                        revert(0, 0)
                    }

                    // Set x to scaled xxRound.
                    x := div(xxRound, scalar)

                    // If n is even:
                    if mod(n, 2) {
                        // Compute z * x.
                        let zx := mul(z, x)

                        // If z * x overflowed:
                        if iszero(eq(div(zx, x), z)) {
                            // Revert if x is non-zero.
                            if iszero(iszero(x)) {
                                revert(0, 0)
                            }
                        }

                        // Round to the nearest number.
                        let zxRound := add(zx, half)

                        // Revert if zx + half overflowed.
                        if lt(zxRound, zx) {
                            revert(0, 0)
                        }

                        // Return properly scaled zxRound.
                        z := div(zxRound, scalar)
                    }
                }
            }
        }
    }

    /*//////////////////////////////////////////////////////////////
                        GENERAL NUMBER UTILITIES
    //////////////////////////////////////////////////////////////*/

    function sqrt(uint256 x) internal pure returns (uint256 z) {
        assembly {
            let y := x // We start y at x, which will help us make our initial estimate.

            z := 181 // The "correct" value is 1, but this saves a multiplication later.

            // This segment is to get a reasonable initial estimate for the Babylonian method. With a bad
            // start, the correct # of bits increases ~linearly each iteration instead of ~quadratically.

            // We check y >= 2^(k + 8) but shift right by k bits
            // each branch to ensure that if x >= 256, then y >= 256.
            if iszero(lt(y, 0x10000000000000000000000000000000000)) {
                y := shr(128, y)
                z := shl(64, z)
            }
            if iszero(lt(y, 0x1000000000000000000)) {
                y := shr(64, y)
                z := shl(32, z)
            }
            if iszero(lt(y, 0x10000000000)) {
                y := shr(32, y)
                z := shl(16, z)
            }
            if iszero(lt(y, 0x1000000)) {
                y := shr(16, y)
                z := shl(8, z)
            }

            // Goal was to get z*z*y within a small factor of x. More iterations could
            // get y in a tighter range. Currently, we will have y in [256, 256*2^16).
            // We ensured y >= 256 so that the relative difference between y and y+1 is small.
            // That's not possible if x < 256 but we can just verify those cases exhaustively.

            // Now, z*z*y <= x < z*z*(y+1), and y <= 2^(16+8), and either y >= 256, or x < 256.
            // Correctness can be checked exhaustively for x < 256, so we assume y >= 256.
            // Then z*sqrt(y) is within sqrt(257)/sqrt(256) of sqrt(x), or about 20bps.

            // For s in the range [1/256, 256], the estimate f(s) = (181/1024) * (s+1) is in the range
            // (1/2.84 * sqrt(s), 2.84 * sqrt(s)), with largest error when s = 1 and when s = 256 or 1/256.

            // Since y is in [256, 256*2^16), let a = y/65536, so that a is in [1/256, 256). Then we can estimate
            // sqrt(y) using sqrt(65536) * 181/1024 * (a + 1) = 181/4 * (y + 65536)/65536 = 181 * (y + 65536)/2^18.

            // There is no overflow risk here since y < 2^136 after the first branch above.
            z := shr(18, mul(z, add(y, 65536))) // A mul() is saved from starting z at 181.

            // Given the worst case multiplicative error of 2.84 above, 7 iterations should be enough.
            z := shr(1, add(z, div(x, z)))
            z := shr(1, add(z, div(x, z)))
            z := shr(1, add(z, div(x, z)))
            z := shr(1, add(z, div(x, z)))
            z := shr(1, add(z, div(x, z)))
            z := shr(1, add(z, div(x, z)))
            z := shr(1, add(z, div(x, z)))

