// File: @chainlink/contracts/src/v0.6/interfaces/AggregatorV3Interface.sol



// SPDX-License-Identifier: MIT
pragma solidity >=0.6.0;

interface AggregatorV3Interface {

  function decimals() external view returns (uint8);
  function description() external view returns (string memory);
  function version() external view returns (uint256);

  // getRoundData and latestRoundData should both raise "No data present"
  // if they do not have data to report, instead of returning unset values
  // which could be misinterpreted as actual reported values.
  function getRoundData(uint80 _roundId)
    external
    view
    returns (
      uint80 roundId,
      int256 answer,
      uint256 startedAt,
      uint256 updatedAt,
      uint80 answeredInRound
    );
  function latestRoundData()
    external
    view
    returns (
      uint80 roundId,
      int256 answer,
      uint256 startedAt,
      uint256 updatedAt,
      uint80 answeredInRound
    );

}

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



// SPDX-License-Identifier: MIT

pragma solidity ^0.8.0;

import "../utils/Context.sol";

/**
 * @dev Contract module which provides a basic access control mechanism, where
 * there is an account (an owner) that can be granted exclusive access to
 * specific functions.
 *
 * By default, the owner account will be the one that deploys the contract. This
 * can later be changed with {transferOwnership}.
 *
 * This module is used through inheritance. It will make available the modifier
 * `onlyOwner`, which can be applied to your functions to restrict their use to
 * the owner.
 */
abstract contract Ownable is Context {
    address private _owner;

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

    /**
     * @dev Initializes the contract setting the deployer as the initial owner.
     */
    constructor() {
        _setOwner(_msgSender());
    }

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

    /**
     * @dev Throws if called by any account other than the owner.
     */
    modifier onlyOwner() {
        require(owner() == _msgSender(), "Ownable: caller is not the owner");
        _;
    }

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

    /**
     * @dev Transfers ownership of the contract to a new account (`newOwner`).
     * Can only be called by the current owner.
     */
    function transferOwnership(address newOwner) public virtual onlyOwner {
        require(newOwner != address(0), "Ownable: new owner is the zero address");
        _setOwner(newOwner);
    }

    function _setOwner(address newOwner) private {
        address oldOwner = _owner;
        _owner = newOwner;
        emit OwnershipTransferred(oldOwner, newOwner);
    }
}

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



// SPDX-License-Identifier: MIT

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 make it call a
     * `private` function that does the actual work.
     */
    modifier nonReentrant() {
        // On the first call to nonReentrant, _notEntered will be true
        require(_status != _ENTERED, "ReentrancyGuard: reentrant call");

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

        _;

        // 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/ERC20/IERC20.sol



// SPDX-License-Identifier: MIT

pragma solidity ^0.8.0;

/**
 * @dev Interface of the ERC20 standard as defined in the EIP.
 */
interface IERC20 {
    /**
     * @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 `recipient`.
     *
     * Returns a boolean value indicating whether the operation succeeded.
     *
     * Emits a {Transfer} event.
     */
    function transfer(address recipient, 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 `sender` to `recipient` 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 sender,
        address recipient,
        uint256 amount
    ) external returns (bool);

    /**
     * @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);
}

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



// SPDX-License-Identifier: MIT

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`, 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 be 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: Usage of this method is discouraged, use {safeTransferFrom} whenever possible.
     *
     * 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 Returns the account approved for `tokenId` token.
     *
     * Requirements:
     *
     * - `tokenId` must exist.
     */
    function getApproved(uint256 tokenId) external view returns (address operator);

    /**
     * @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 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);

    /**
     * @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;
}

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



// SPDX-License-Identifier: MIT

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 `IERC721.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

pragma solidity ^0.8.0;

/**
 * @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
     * ====
     */
    function isContract(address account) internal view returns (bool) {
        // This method relies on extcodesize, which returns 0 for contracts in
        // construction, since the code is only stored at the end of the
        // constructor execution.

        uint256 size;
        assembly {
            size := extcodesize(account)
        }
        return size > 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 functionCall(target, data, "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");
        require(isContract(target), "Address: call to non-contract");

        (bool success, bytes memory returndata) = target.call{value: value}(data);
        return _verifyCallResult(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) {
        require(isContract(target), "Address: static call to non-contract");

        (bool success, bytes memory returndata) = target.staticcall(data);
        return _verifyCallResult(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) {
        require(isContract(target), "Address: delegate call to non-contract");

        (bool success, bytes memory returndata) = target.delegatecall(data);
        return _verifyCallResult(success, returndata, errorMessage);
    }

    function _verifyCallResult(
        bool success,
        bytes memory returndata,
        string memory errorMessage
    ) private pure returns (bytes memory) {
        if (success) {
            return returndata;
        } else {
            // Look for revert reason and bubble it up if present
            if (returndata.length > 0) {
                // The easiest way to bubble the revert reason is using memory via assembly

                assembly {
                    let returndata_size := mload(returndata)
                    revert(add(32, returndata), returndata_size)
                }
            } else {
                revert(errorMessage);
            }
        }
    }
}

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



// SPDX-License-Identifier: MIT

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/introspection/IERC165.sol



// SPDX-License-Identifier: MIT

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: @paulrberg/contracts/math/PRBMath.sol



// SPDX-License-Identifier: UNLICENSED
pragma solidity >=0.8.4;

import "prb-math/contracts/PRBMath.sol";

// File: @paulrberg/contracts/math/PRBMathUD60x18.sol



// SPDX-License-Identifier: UNLICENSED
pragma solidity >=0.8.4;

import "prb-math/contracts/PRBMathUD60x18.sol";

// File: contracts/TerminalV1Rescue.sol



// SPDX-License-Identifier: MIT
pragma solidity 0.8.6;

import '@openzeppelin/contracts/security/ReentrancyGuard.sol';
import '@openzeppelin/contracts/utils/Address.sol';

import '@paulrberg/contracts/math/PRBMath.sol';
import '@paulrberg/contracts/math/PRBMathUD60x18.sol';

import './interfaces/ITerminalV1Rescue.sol';
import './abstract/JuiceboxProject.sol';
import './abstract/Operatable.sol';

import './libraries/Operations.sol';

/**
  @notice 
  Terminal allowing allow listed projects with one-time funding cycles to rescue stuck ETH.
*/
contract TerminalV1Rescue is Operatable, ITerminalV1Rescue, ITerminal, ReentrancyGuard, Ownable {
  /// @notice The Projects contract which mints ERC-721's that represent project ownership and transfers.
  IProjects public immutable override projects;

  /// @notice The contract storing all funding cycle configurations.
  IFundingCycles public immutable override fundingCycles;

  /// @notice The contract that manages Ticket printing and redeeming.
  ITicketBooth public immutable override ticketBooth;

  /// @notice The directory of terminals.
  ITerminalDirectory public immutable override terminalDirectory;

  /// @notice The amount of ETH that each project is responsible for.
  mapping(uint256 => uint256) public override balanceOf;

  /// @notice The addresses that are allowed to be rescued.
  mapping(uint256 => bool) public override rescueAllowed;

  // Whether or not a particular contract is available for projects to migrate their funds and Tickets to.
  mapping(ITerminal => bool) public override migrationIsAllowed;

  /** 
    @param _projects A Projects contract which mints ERC-721's that represent project ownership and transfers.
    @param _fundingCycles A funding cycle configuration store.
    @param _ticketBooth A contract that manages Ticket printing and redeeming.
    @param _operatorStore A contract storing operator assignments.
    @param _terminalDirectory A directory of a project's current Juicebox terminal to receive payments in.
  */
  constructor(
    IProjects _projects,
    IFundingCycles _fundingCycles,
    ITicketBooth _ticketBooth,
    IOperatorStore _operatorStore,
    ITerminalDirectory _terminalDirectory,
    address _owner
  ) Operatable(_operatorStore) {
    require(
      _projects != IProjects(address(0)) &&
        _fundingCycles != IFundingCycles(address(0)) &&
        _ticketBooth != ITicketBooth(address(0)) &&
        _terminalDirectory != ITerminalDirectory(address(0)) &&
        _owner != address(0),
      'zero address'
    );
    projects = _projects;
    fundingCycles = _fundingCycles;
    ticketBooth = _ticketBooth;
    terminalDirectory = _terminalDirectory;

    transferOwnership(_owner);
  }

  /** 
    @notice 
    Allows a project to print tickets for a specified beneficiary.

    @dev
    Only a project's owner or a designated operator can print tickets.

    @param _projectId The ID of the project to print tickets for.
    @param _amount The amount of tickets to print.
    @param _beneficiary The address to send the printed tickets to.
    @param _memo A memo to leave with the printing.
    @param _preferUnstakedTickets If there is a preference to unstake the printed tickets.
  */
  function printTickets(
    uint256 _projectId,
    uint256 _amount,
    address _beneficiary,
    string memory _memo,
    bool _preferUnstakedTickets
  )
    external
    override
    requirePermission(projects.ownerOf(_projectId), _projectId, Operations.PrintTickets)
  {
    // Can't send to the zero address.
    require(_beneficiary != address(0), 'zero address');

    // Print the project's tickets for the beneficiary.
    ticketBooth.print(_beneficiary, _projectId, _amount, _preferUnstakedTickets);

    emit PrintTickets(_projectId, _beneficiary, _amount, _memo, msg.sender);
  }

  /** 
    @notice
    A function that burns the supply of the dead address for a project. 

    @dev
    Callable only by project owner, if rescue is allowed by the projectId, if the project's current funding cycle is non recurring.

    @param _projectId The ID of the project whose ETH is being resued.
    @param _beneficiary The recipient of the resucued funds.
    @param _amount The amount to rescue as a fixed point number.
  */
  function rescue(
    uint256 _projectId,
    address payable _beneficiary,
    uint256 _amount
  ) external override nonReentrant {
    // Must be project owner.
    require(msg.sender == projects.ownerOf(_projectId), 'not owner');

    // Project must be allow listed.
    require(rescueAllowed[_projectId], 'not allowed');

    // Amount must have been specified.
    require(_amount > 0, 'must be rescuing something');

    // Get a referrence to the original balance.
    uint256 _originalBalance = balanceOf[_projectId];

    // Balance must exist.
    require(_originalBalance >= _amount, 'not enough to rescue');

    // Get a reference to the current funding cycle for the project.
    FundingCycle memory _fundingCycle = fundingCycles.get(fundingCycles.latestIdOf(_projectId));

    // Only one-time funding cycles are rescuable.
    require(_fundingCycle.discountRate == 201, 'cant rescue');

    balanceOf[_projectId] = balanceOf[_projectId] - _amount;

    // Send funds to beneficiary.
    if (_amount > 0) Address.sendValue(_beneficiary, _amount);

    emit Rescued(_projectId, _beneficiary, _originalBalance, _amount, msg.sender);
  }

  /**
    @notice 
    Receives and allocates funds belonging to the specified project.

    @param _projectId The ID of the project to which the funds received belong.
  */
  function addToBalance(uint256 _projectId) external payable override {
    require(rescueAllowed[_projectId], 'not allowed');
    balanceOf[_projectId] = balanceOf[_projectId] + msg.value;
    emit AddToBalance(_projectId, msg.value, msg.sender);
  }

  /**
    @notice 
    Allows certain projects to migrate to have funds rescued.

    @param _projectId The ID of the project to allow rescuing.
  */
  function toggleRescue(uint256 _projectId) external override onlyOwner {
    rescueAllowed[_projectId] = !rescueAllowed[_projectId];

    emit ToggleRescue(_projectId, rescueAllowed[_projectId], msg.sender);
  }

  /**
    @notice 
    NO-OP
  */
  function migrate(uint256, ITerminal) external pure override {
    require(false, 'cant migrate');
  }

  /**
    @notice 
    NO-OP
  */
  function allowMigration(ITerminal) external pure override {
    require(false, 'cant allow migration');
  }

  /**
    @notice 
    NO-OP
  */
  function pay(
    uint256,
    address,
    string calldata,
    bool
  ) external payable override returns (uint256) {
    require(false, 'cant pay');
    return 0;
  }
}

// File: contracts/abstract/JuiceboxProject.sol



// SPDX-License-Identifier: MIT
pragma solidity 0.8.6;

import "@openzeppelin/contracts/token/ERC721/IERC721Receiver.sol";
import "@openzeppelin/contracts/access/Ownable.sol";
import "@openzeppelin/contracts/utils/Address.sol";

import "./../interfaces/ITerminalV1.sol";

/** 
  @notice A contract that inherits from JuiceboxProject can use Juicebox as a business-model-as-a-service.
  @dev The owner of the contract makes admin decisions such as:
    - Which address is the funding cycle owner, which can tap funds from the funding cycle.
    - Should this project's Tickets be migrated to a new TerminalV1. 
*/
abstract contract JuiceboxProject is IERC721Receiver, Ownable {
    /// @notice The direct deposit terminals.
    ITerminalDirectory public immutable terminalDirectory;

    /// @notice The ID of the project that should be used to forward this contract's received payments.
    uint256 public projectId;

    /** 
      @param _projectId The ID of the project that should be used to forward this contract's received payments.
      @param _terminalDirectory A directory of a project's current Juicebox terminal to receive payments in.
    */
    constructor(uint256 _projectId, ITerminalDirectory _terminalDirectory) {
        projectId = _projectId;
        terminalDirectory = _terminalDirectory;
    }

    receive() external payable {}

    /** 
      @notice Withdraws funds stored in this contract.
      @param _beneficiary The address to send the funds to.
      @param _amount The amount to send.
    */
    function withdraw(address payable _beneficiary, uint256 _amount)
        external
        onlyOwner
    {
        Address.sendValue(_beneficiary, _amount);
    }

    /** 
      @notice Allows the project that is being managed to be set.
      @param _projectId The ID of the project that is being managed.
    */
    function setProjectId(uint256 _projectId) external onlyOwner {
        projectId = _projectId;
    }

    /** 
      @notice Make a payment to this project.
      @param _beneficiary The address who will receive tickets from this fee.
      @param _memo A memo that will be included in the published event.
      @param _preferUnstakedTickets Whether ERC20's should be claimed automatically if they have been issued.
    */
    function pay(
        address _beneficiary,
        string calldata _memo,
        bool _preferUnstakedTickets
    ) external payable {
        require(projectId != 0, "JuiceboxProject::pay: PROJECT_NOT_FOUND");

        // Get the terminal for this contract's project.
        ITerminal _terminal = terminalDirectory.terminalOf(projectId);

        // There must be a terminal.
        require(
            _terminal != ITerminal(address(0)),
            "JuiceboxProject::pay: TERMINAL_NOT_FOUND"
        );

        _terminal.pay{value: msg.value}(
            projectId,
            _beneficiary,
            _memo,
            _preferUnstakedTickets
        );
    }

    /** 
        @notice Transfer the ownership of the project to a new owner.  
        @dev This contract will no longer be able to reconfigure or tap funds from this project.
        @param _projects The projects contract.
        @param _newOwner The new project owner.
        @param _projectId The ID of the project to transfer ownership of.
        @param _data Arbitrary data to include in the transaction.
    */
    function transferProjectOwnership(
        IProjects _projects,
        address _newOwner,
        uint256 _projectId,
        bytes calldata _data
    ) external onlyOwner {
        _projects.safeTransferFrom(address(this), _newOwner, _projectId, _data);
    }

    /** 
      @notice Allows this contract to receive a project.
    */
    function onERC721Received(
        address,
        address,
        uint256,
        bytes calldata
    ) public pure override returns (bytes4) {
        return this.onERC721Received.selector;
    }

    function setOperator(
        IOperatorStore _operatorStore,
        address _operator,
        uint256 _projectId,
        uint256[] calldata _permissionIndexes
    ) external onlyOwner {
        _operatorStore.setOperator(_operator, _projectId, _permissionIndexes);
    }

    function setOperators(
        IOperatorStore _operatorStore,
        address[] calldata _operators,
        uint256[] calldata _projectIds,
        uint256[][] calldata _permissionIndexes
    ) external onlyOwner {
        _operatorStore.setOperators(
            _operators,
            _projectIds,
            _permissionIndexes
        );
    }

    /** 
      @notice Take a fee for this project from this contract.
      @param _amount The payment amount.
      @param _beneficiary The address who will receive tickets from this fee.
      @param _memo A memo that will be included in the published event.
      @param _preferUnstakedTickets Whether ERC20's should be claimed automatically if they have been issued.
    */
    function _takeFee(
        uint256 _amount,
        address _beneficiary,
        string memory _memo,
        bool _preferUnstakedTickets
    ) internal {
        require(projectId != 0, "JuiceboxProject::takeFee: PROJECT_NOT_FOUND");
        // Find the terminal for this contract's project.
        ITerminal _terminal = terminalDirectory.terminalOf(projectId);

        // There must be a terminal.
        require(
            _terminal != ITerminal(address(0)),
            "JuiceboxProject::takeFee: TERMINAL_NOT_FOUND"
        );

        // There must be enough funds in the contract to take the fee.
        require(
            address(this).balance >= _amount,
            "JuiceboxProject::takeFee: INSUFFICIENT_FUNDS"
        );

        // Send funds to the terminal.
        _terminal.pay{value: _amount}(
            projectId,
            _beneficiary,
            _memo,
            _preferUnstakedTickets
        );
    }
}