            // If x+1 is a perfect square, the Babylonian method cycles between
            // floor(sqrt(x)) and ceil(sqrt(x)). This statement ensures we return floor.
            // See: https://en.wikipedia.org/wiki/Integer_square_root#Using_only_integer_division
            // Since the ceil is rare, we save gas on the assignment and repeat division in the rare case.
            // If you don't care whether the floor or ceil square root is returned, you can remove this statement.
            z := sub(z, lt(div(x, z), z))
        }
    }

    function log2(uint256 x) internal pure returns (uint256 r) {
        require(x > 0, "UNDEFINED");

        assembly {
            r := shl(7, lt(0xffffffffffffffffffffffffffffffff, x))
            r := or(r, shl(6, lt(0xffffffffffffffff, shr(r, x))))
            r := or(r, shl(5, lt(0xffffffff, shr(r, x))))
            r := or(r, shl(4, lt(0xffff, shr(r, x))))
            r := or(r, shl(3, lt(0xff, shr(r, x))))
            r := or(r, shl(2, lt(0xf, shr(r, x))))
            r := or(r, shl(1, lt(0x3, shr(r, x))))
            r := or(r, lt(0x1, shr(r, x)))
        }
    }

    function unsafeMod(uint256 x, uint256 y) internal pure returns (uint256 z) {
        assembly {
            // z will equal 0 if y is 0, unlike in Solidity where it will revert.
            z := mod(x, y)
        }
    }

    function unsafeDiv(uint256 x, uint256 y) internal pure returns (uint256 z) {
        assembly {
            // z will equal 0 if y is 0, unlike in Solidity where it will revert.
            z := div(x, y)
        }
    }

    /// @dev Will return 0 instead of reverting if y is zero.
    function unsafeDivUp(uint256 x, uint256 y) internal pure returns (uint256 z) {
        assembly {
            // Add 1 to x * y if x % y > 0.
            z := add(gt(mod(x, y), 0), div(x, y))
        }
    }
}

// File: src/common/Governable.sol



// SPDX-License-Identifier: MIT
pragma solidity ^0.8.10;

import {AccessControl} from "@openzeppelin/contracts/access/AccessControl.sol";

abstract contract Governable is AccessControl {
    bytes32 public constant GOVERNOR = bytes32("GOVERNOR");

    constructor(address _governor) {
        _grantRole(GOVERNOR, _governor);
    }

    modifier onlyGovernor() {
        _onlyGovernor();
        _;
    }

    function updateGovernor(address _newGovernor) external onlyGovernor {
        _revokeRole(GOVERNOR, msg.sender);
        _grantRole(GOVERNOR, _newGovernor);

        emit GovernorUpdated(msg.sender, _newGovernor);
    }

    function _onlyGovernor() private view {
        if (!hasRole(GOVERNOR, msg.sender)) {
            revert CallerIsNotGovernor();
        }
    }

    event GovernorUpdated(address _oldGovernor, address _newGovernor);

    error CallerIsNotGovernor();
}

// File: src/common/OperableKeepable.sol



// SPDX-License-Identifier: MIT
pragma solidity ^0.8.10;

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

abstract contract OperableKeepable is Governable {
    bytes32 public constant OPERATOR = bytes32("OPERATOR");
    bytes32 public constant KEEPER = bytes32("KEEPER");

    modifier onlyOperator() {
        if (!hasRole(OPERATOR, msg.sender)) {
            revert CallerIsNotOperator();
        }

        _;
    }

    modifier onlyKeeper() {
        if (!hasRole(KEEPER, msg.sender)) {
            revert CallerIsNotKeeper();
        }

        _;
    }

    modifier onlyOperatorOrKeeper() {
        if (!(hasRole(OPERATOR, msg.sender) || hasRole(KEEPER, msg.sender))) {
            revert CallerIsNotAllowed();
        }

        _;
    }

    modifier onlyGovernorOrKeeper() {
        if (!(hasRole(GOVERNOR, msg.sender) || hasRole(KEEPER, msg.sender))) {
            revert CallerIsNotAllowed();
        }

        _;
    }

    function addOperator(address _newOperator) external onlyGovernor {
        _grantRole(OPERATOR, _newOperator);

        emit OperatorAdded(_newOperator);
    }

    function removeOperator(address _operator) external onlyGovernor {
        _revokeRole(OPERATOR, _operator);

        emit OperatorRemoved(_operator);
    }

    function addKeeper(address _newKeeper) external onlyGovernor {
        _grantRole(KEEPER, _newKeeper);

        emit KeeperAdded(_newKeeper);
    }

    function removeKeeper(address _operator) external onlyGovernor {
        _revokeRole(KEEPER, _operator);

        emit KeeperRemoved(_operator);
    }

    event OperatorAdded(address _newOperator);
    event OperatorRemoved(address _operator);