// File: contracts/abstract/Operatable.sol



// SPDX-License-Identifier: MIT
pragma solidity 0.8.6;

import "./../interfaces/IOperatable.sol";

abstract contract Operatable is IOperatable {
    modifier requirePermission(
        address _account,
        uint256 _domain,
        uint256 _index
    ) {
        require(
            msg.sender == _account ||
                operatorStore.hasPermission(
                    msg.sender,
                    _account,
                    _domain,
                    _index
                ),
            "Operatable: UNAUTHORIZED"
        );
        _;
    }

    modifier requirePermissionAllowingWildcardDomain(
        address _account,
        uint256 _domain,
        uint256 _index
    ) {
        require(
            msg.sender == _account ||
                operatorStore.hasPermission(
                    msg.sender,
                    _account,
                    _domain,
                    _index
                ) ||
                operatorStore.hasPermission(msg.sender, _account, 0, _index),
            "Operatable: UNAUTHORIZED"
        );
        _;
    }

    modifier requirePermissionAcceptingAlternateAddress(
        address _account,
        uint256 _domain,
        uint256 _index,
        address _alternate
    ) {
        require(
            msg.sender == _account ||
                operatorStore.hasPermission(
                    msg.sender,
                    _account,
                    _domain,
                    _index
                ) ||
                msg.sender == _alternate,
            "Operatable: UNAUTHORIZED"
        );
        _;
    }

    /// @notice A contract storing operator assignments.
    IOperatorStore public immutable override operatorStore;

    /** 
      @param _operatorStore A contract storing operator assignments.
    */
    constructor(IOperatorStore _operatorStore) {
        operatorStore = _operatorStore;
    }
}

// File: contracts/interfaces/IDirectPaymentAddress.sol



// SPDX-License-Identifier: MIT
pragma solidity 0.8.6;

import "./ITerminalDirectory.sol";
import "./ITerminal.sol";

interface IDirectPaymentAddress {
    event Forward(
        address indexed payer,
        uint256 indexed projectId,
        address beneficiary,
        uint256 value,
        string memo,
        bool preferUnstakedTickets
    );

    function terminalDirectory() external returns (ITerminalDirectory);

    function projectId() external returns (uint256);

    function memo() external returns (string memory);
}

// File: contracts/interfaces/IFundingCycleBallot.sol



// SPDX-License-Identifier: MIT
pragma solidity 0.8.6;

import "./ITerminalV1.sol";

enum BallotState {
    Approved,
    Active,
    Failed,
    Standby
}

interface IFundingCycleBallot {
    function duration() external view returns (uint256);

    function state(uint256 _fundingCycleId, uint256 _configured)
        external
        view
        returns (BallotState);
}

// File: contracts/interfaces/IFundingCycles.sol



// SPDX-License-Identifier: MIT
pragma solidity 0.8.6;

import "./IPrices.sol";
import "./IProjects.sol";
import "./IFundingCycleBallot.sol";

/// @notice The funding cycle structure represents a project stewarded by an address, and accounts for which addresses have helped sustain the project.
struct FundingCycle {
    // A unique number that's incremented for each new funding cycle, starting with 1.
    uint256 id;
    // The ID of the project contract that this funding cycle belongs to.
    uint256 projectId;
    // The number of this funding cycle for the project.
    uint256 number;
    // The ID of a previous funding cycle that this one is based on.
    uint256 basedOn;
    // The time when this funding cycle was last configured.
    uint256 configured;
    // The number of cycles that this configuration should last for before going back to the last permanent.
    uint256 cycleLimit;
    // A number determining the amount of redistribution shares this funding cycle will issue to each sustainer.
    uint256 weight;
    // The ballot contract to use to determine a subsequent funding cycle's reconfiguration status.
    IFundingCycleBallot ballot;
    // The time when this funding cycle will become active.
    uint256 start;
    // The number of seconds until this funding cycle's surplus is redistributed.
    uint256 duration;
    // The amount that this funding cycle is targeting in terms of the currency.
    uint256 target;
    // The currency that the target is measured in.
    uint256 currency;
    // The percentage of each payment to send as a fee to the Juicebox admin.
    uint256 fee;
    // A percentage indicating how much more weight to give a funding cycle compared to its predecessor.
    uint256 discountRate;
    // The amount of available funds that have been tapped by the project in terms of the currency.
    uint256 tapped;
    // A packed list of extra data. The first 8 bytes are reserved for versioning.
    uint256 metadata;
}

struct FundingCycleProperties {
    uint256 target;
    uint256 currency;
    uint256 duration;
    uint256 cycleLimit;
    uint256 discountRate;
    IFundingCycleBallot ballot;
}

interface IFundingCycles {
    event Configure(
        uint256 indexed fundingCycleId,
        uint256 indexed projectId,
        uint256 reconfigured,
        FundingCycleProperties _properties,
        uint256 metadata,
        address caller
    );

    event Tap(
        uint256 indexed fundingCycleId,
        uint256 indexed projectId,
        uint256 amount,
        uint256 newTappedAmount,
        address caller
    );

    event Init(
        uint256 indexed fundingCycleId,
        uint256 indexed projectId,
        uint256 number,
        uint256 previous,
        uint256 weight,
        uint256 start
    );

    function latestIdOf(uint256 _projectId) external view returns (uint256);

    function count() external view returns (uint256);

    function BASE_WEIGHT() external view returns (uint256);

    function MAX_CYCLE_LIMIT() external view returns (uint256);

    function get(uint256 _fundingCycleId)
        external
        view
        returns (FundingCycle memory);

    function queuedOf(uint256 _projectId)
        external
        view
        returns (FundingCycle memory);

    function currentOf(uint256 _projectId)
        external
        view
        returns (FundingCycle memory);

    function currentBallotStateOf(uint256 _projectId)
        external
        view
        returns (BallotState);

    function configure(
        uint256 _projectId,
        FundingCycleProperties calldata _properties,
        uint256 _metadata,
        uint256 _fee,
        bool _configureActiveFundingCycle
    ) external returns (FundingCycle memory fundingCycle);

    function tap(uint256 _projectId, uint256 _amount)
        external
        returns (FundingCycle memory fundingCycle);
}

// File: contracts/interfaces/IModAllocator.sol



// SPDX-License-Identifier: MIT
pragma solidity 0.8.6;

interface IModAllocator {
    event Allocate(
        uint256 indexed projectId,
        uint256 indexed forProjectId,
        address indexed beneficiary,
        uint256 amount,
        address caller
    );

    function allocate(
        uint256 _projectId,
        uint256 _forProjectId,
        address _beneficiary
    ) external payable;
}

// File: contracts/interfaces/IModStore.sol



// SPDX-License-Identifier: MIT
pragma solidity 0.8.6;

import "./IOperatorStore.sol";
import "./IProjects.sol";
import "./IModAllocator.sol";

struct PayoutMod {
    bool preferUnstaked;
    uint16 percent;
    uint48 lockedUntil;
    address payable beneficiary;
    IModAllocator allocator;
    uint56 projectId;
}

struct TicketMod {
    bool preferUnstaked;
    uint16 percent;
    uint48 lockedUntil;
    address payable beneficiary;
}

interface IModStore {
    event SetPayoutMod(
        uint256 indexed projectId,
        uint256 indexed configuration,
        PayoutMod mods,
        address caller
    );

    event SetTicketMod(
        uint256 indexed projectId,
        uint256 indexed configuration,
        TicketMod mods,
        address caller
    );

    function projects() external view returns (IProjects);

    function payoutModsOf(uint256 _projectId, uint256 _configuration)
        external
        view
        returns (PayoutMod[] memory);

    function ticketModsOf(uint256 _projectId, uint256 _configuration)
        external
        view
        returns (TicketMod[] memory);

    function setPayoutMods(
        uint256 _projectId,
        uint256 _configuration,
        PayoutMod[] memory _mods
    ) external;

    function setTicketMods(
        uint256 _projectId,
        uint256 _configuration,
        TicketMod[] memory _mods
    ) external;
}

// File: contracts/interfaces/IOperatable.sol



// SPDX-License-Identifier: MIT
pragma solidity 0.8.6;

import "./IOperatorStore.sol";

interface IOperatable {
    function operatorStore() external view returns (IOperatorStore);
}

// File: contracts/interfaces/IOperatorStore.sol



// SPDX-License-Identifier: MIT
pragma solidity 0.8.6;

interface IOperatorStore {
    event SetOperator(
        address indexed operator,
        address indexed account,
        uint256 indexed domain,
        uint256[] permissionIndexes,
        uint256 packed
    );

    function permissionsOf(
        address _operator,
        address _account,
        uint256 _domain
    ) external view returns (uint256);

    function hasPermission(
        address _operator,
        address _account,
        uint256 _domain,
        uint256 _permissionIndex
    ) external view returns (bool);

    function hasPermissions(
        address _operator,
        address _account,
        uint256 _domain,
        uint256[] calldata _permissionIndexes
    ) external view returns (bool);

    function setOperator(
        address _operator,
        uint256 _domain,
        uint256[] calldata _permissionIndexes
    ) external;

    function setOperators(
        address[] calldata _operators,
        uint256[] calldata _domains,
        uint256[][] calldata _permissionIndexes
    ) external;
}

// File: contracts/interfaces/IPrices.sol



// SPDX-License-Identifier: MIT
pragma solidity 0.8.6;

import "@chainlink/contracts/src/v0.6/interfaces/AggregatorV3Interface.sol";

interface IPrices {
    event AddFeed(uint256 indexed currency, AggregatorV3Interface indexed feed);

    function feedDecimalAdjuster(uint256 _currency) external returns (uint256);

    function targetDecimals() external returns (uint256);

    function feedFor(uint256 _currency)
        external
        returns (AggregatorV3Interface);

    function getETHPriceFor(uint256 _currency) external view returns (uint256);

    function addFeed(AggregatorV3Interface _priceFeed, uint256 _currency)
        external;
}

// File: contracts/interfaces/IProjects.sol



// SPDX-License-Identifier: MIT
pragma solidity 0.8.6;

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

import "./ITerminal.sol";
import "./IOperatorStore.sol";

interface IProjects is IERC721 {
    event Create(
        uint256 indexed projectId,
        address indexed owner,
        bytes32 indexed handle,
        string uri,
        ITerminal terminal,
        address caller
    );

    event SetHandle(
        uint256 indexed projectId,
        bytes32 indexed handle,
        address caller
    );

    event SetUri(uint256 indexed projectId, string uri, address caller);

    event TransferHandle(
        uint256 indexed projectId,
        address indexed to,
        bytes32 indexed handle,
        bytes32 newHandle,
        address caller
    );

    event ClaimHandle(
        address indexed account,
        uint256 indexed projectId,
        bytes32 indexed handle,
        address caller
    );

    event ChallengeHandle(
        bytes32 indexed handle,
        uint256 challengeExpiry,
        address caller
    );

    event RenewHandle(
        bytes32 indexed handle,
        uint256 indexed projectId,
        address caller
    );

    function count() external view returns (uint256);

    function uriOf(uint256 _projectId) external view returns (string memory);

    function handleOf(uint256 _projectId) external returns (bytes32 handle);

    function projectFor(bytes32 _handle) external returns (uint256 projectId);

    function transferAddressFor(bytes32 _handle)
        external
        returns (address receiver);

    function challengeExpiryOf(bytes32 _handle) external returns (uint256);

    function exists(uint256 _projectId) external view returns (bool);

    function create(
        address _owner,
        bytes32 _handle,
        string calldata _uri,
        ITerminal _terminal
    ) external returns (uint256 id);

    function setHandle(uint256 _projectId, bytes32 _handle) external;

    function setUri(uint256 _projectId, string calldata _uri) external;

    function transferHandle(
        uint256 _projectId,
        address _to,
        bytes32 _newHandle
    ) external returns (bytes32 _handle);

    function claimHandle(
        bytes32 _handle,
        address _for,
        uint256 _projectId
    ) external;
}

// File: contracts/interfaces/ITerminal.sol



// SPDX-License-Identifier: MIT
pragma solidity 0.8.6;

import './ITerminalDirectory.sol';

interface ITerminal {
  function terminalDirectory() external view returns (ITerminalDirectory);

  function migrationIsAllowed(ITerminal _terminal) external view returns (bool);

  function pay(
    uint256 _projectId,
    address _beneficiary,
    string calldata _memo,
    bool _preferUnstakedTickets
  ) external payable returns (uint256 fundingCycleId);

  function addToBalance(uint256 _projectId) external payable;

  function allowMigration(ITerminal _contract) external;

  function migrate(uint256 _projectId, ITerminal _to) external;
}

// File: contracts/interfaces/ITerminalDirectory.sol



// SPDX-License-Identifier: MIT
pragma solidity 0.8.6;

import "./IDirectPaymentAddress.sol";
import "./ITerminal.sol";
import "./IProjects.sol";
import "./IProjects.sol";

interface ITerminalDirectory {
    event DeployAddress(
        uint256 indexed projectId,
        string memo,
        address indexed caller
    );

    event SetTerminal(
        uint256 indexed projectId,
        ITerminal indexed terminal,
        address caller
    );

    event SetPayerPreferences(
        address indexed account,
        address beneficiary,
        bool preferUnstakedTickets
    );

    function projects() external view returns (IProjects);

    function terminalOf(uint256 _projectId) external view returns (ITerminal);

    function beneficiaryOf(address _account) external returns (address);

    function unstakedTicketsPreferenceOf(address _account)
        external
        returns (bool);

    function addressesOf(uint256 _projectId)
        external
        view
        returns (IDirectPaymentAddress[] memory);

    function deployAddress(uint256 _projectId, string calldata _memo) external;

    function setTerminal(uint256 _projectId, ITerminal _terminal) external;

    function setPayerPreferences(
        address _beneficiary,
        bool _preferUnstakedTickets
    ) external;
}

// File: contracts/interfaces/ITerminalV1.sol



// SPDX-License-Identifier: MIT
pragma solidity 0.8.6;

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

import './ITicketBooth.sol';
import './IFundingCycles.sol';
import './IYielder.sol';
import './IProjects.sol';
import './IModStore.sol';
import './IPrices.sol';
import './ITerminal.sol';
import './IOperatorStore.sol';

struct FundingCycleMetadata {
  uint256 reservedRate;
  uint256 bondingCurveRate;
  uint256 reconfigurationBondingCurveRate;
}

interface ITerminalV1 {
  event Pay(
    uint256 indexed fundingCycleId,
    uint256 indexed projectId,
    address indexed beneficiary,
    uint256 amount,
    string note,
    address caller
  );

  event AddToBalance(uint256 indexed projectId, uint256 value, address caller);

  event AllowMigration(ITerminal allowed);

  event Migrate(uint256 indexed projectId, ITerminal indexed to, uint256 _amount, address caller);

  event Configure(uint256 indexed fundingCycleId, uint256 indexed projectId, address caller);

  event Tap(
    uint256 indexed fundingCycleId,
    uint256 indexed projectId,
    address indexed beneficiary,
    uint256 amount,
    uint256 currency,
    uint256 netTransferAmount,
    uint256 beneficiaryTransferAmount,
    uint256 govFeeAmount,
    address caller
  );
  event Redeem(
    address indexed holder,
    address indexed beneficiary,
    uint256 indexed _projectId,
    uint256 amount,
    uint256 returnAmount,
    address caller
  );

  event PrintReserveTickets(
    uint256 indexed fundingCycleId,
    uint256 indexed projectId,
    address indexed beneficiary,
    uint256 count,
    uint256 beneficiaryTicketAmount,
    address caller
  );

  event DistributeToPayoutMod(
    uint256 indexed fundingCycleId,
    uint256 indexed projectId,
    PayoutMod mod,
    uint256 modCut,
    address caller
  );
  event DistributeToTicketMod(
    uint256 indexed fundingCycleId,
    uint256 indexed projectId,
    TicketMod mod,
    uint256 modCut,
    address caller
  );
  event AppointGovernance(address governance);

  event AcceptGovernance(address governance);

  event PrintPreminedTickets(
    uint256 indexed projectId,
    address indexed beneficiary,
    uint256 amount,
    uint256 currency,
    string memo,
    address caller
  );

  event Deposit(uint256 amount);

  event EnsureTargetLocalWei(uint256 target);

  event SetYielder(IYielder newYielder);

  event SetFee(uint256 _amount);

  event SetTargetLocalWei(uint256 amount);

  function governance() external view returns (address payable);

  function pendingGovernance() external view returns (address payable);

  function projects() external view returns (IProjects);

  function fundingCycles() external view returns (IFundingCycles);

  function ticketBooth() external view returns (ITicketBooth);

  function prices() external view returns (IPrices);

  function modStore() external view returns (IModStore);

  function reservedTicketBalanceOf(uint256 _projectId, uint256 _reservedRate)
    external
    view
    returns (uint256);

  function canPrintPreminedTickets(uint256 _projectId) external view returns (bool);

  function balanceOf(uint256 _projectId) external view returns (uint256);

  function currentOverflowOf(uint256 _projectId) external view returns (uint256);

  function claimableOverflowOf(
    address _account,
    uint256 _amount,
    uint256 _projectId
  ) external view returns (uint256);

  function fee() external view returns (uint256);

  function deploy(
    address _owner,
    bytes32 _handle,
    string calldata _uri,
    FundingCycleProperties calldata _properties,
    FundingCycleMetadata calldata _metadata,
    PayoutMod[] memory _payoutMods,
    TicketMod[] memory _ticketMods
  ) external;

  function configure(
    uint256 _projectId,
    FundingCycleProperties calldata _properties,
    FundingCycleMetadata calldata _metadata,
    PayoutMod[] memory _payoutMods,
    TicketMod[] memory _ticketMods
  ) external returns (uint256);

  function printPreminedTickets(
    uint256 _projectId,
    uint256 _amount,
    uint256 _currency,
    address _beneficiary,
    string memory _memo,
    bool _preferUnstakedTickets
  ) external;

  function tap(
    uint256 _projectId,
    uint256 _amount,
    uint256 _currency,
    uint256 _minReturnedWei
  ) external returns (uint256);

  function redeem(
    address _account,
    uint256 _projectId,
    uint256 _amount,
    uint256 _minReturnedWei,
    address payable _beneficiary,
    bool _preferUnstaked
  ) external returns (uint256 returnAmount);

  function printReservedTickets(uint256 _projectId)
    external
    returns (uint256 reservedTicketsToPrint);

  function setFee(uint256 _fee) external;

  function appointGovernance(address payable _pendingGovernance) external;

  function acceptGovernance() external;
}

// File: contracts/interfaces/ITerminalV1Rescue.sol



// SPDX-License-Identifier: MIT
pragma solidity 0.8.6;