    error CallerIsNotOperator();

    event KeeperAdded(address _newKeeper);
    event KeeperRemoved(address _operator);

    error CallerIsNotKeeper();

    error CallerIsNotAllowed();
}

// File: src/compounder/vaults/AuraVirtualVault.sol



// SPDX-License-Identifier: UNLICENSED

// Copyright (c) 2023 JonesDAO - All rights reserved
// Jones DAO: https://www.jonesdao.io/

pragma solidity ^0.8.10;

import {IStrategy} from "src/interfaces/IStrategy.sol";
import {IAuraRouter} from "src/interfaces/IAuraRouter.sol";
import {IAuraVirtualVault} from "src/interfaces/IAuraVirtualVault.sol";
import {OperableKeepable, Governable} from "src/common/OperableKeepable.sol";
import {Errors} from "src/errors/Errors.sol";
import {FixedPointMathLib} from "solmate/utils/FixedPointMathLib.sol";
import {IERC20} from "@openzeppelin/contracts/token/ERC20/IERC20.sol";

contract AuraVirtualVault is IAuraVirtualVault, OperableKeepable {
    using FixedPointMathLib for uint256;

    IAuraRouter public router;
    IStrategy public strategy;
    IERC20 public constant AURA = IERC20(0xC0c293ce456fF0ED870ADd98a0828Dd4d2903DBF);
    address public incentiveReceiver;

    mapping(address => uint256) public virtualShares;

    uint256 public totalSupply;

    event Deposit(address indexed receiver, uint256 assets);
    event Withdraw(address indexed receiver, uint256 assets);

    constructor() Governable(msg.sender) {}

    // Operator functions
    function deposit(address receiver, uint256 assets) external onlyOperator returns (uint256 shares) {
        if (assets == 0) {
            revert Errors.ZeroAmount();
        }

        shares = previewDeposit(assets);

        _mintVirtual(receiver, shares);

        emit Deposit(receiver, assets);
    }

    function withdraw(address receiver, uint256 assets) external onlyOperator {
        uint256 shares = previewWithdraw(assets);
        uint256 userShares = virtualShares[receiver];

        if (shares > userShares) {
            revert Errors.InsufficientAssets();
        }

        _burnVirtual(receiver, shares);

        emit Withdraw(receiver, assets);
    }

    function mint(uint256 _shares, address _to) public onlyOperator {
        _mintVirtual(_to, _shares);
    }

    function burn(address _user, uint256 _shares) public onlyOperator {
        uint256 userShares = virtualShares[_user];

        if (_shares > userShares) {
            revert Errors.InsufficientAssets();
        }

        _burnVirtual(_user, _shares);
    }

    // Private functions
    function _mintVirtual(address _to, uint256 _shares) private {
        if (_to == address(0)) {
            revert Errors.ZeroAddress();
        }

        unchecked {
            totalSupply += _shares;
            virtualShares[_to] += _shares;
        }
    }

    function _burnVirtual(address _user, uint256 _shares) private {
        if (_user == address(0)) {
            revert Errors.ZeroAddress();
        }

        if (_shares > virtualShares[_user]) {
            revert Errors.InsufficientShares();
        }

        unchecked {
            virtualShares[_user] -= _shares;
            totalSupply -= _shares;
        }
    }

    // Public view functions
    function convertToShares(uint256 _assets) public view returns (uint256) {
        uint256 supply = totalSupply; // Saves an extra SLOAD if totalSupply is non-zero.

        return supply == 0 ? _assets : _assets.mulDivDown(supply, totalAssets());
    }

    function convertToAssets(uint256 _shares) public view returns (uint256) {
        uint256 supply = totalSupply; // Saves an extra SLOAD if totalSupply is non-zero.

        return supply == 0 ? _shares : _shares.mulDivDown(totalAssets(), supply);
    }

    function previewRedeem(uint256 _shares) public view returns (uint256) {
        return convertToAssets(_shares);
    }

    function previewDeposit(uint256 _assets) public view returns (uint256) {
        return convertToShares(_assets);
    }

    function previewMint(uint256 shares) public view returns (uint256) {
        uint256 supply = totalSupply; // Saves an extra SLOAD if totalSupply is non-zero.