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

import './ITicketBooth.sol';
import './IFundingCycles.sol';
import './IYielder.sol';
import './IProjects.sol';
import './IModStore.sol';
import './ITerminal.sol';
import './IOperatorStore.sol';
import './ITreasuryExtension.sol';

struct FundingCycleMetadata2 {
  uint256 reservedRate;
  uint256 bondingCurveRate;
  uint256 reconfigurationBondingCurveRate;
  bool payIsPaused;
  bool ticketPrintingIsAllowed;
  ITreasuryExtension treasuryExtension;
}

interface ITerminalV1Rescue {
  event AddToBalance(uint256 indexed projectId, uint256 value, address caller);
  event PrintTickets(
    uint256 indexed projectId,
    address indexed beneficiary,
    uint256 amount,
    string memo,
    address caller
  );

  event Rescued(
    uint256 projectId,
    address beneficiary,
    uint256 originalBalance,
    uint256 amount,
    address caller
  );

  event ToggleRescue(uint256 projectId, bool newValue, address caller);

  function projects() external view returns (IProjects);

  function fundingCycles() external view returns (IFundingCycles);

  function ticketBooth() external view returns (ITicketBooth);

  function rescueAllowed(uint256 _projectId) external view returns (bool);

  function balanceOf(uint256 _projectId) external view returns (uint256);

  function rescue(
    uint256 _projectId,
    address payable _beneficiary,
    uint256 _amount
  ) external;

  function toggleRescue(uint256 _projectId) external;

  function printTickets(
    uint256 _projectId,
    uint256 _amount,
    address _beneficiary,
    string memory _memo,
    bool _preferUnstakedTickets
  ) external;
}

// File: contracts/interfaces/ITicketBooth.sol



// SPDX-License-Identifier: MIT
pragma solidity 0.8.6;

import "./IProjects.sol";
import "./IOperatorStore.sol";
import "./ITickets.sol";

interface ITicketBooth {
    event Issue(
        uint256 indexed projectId,
        string name,
        string symbol,
        address caller
    );
    event Print(
        address indexed holder,
        uint256 indexed projectId,
        uint256 amount,
        bool convertedTickets,
        bool preferUnstakedTickets,
        address controller
    );

    event Redeem(
        address indexed holder,
        uint256 indexed projectId,
        uint256 amount,
        uint256 stakedTickets,
        bool preferUnstaked,
        address controller
    );

    event Stake(
        address indexed holder,
        uint256 indexed projectId,
        uint256 amount,
        address caller
    );

    event Unstake(
        address indexed holder,
        uint256 indexed projectId,
        uint256 amount,
        address caller
    );

    event Lock(
        address indexed holder,
        uint256 indexed projectId,
        uint256 amount,
        address caller
    );

    event Unlock(
        address indexed holder,
        uint256 indexed projectId,
        uint256 amount,
        address caller
    );

    event Transfer(
        address indexed holder,
        uint256 indexed projectId,
        address indexed recipient,
        uint256 amount,
        address caller
    );

    function ticketsOf(uint256 _projectId) external view returns (ITickets);

    function projects() external view returns (IProjects);

    function lockedBalanceOf(address _holder, uint256 _projectId)
        external
        view
        returns (uint256);

    function lockedBalanceBy(
        address _operator,
        address _holder,
        uint256 _projectId
    ) external view returns (uint256);

    function stakedBalanceOf(address _holder, uint256 _projectId)
        external
        view
        returns (uint256);

    function stakedTotalSupplyOf(uint256 _projectId)
        external
        view
        returns (uint256);

    function totalSupplyOf(uint256 _projectId) external view returns (uint256);

    function balanceOf(address _holder, uint256 _projectId)
        external
        view
        returns (uint256 _result);

    function issue(
        uint256 _projectId,
        string calldata _name,
        string calldata _symbol
    ) external;

    function print(
        address _holder,
        uint256 _projectId,
        uint256 _amount,
        bool _preferUnstakedTickets
    ) external;

    function redeem(
        address _holder,
        uint256 _projectId,
        uint256 _amount,
        bool _preferUnstaked
    ) external;

    function stake(
        address _holder,
        uint256 _projectId,
        uint256 _amount
    ) external;

    function unstake(
        address _holder,
        uint256 _projectId,
        uint256 _amount
    ) external;

    function lock(
        address _holder,
        uint256 _projectId,
        uint256 _amount
    ) external;

    function unlock(
        address _holder,
        uint256 _projectId,
        uint256 _amount
    ) external;

    function transfer(
        address _holder,
        uint256 _projectId,
        uint256 _amount,
        address _recipient
    ) external;
}

// File: contracts/interfaces/ITickets.sol



// SPDX-License-Identifier: MIT
pragma solidity 0.8.6;

import "@openzeppelin/contracts/token/ERC20/IERC20.sol";

interface ITickets is IERC20 {
    function print(address _account, uint256 _amount) external;

    function redeem(address _account, uint256 _amount) external;
}

// File: contracts/interfaces/ITreasuryExtension.sol



// SPDX-License-Identifier: MIT
pragma solidity 0.8.6;

interface ITreasuryExtension {
  function ETHValue(uint256 _projectId) external view returns (uint256);
}

// File: contracts/interfaces/IYielder.sol



// SPDX-License-Identifier: MIT
pragma solidity 0.8.6;

import "@openzeppelin/contracts/token/ERC20/IERC20.sol";

import "./ITerminalV1.sol";

// In constructure, give unlimited access for TerminalV1 to take money from this.
interface IYielder {
    function deposited() external view returns (uint256);

    function getCurrentBalance() external view returns (uint256);

    function deposit() external payable;

    function withdraw(uint256 _amount, address payable _beneficiary) external;

    function withdrawAll(address payable _beneficiary)
        external
        returns (uint256);
}

// File: contracts/libraries/Operations.sol



// SPDX-License-Identifier: MIT
pragma solidity 0.8.6;

library Operations {
  uint256 public constant Configure = 1;
  uint256 public constant PrintPreminedTickets = 2;
  uint256 public constant Redeem = 3;
  uint256 public constant Migrate = 4;
  uint256 public constant SetHandle = 5;
  uint256 public constant SetUri = 6;
  uint256 public constant ClaimHandle = 7;
  uint256 public constant RenewHandle = 8;
  uint256 public constant Issue = 9;
  uint256 public constant Stake = 10;
  uint256 public constant Unstake = 11;
  uint256 public constant Transfer = 12;
  uint256 public constant Lock = 13;
  uint256 public constant SetPayoutMods = 14;
  uint256 public constant SetTicketMods = 15;
  uint256 public constant SetTerminal = 16;
  uint256 public constant PrintTickets = 17;
}

// File: prb-math/contracts/PRBMath.sol



// SPDX-License-Identifier: WTFPL
pragma solidity >=0.8.4;

/// @notice Emitted when the result overflows uint256.
error PRBMath__MulDivFixedPointOverflow(uint256 prod1);

/// @notice Emitted when the result overflows uint256.
error PRBMath__MulDivOverflow(uint256 prod1, uint256 denominator);

/// @notice Emitted when one of the inputs is type(int256).min.
error PRBMath__MulDivSignedInputTooSmall();

/// @notice Emitted when the intermediary absolute result overflows int256.
error PRBMath__MulDivSignedOverflow(uint256 rAbs);

/// @notice Emitted when the input is MIN_SD59x18.
error PRBMathSD59x18__AbsInputTooSmall();

/// @notice Emitted when ceiling a number overflows SD59x18.
error PRBMathSD59x18__CeilOverflow(int256 x);