        return supply == 0 ? shares : shares.mulDivUp(totalAssets(), supply);
    }

    function previewWithdraw(uint256 assets) public view returns (uint256) {
        uint256 supply = totalSupply; // Saves an extra SLOAD if totalSupply is non-zero.

        return supply == 0 ? assets : assets.mulDivUp(supply, totalAssets());
    }

    function totalAssets() public view returns (uint256) {
        (uint256 assets,) = strategy.vaultsPosition();
        return assets - router.totalWithdrawRequestsNoTokenized();
    }

    // Gov functions
    function setRouter(address _router) external onlyGovernor {
        if (_router == address(0)) {
            revert Errors.ZeroAddress();
        }
        router = IAuraRouter(_router);
    }

    function setStrategy(address _strategy) external onlyGovernor {
        if (_strategy == address(0)) {
            revert Errors.ZeroAddress();
        }
        strategy = IStrategy(_strategy);
    }

    function setReceiver(address _receiver) external onlyGovernor {
        if (_receiver == address(0)) {
            revert Errors.ZeroAddress();
        }
        incentiveReceiver = _receiver;
    }
}

// File: src/errors/Errors.sol



// SPDX-License-Identifier: MIT
pragma solidity ^0.8.10;

interface Errors {
    // Vault
    error ZeroAddress();
    error ZeroAmount();
    error DepositCooldown();
    error WithdrawCooldown();
    error InsufficientShares();
    error InsufficientAssets();
    error InsufficientRequest();
    error notOwner();

    // Strategy
    error OnlyFromHiddenHand();
    error Unauthorized();
    error InsufficientWithdraw();
    error NoReward();
    error NoSwapper();

    // Swapper
    error Slippage(uint256 amountOut, uint256 minAmountOut);
    error InvalidToken();

    // Misc.
    error InvalidTokenIn(address have, address want);
    error InvalidTokenOut(address have, address want);
    error InvalidAmountIn(uint256 have, uint256 want);
    error InvalidMinAmountOut(uint256 have, uint256 want);
    error InvalidReceiver(address have, address want);
    error InvalidPathSegment(address from, address to);
    error EmptyPath();
    error EmptyTokenIn();
    error EmptyTokenOut();
    error EmptyRouter();
}

// File: src/interfaces/IAuraRouter.sol



// SPDX-License-Identifier: MIT
pragma solidity ^0.8.10;

interface IAuraRouter {
    function deposit(uint256 _assets, bool _tokenized) external returns (uint256);
    function withdrawRequest(uint256 _shares, bool _tokenized) external;
    function withdraw(uint256 _assets, bool _tokenized) external returns (uint256);
    function rehypothecate(uint256 assets, bool _tokenized) external returns (uint256);

    function noTokenizedUserInfo(address _user) external view returns (uint128, uint64, uint64);
    function lsdUserInfo(address _user) external view returns (uint128, uint64, uint64);

    function totalWithdrawRequests() external view returns (uint256);
    function totalWithdrawRequestsLSD() external view returns (uint256);
    function totalWithdrawRequestsNoTokenized() external view returns (uint256);
}

// File: src/interfaces/IAuraVirtualVault.sol



// SPDX-License-Identifier: MIT
pragma solidity ^0.8.10;

interface IAuraVirtualVault {
    function deposit(address receiver, uint256 assets) external returns (uint256);
    function withdraw(address receiver, uint256 assets) external;
    function totalAssets() external view returns (uint256);
    function previewRedeem(uint256 _shares) external view returns (uint256);
    function burn(address _user, uint256 _shares) external;
    function virtualShares(address _user) external view returns (uint256);
}

// File: src/interfaces/IStrategy.sol



// SPDX-License-Identifier: MIT
pragma solidity ^0.8.10;

interface IStrategy {
    function totalAssets() external view returns (uint256);
    function totalAssetsLSD() external view returns (uint256);
    function totalNoTokenizedAssets() external view returns (uint256);

    function deposit(uint256 auraAmount, bool tokenized) external;
    function withdrawRetention() external view returns (address recipient, uint64 percent);
    function withdraw(address user, uint256 amount, bool tokenized) external returns (uint256);

    function afterRehyphotecate(uint256 auraAmount, bool tokenized) external;

    function vaultsPosition() external view returns (uint256, uint256);
}