/// @notice Emitted when one of the inputs is MIN_SD59x18.
error PRBMathSD59x18__DivInputTooSmall();

/// @notice Emitted when one of the intermediary unsigned results overflows SD59x18.
error PRBMathSD59x18__DivOverflow(uint256 rAbs);

/// @notice Emitted when the input is greater than 133.084258667509499441.
error PRBMathSD59x18__ExpInputTooBig(int256 x);

/// @notice Emitted when the input is greater than 192.
error PRBMathSD59x18__Exp2InputTooBig(int256 x);

/// @notice Emitted when flooring a number underflows SD59x18.
error PRBMathSD59x18__FloorUnderflow(int256 x);

/// @notice Emitted when converting a basic integer to the fixed-point format overflows SD59x18.
error PRBMathSD59x18__FromIntOverflow(int256 x);

/// @notice Emitted when converting a basic integer to the fixed-point format underflows SD59x18.
error PRBMathSD59x18__FromIntUnderflow(int256 x);

/// @notice Emitted when the product of the inputs is negative.
error PRBMathSD59x18__GmNegativeProduct(int256 x, int256 y);

/// @notice Emitted when multiplying the inputs overflows SD59x18.
error PRBMathSD59x18__GmOverflow(int256 x, int256 y);

/// @notice Emitted when the input is less than or equal to zero.
error PRBMathSD59x18__LogInputTooSmall(int256 x);

/// @notice Emitted when one of the inputs is MIN_SD59x18.
error PRBMathSD59x18__MulInputTooSmall();

/// @notice Emitted when the intermediary absolute result overflows SD59x18.
error PRBMathSD59x18__MulOverflow(uint256 rAbs);

/// @notice Emitted when the intermediary absolute result overflows SD59x18.
error PRBMathSD59x18__PowuOverflow(uint256 rAbs);

/// @notice Emitted when the input is negative.
error PRBMathSD59x18__SqrtNegativeInput(int256 x);

/// @notice Emitted when the calculting the square root overflows SD59x18.
error PRBMathSD59x18__SqrtOverflow(int256 x);

/// @notice Emitted when addition overflows UD60x18.
error PRBMathUD60x18__AddOverflow(uint256 x, uint256 y);

/// @notice Emitted when ceiling a number overflows UD60x18.
error PRBMathUD60x18__CeilOverflow(uint256 x);

/// @notice Emitted when the input is greater than 133.084258667509499441.
error PRBMathUD60x18__ExpInputTooBig(uint256 x);

/// @notice Emitted when the input is greater than 192.
error PRBMathUD60x18__Exp2InputTooBig(uint256 x);

/// @notice Emitted when converting a basic integer to the fixed-point format format overflows UD60x18.
error PRBMathUD60x18__FromUintOverflow(uint256 x);

/// @notice Emitted when multiplying the inputs overflows UD60x18.
error PRBMathUD60x18__GmOverflow(uint256 x, uint256 y);

/// @notice Emitted when the input is less than 1.
error PRBMathUD60x18__LogInputTooSmall(uint256 x);

/// @notice Emitted when the calculting the square root overflows UD60x18.
error PRBMathUD60x18__SqrtOverflow(uint256 x);

/// @notice Emitted when subtraction underflows UD60x18.
error PRBMathUD60x18__SubUnderflow(uint256 x, uint256 y);

/// @dev Common mathematical functions used in both PRBMathSD59x18 and PRBMathUD60x18. Note that this shared library
/// does not always assume the signed 59.18-decimal fixed-point or the unsigned 60.18-decimal fixed-point
/// representation. When it does not, it is explictly mentioned in the NatSpec documentation.
library PRBMath {
    /// STRUCTS ///

    struct SD59x18 {
        int256 value;
    }

    struct UD60x18 {
        uint256 value;
    }

    /// STORAGE ///

    /// @dev How many trailing decimals can be represented.
    uint256 internal constant SCALE = 1e18;

    /// @dev Largest power of two divisor of SCALE.
    uint256 internal constant SCALE_LPOTD = 262144;

    /// @dev SCALE inverted mod 2^256.
    uint256 internal constant SCALE_INVERSE = 78156646155174841979727994598816262306175212592076161876661508869554232690281;

    /// FUNCTIONS ///

    /// @notice Calculates the binary exponent of x using the binary fraction method.
    /// @dev Has to use 192.64-bit fixed-point numbers.
    /// See https://ethereum.stackexchange.com/a/96594/24693.
    /// @param x The exponent as an unsigned 192.64-bit fixed-point number.
    /// @return result The result as an unsigned 60.18-decimal fixed-point number.
    function exp2(uint256 x) internal pure returns (uint256 result) {
        unchecked {
            // Start from 0.5 in the 192.64-bit fixed-point format.
            result = 0x800000000000000000000000000000000000000000000000;

            // Multiply the result by root(2, 2^-i) when the bit at position i is 1. None of the intermediary results overflows
            // because the initial result is 2^191 and all magic factors are less than 2^65.
            if (x & 0x8000000000000000 > 0) {
                result = (result * 0x16A09E667F3BCC909) >> 64;
            }
            if (x & 0x4000000000000000 > 0) {
                result = (result * 0x1306FE0A31B7152DF) >> 64;
            }
            if (x & 0x2000000000000000 > 0) {
                result = (result * 0x1172B83C7D517ADCE) >> 64;
            }
            if (x & 0x1000000000000000 > 0) {
                result = (result * 0x10B5586CF9890F62A) >> 64;
            }
            if (x & 0x800000000000000 > 0) {
                result = (result * 0x1059B0D31585743AE) >> 64;
            }
            if (x & 0x400000000000000 > 0) {
                result = (result * 0x102C9A3E778060EE7) >> 64;
            }
            if (x & 0x200000000000000 > 0) {
                result = (result * 0x10163DA9FB33356D8) >> 64;
            }
            if (x & 0x100000000000000 > 0) {
                result = (result * 0x100B1AFA5ABCBED61) >> 64;
            }
            if (x & 0x80000000000000 > 0) {
                result = (result * 0x10058C86DA1C09EA2) >> 64;
            }
            if (x & 0x40000000000000 > 0) {
                result = (result * 0x1002C605E2E8CEC50) >> 64;
            }
            if (x & 0x20000000000000 > 0) {
                result = (result * 0x100162F3904051FA1) >> 64;
            }
            if (x & 0x10000000000000 > 0) {
                result = (result * 0x1000B175EFFDC76BA) >> 64;
            }
            if (x & 0x8000000000000 > 0) {
                result = (result * 0x100058BA01FB9F96D) >> 64;
            }
            if (x & 0x4000000000000 > 0) {
                result = (result * 0x10002C5CC37DA9492) >> 64;
            }
            if (x & 0x2000000000000 > 0) {
                result = (result * 0x1000162E525EE0547) >> 64;
            }
            if (x & 0x1000000000000 > 0) {
                result = (result * 0x10000B17255775C04) >> 64;
            }
            if (x & 0x800000000000 > 0) {
                result = (result * 0x1000058B91B5BC9AE) >> 64;
            }
            if (x & 0x400000000000 > 0) {
                result = (result * 0x100002C5C89D5EC6D) >> 64;
            }
            if (x & 0x200000000000 > 0) {
                result = (result * 0x10000162E43F4F831) >> 64;
            }
            if (x & 0x100000000000 > 0) {
                result = (result * 0x100000B1721BCFC9A) >> 64;
            }
            if (x & 0x80000000000 > 0) {
                result = (result * 0x10000058B90CF1E6E) >> 64;
            }
            if (x & 0x40000000000 > 0) {
                result = (result * 0x1000002C5C863B73F) >> 64;
            }
            if (x & 0x20000000000 > 0) {
                result = (result * 0x100000162E430E5A2) >> 64;
            }
            if (x & 0x10000000000 > 0) {
                result = (result * 0x1000000B172183551) >> 64;
            }
            if (x & 0x8000000000 > 0) {
                result = (result * 0x100000058B90C0B49) >> 64;
            }
            if (x & 0x4000000000 > 0) {
                result = (result * 0x10000002C5C8601CC) >> 64;
            }
            if (x & 0x2000000000 > 0) {
                result = (result * 0x1000000162E42FFF0) >> 64;
            }
            if (x & 0x1000000000 > 0) {
                result = (result * 0x10000000B17217FBB) >> 64;
            }
            if (x & 0x800000000 > 0) {
                result = (result * 0x1000000058B90BFCE) >> 64;
            }
            if (x & 0x400000000 > 0) {
                result = (result * 0x100000002C5C85FE3) >> 64;
            }
            if (x & 0x200000000 > 0) {
                result = (result * 0x10000000162E42FF1) >> 64;
            }
            if (x & 0x100000000 > 0) {
                result = (result * 0x100000000B17217F8) >> 64;
            }
            if (x & 0x80000000 > 0) {
                result = (result * 0x10000000058B90BFC) >> 64;
            }
            if (x & 0x40000000 > 0) {
                result = (result * 0x1000000002C5C85FE) >> 64;
            }
            if (x & 0x20000000 > 0) {
                result = (result * 0x100000000162E42FF) >> 64;
            }
            if (x & 0x10000000 > 0) {
                result = (result * 0x1000000000B17217F) >> 64;
            }
            if (x & 0x8000000 > 0) {
                result = (result * 0x100000000058B90C0) >> 64;
            }
            if (x & 0x4000000 > 0) {
                result = (result * 0x10000000002C5C860) >> 64;
            }
            if (x & 0x2000000 > 0) {
                result = (result * 0x1000000000162E430) >> 64;
            }
            if (x & 0x1000000 > 0) {
                result = (result * 0x10000000000B17218) >> 64;
            }
            if (x & 0x800000 > 0) {
                result = (result * 0x1000000000058B90C) >> 64;
            }
            if (x & 0x400000 > 0) {
                result = (result * 0x100000000002C5C86) >> 64;
            }
            if (x & 0x200000 > 0) {
                result = (result * 0x10000000000162E43) >> 64;
            }
            if (x & 0x100000 > 0) {
                result = (result * 0x100000000000B1721) >> 64;
            }
            if (x & 0x80000 > 0) {
                result = (result * 0x10000000000058B91) >> 64;
            }
            if (x & 0x40000 > 0) {
                result = (result * 0x1000000000002C5C8) >> 64;
            }
            if (x & 0x20000 > 0) {
                result = (result * 0x100000000000162E4) >> 64;
            }
            if (x & 0x10000 > 0) {
                result = (result * 0x1000000000000B172) >> 64;
            }
            if (x & 0x8000 > 0) {
                result = (result * 0x100000000000058B9) >> 64;
            }
            if (x & 0x4000 > 0) {
                result = (result * 0x10000000000002C5D) >> 64;
            }
            if (x & 0x2000 > 0) {
                result = (result * 0x1000000000000162E) >> 64;
            }
            if (x & 0x1000 > 0) {
                result = (result * 0x10000000000000B17) >> 64;
            }
            if (x & 0x800 > 0) {
                result = (result * 0x1000000000000058C) >> 64;
            }
            if (x & 0x400 > 0) {
                result = (result * 0x100000000000002C6) >> 64;
            }
            if (x & 0x200 > 0) {
                result = (result * 0x10000000000000163) >> 64;
            }
            if (x & 0x100 > 0) {
                result = (result * 0x100000000000000B1) >> 64;
            }
            if (x & 0x80 > 0) {
                result = (result * 0x10000000000000059) >> 64;
            }
            if (x & 0x40 > 0) {
                result = (result * 0x1000000000000002C) >> 64;
            }
            if (x & 0x20 > 0) {
                result = (result * 0x10000000000000016) >> 64;
            }
            if (x & 0x10 > 0) {
                result = (result * 0x1000000000000000B) >> 64;
            }
            if (x & 0x8 > 0) {
                result = (result * 0x10000000000000006) >> 64;
            }
            if (x & 0x4 > 0) {
                result = (result * 0x10000000000000003) >> 64;
            }
            if (x & 0x2 > 0) {
                result = (result * 0x10000000000000001) >> 64;
            }
            if (x & 0x1 > 0) {
                result = (result * 0x10000000000000001) >> 64;
            }

            // We're doing two things at the same time:
            //
            //   1. Multiply the result by 2^n + 1, where "2^n" is the integer part and the one is added to account for
            //      the fact that we initially set the result to 0.5. This is accomplished by subtracting from 191
            //      rather than 192.
            //   2. Convert the result to the unsigned 60.18-decimal fixed-point format.
            //
            // This works because 2^(191-ip) = 2^ip / 2^191, where "ip" is the integer part "2^n".
            result *= SCALE;
            result >>= (191 - (x >> 64));
        }
    }

    /// @notice Finds the zero-based index of the first one in the binary representation of x.
    /// @dev See the note on msb in the "Find First Set" Wikipedia article https://en.wikipedia.org/wiki/Find_first_set
    /// @param x The uint256 number for which to find the index of the most significant bit.
    /// @return msb The index of the most significant bit as an uint256.
    function mostSignificantBit(uint256 x) internal pure returns (uint256 msb) {
        if (x >= 2**128) {
            x >>= 128;
            msb += 128;
        }
        if (x >= 2**64) {
            x >>= 64;
            msb += 64;
        }
        if (x >= 2**32) {
            x >>= 32;
            msb += 32;
        }
        if (x >= 2**16) {
            x >>= 16;
            msb += 16;
        }
        if (x >= 2**8) {
            x >>= 8;
            msb += 8;
        }
        if (x >= 2**4) {
            x >>= 4;
            msb += 4;
        }
        if (x >= 2**2) {
            x >>= 2;
            msb += 2;
        }
        if (x >= 2**1) {
            // No need to shift x any more.
            msb += 1;
        }
    }

    /// @notice Calculates floor(x*y÷denominator) with full precision.
    ///
    /// @dev Credit to Remco Bloemen under MIT license https://xn--2-umb.com/21/muldiv.
    ///
    /// Requirements:
    /// - The denominator cannot be zero.
    /// - The result must fit within uint256.
    ///
    /// Caveats:
    /// - This function does not work with fixed-point numbers.
    ///
    /// @param x The multiplicand as an uint256.
    /// @param y The multiplier as an uint256.
    /// @param denominator The divisor as an uint256.
    /// @return result The result as an uint256.
    function mulDiv(
        uint256 x,
        uint256 y,
        uint256 denominator
    ) internal pure returns (uint256 result) {
        // 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) {
            unchecked {
                result = prod0 / denominator;
            }
            return result;
        }

        // Make sure the result is less than 2^256. Also prevents denominator == 0.
        if (prod1 >= denominator) {
            revert PRBMath__MulDivOverflow(prod1, denominator);
        }

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

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

                // Flip lpotdod such that it is 2^256 / lpotdod. If lpotdod is zero, then it becomes one.
                lpotdod := add(div(sub(0, lpotdod), lpotdod), 1)
            }

            // Shift in bits from prod1 into prod0.
            prod0 |= prod1 * lpotdod;

            // 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;

            // Now use 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 floor(x*y÷1e18) with full precision.
    ///
    /// @dev Variant of "mulDiv" with constant folding, i.e. in which the denominator is always 1e18. Before returning the
    /// final result, we add 1 if (x * y) % SCALE >= HALF_SCALE. Without this, 6.6e-19 would be truncated to 0 instead of
    /// being rounded to 1e-18.  See "Listing 6" and text above it at https://accu.org/index.php/journals/1717.
    ///
    /// Requirements:
    /// - The result must fit within uint256.
    ///
    /// Caveats:
    /// - The body is purposely left uncommented; see the NatSpec comments in "PRBMath.mulDiv" to understand how this works.
    /// - It is assumed that the result can never be type(uint256).max when x and y solve the following two equations:
    ///     1. x * y = type(uint256).max * SCALE
    ///     2. (x * y) % SCALE >= SCALE / 2
    ///
    /// @param x The multiplicand as an unsigned 60.18-decimal fixed-point number.
    /// @param y The multiplier as an unsigned 60.18-decimal fixed-point number.
    /// @return result The result as an unsigned 60.18-decimal fixed-point number.
    function mulDivFixedPoint(uint256 x, uint256 y) internal pure returns (uint256 result) {
        uint256 prod0;
        uint256 prod1;
        assembly {
            let mm := mulmod(x, y, not(0))
            prod0 := mul(x, y)
            prod1 := sub(sub(mm, prod0), lt(mm, prod0))
        }

        if (prod1 >= SCALE) {
            revert PRBMath__MulDivFixedPointOverflow(prod1);
        }

        uint256 remainder;
        uint256 roundUpUnit;
        assembly {
            remainder := mulmod(x, y, SCALE)
            roundUpUnit := gt(remainder, 499999999999999999)
        }

        if (prod1 == 0) {
            unchecked {
                result = (prod0 / SCALE) + roundUpUnit;
                return result;
            }
        }

        assembly {
            result := add(
                mul(
                    or(
                        div(sub(prod0, remainder), SCALE_LPOTD),
                        mul(sub(prod1, gt(remainder, prod0)), add(div(sub(0, SCALE_LPOTD), SCALE_LPOTD), 1))
                    ),
                    SCALE_INVERSE
                ),
                roundUpUnit
            )
        }
    }

    /// @notice Calculates floor(x*y÷denominator) with full precision.
    ///
    /// @dev An extension of "mulDiv" for signed numbers. Works by computing the signs and the absolute values separately.
    ///
    /// Requirements:
    /// - None of the inputs can be type(int256).min.
    /// - The result must fit within int256.
    ///
    /// @param x The multiplicand as an int256.
    /// @param y The multiplier as an int256.
    /// @param denominator The divisor as an int256.
    /// @return result The result as an int256.
    function mulDivSigned(
        int256 x,
        int256 y,
        int256 denominator
    ) internal pure returns (int256 result) {
        if (x == type(int256).min || y == type(int256).min || denominator == type(int256).min) {
            revert PRBMath__MulDivSignedInputTooSmall();
        }

        // Get hold of the absolute values of x, y and the denominator.
        uint256 ax;
        uint256 ay;
        uint256 ad;
        unchecked {
            ax = x < 0 ? uint256(-x) : uint256(x);
            ay = y < 0 ? uint256(-y) : uint256(y);
            ad = denominator < 0 ? uint256(-denominator) : uint256(denominator);
        }

        // Compute the absolute value of (x*y)÷denominator. The result must fit within int256.
        uint256 rAbs = mulDiv(ax, ay, ad);
        if (rAbs > uint256(type(int256).max)) {
            revert PRBMath__MulDivSignedOverflow(rAbs);
        }

        // Get the signs of x, y and the denominator.
        uint256 sx;
        uint256 sy;
        uint256 sd;
        assembly {
            sx := sgt(x, sub(0, 1))
            sy := sgt(y, sub(0, 1))
            sd := sgt(denominator, sub(0, 1))
        }

        // XOR over sx, sy and sd. This is checking whether there are one or three negative signs in the inputs.
        // If yes, the result should be negative.
        result = sx ^ sy ^ sd == 0 ? -int256(rAbs) : int256(rAbs);
    }

    /// @notice Calculates the square root of x, rounding down.
    /// @dev Uses the Babylonian method https://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Babylonian_method.
    ///
    /// Caveats:
    /// - This function does not work with fixed-point numbers.
    ///
    /// @param x The uint256 number for which to calculate the square root.
    /// @return result The result as an uint256.
    function sqrt(uint256 x) internal pure returns (uint256 result) {
        if (x == 0) {
            return 0;
        }

        // Set the initial guess to the closest power of two that is higher than x.
        uint256 xAux = uint256(x);
        result = 1;
        if (xAux >= 0x100000000000000000000000000000000) {
            xAux >>= 128;
            result <<= 64;
        }
        if (xAux >= 0x10000000000000000) {
            xAux >>= 64;
            result <<= 32;
        }
        if (xAux >= 0x100000000) {
            xAux >>= 32;
            result <<= 16;
        }
        if (xAux >= 0x10000) {
            xAux >>= 16;
            result <<= 8;
        }
        if (xAux >= 0x100) {
            xAux >>= 8;
            result <<= 4;
        }
        if (xAux >= 0x10) {
            xAux >>= 4;
            result <<= 2;
        }
        if (xAux >= 0x8) {
            result <<= 1;
        }

        // The operations can never overflow because the result is max 2^127 when it enters this block.
        unchecked {
            result = (result + x / result) >> 1;
            result = (result + x / result) >> 1;
            result = (result + x / result) >> 1;
            result = (result + x / result) >> 1;
            result = (result + x / result) >> 1;
            result = (result + x / result) >> 1;
            result = (result + x / result) >> 1; // Seven iterations should be enough
            uint256 roundedDownResult = x / result;
            return result >= roundedDownResult ? roundedDownResult : result;
        }
    }
}

// File: prb-math/contracts/PRBMathUD60x18.sol



// SPDX-License-Identifier: WTFPL
pragma solidity >=0.8.4;

import "./PRBMath.sol";

/// @title PRBMathUD60x18
/// @author Paul Razvan Berg
/// @notice Smart contract library for advanced fixed-point math that works with uint256 numbers considered to have 18
/// trailing decimals. We call this number representation unsigned 60.18-decimal fixed-point, since there can be up to 60
/// digits in the integer part and up to 18 decimals in the fractional part. The numbers are bound by the minimum and the
/// maximum values permitted by the Solidity type uint256.
library PRBMathUD60x18 {
    /// @dev Half the SCALE number.
    uint256 internal constant HALF_SCALE = 5e17;

    /// @dev log2(e) as an unsigned 60.18-decimal fixed-point number.
    uint256 internal constant LOG2_E = 1442695040888963407;

    /// @dev The maximum value an unsigned 60.18-decimal fixed-point number can have.
    uint256 internal constant MAX_UD60x18 = 115792089237316195423570985008687907853269984665640564039457584007913129639935;

    /// @dev The maximum whole value an unsigned 60.18-decimal fixed-point number can have.
    uint256 internal constant MAX_WHOLE_UD60x18 = 115792089237316195423570985008687907853269984665640564039457000000000000000000;

    /// @dev How many trailing decimals can be represented.
    uint256 internal constant SCALE = 1e18;

    /// @notice Calculates arithmetic average of x and y, rounding down.
    /// @param x The first operand as an unsigned 60.18-decimal fixed-point number.
    /// @param y The second operand as an unsigned 60.18-decimal fixed-point number.
    /// @return result The arithmetic average as an unsigned 60.18-decimal fixed-point number.
    function avg(uint256 x, uint256 y) internal pure returns (uint256 result) {
        // The operations can never overflow.
        unchecked {
            // The last operand checks if both x and y are odd and if that is the case, we add 1 to the result. We need
            // to do this because if both numbers are odd, the 0.5 remainder gets truncated twice.
            result = (x >> 1) + (y >> 1) + (x & y & 1);
        }
    }

    /// @notice Yields the least unsigned 60.18 decimal fixed-point number greater than or equal to x.
    ///
    /// @dev Optimised for fractional value inputs, because for every whole value there are (1e18 - 1) fractional counterparts.
    /// See https://en.wikipedia.org/wiki/Floor_and_ceiling_functions.
    ///
    /// Requirements:
    /// - x must be less than or equal to MAX_WHOLE_UD60x18.
    ///
    /// @param x The unsigned 60.18-decimal fixed-point number to ceil.
    /// @param result The least integer greater than or equal to x, as an unsigned 60.18-decimal fixed-point number.
    function ceil(uint256 x) internal pure returns (uint256 result) {
        if (x > MAX_WHOLE_UD60x18) {
            revert PRBMathUD60x18__CeilOverflow(x);
        }
        assembly {
            // Equivalent to "x % SCALE" but faster.
            let remainder := mod(x, SCALE)

            // Equivalent to "SCALE - remainder" but faster.
            let delta := sub(SCALE, remainder)

            // Equivalent to "x + delta * (remainder > 0 ? 1 : 0)" but faster.
            result := add(x, mul(delta, gt(remainder, 0)))
        }
    }

    /// @notice Divides two unsigned 60.18-decimal fixed-point numbers, returning a new unsigned 60.18-decimal fixed-point number.
    ///
    /// @dev Uses mulDiv to enable overflow-safe multiplication and division.
    ///
    /// Requirements:
    /// - The denominator cannot be zero.
    ///
    /// @param x The numerator as an unsigned 60.18-decimal fixed-point number.
    /// @param y The denominator as an unsigned 60.18-decimal fixed-point number.
    /// @param result The quotient as an unsigned 60.18-decimal fixed-point number.
    function div(uint256 x, uint256 y) internal pure returns (uint256 result) {
        result = PRBMath.mulDiv(x, SCALE, y);
    }

    /// @notice Returns Euler's number as an unsigned 60.18-decimal fixed-point number.
    /// @dev See https://en.wikipedia.org/wiki/E_(mathematical_constant).
    function e() internal pure returns (uint256 result) {
        result = 2718281828459045235;
    }

    /// @notice Calculates the natural exponent of x.
    ///
    /// @dev Based on the insight that e^x = 2^(x * log2(e)).
    ///
    /// Requirements:
    /// - All from "log2".
    /// - x must be less than 133.084258667509499441.
    ///
    /// @param x The exponent as an unsigned 60.18-decimal fixed-point number.
    /// @return result The result as an unsigned 60.18-decimal fixed-point number.
    function exp(uint256 x) internal pure returns (uint256 result) {
        // Without this check, the value passed to "exp2" would be greater than 192.
        if (x >= 133084258667509499441) {
            revert PRBMathUD60x18__ExpInputTooBig(x);
        }

        // Do the fixed-point multiplication inline to save gas.
        unchecked {
            uint256 doubleScaleProduct = x * LOG2_E;
            result = exp2((doubleScaleProduct + HALF_SCALE) / SCALE);
        }
    }

    /// @notice Calculates the binary exponent of x using the binary fraction method.
    ///
    /// @dev See https://ethereum.stackexchange.com/q/79903/24693.
    ///
    /// Requirements:
    /// - x must be 192 or less.
    /// - The result must fit within MAX_UD60x18.
    ///
    /// @param x The exponent as an unsigned 60.18-decimal fixed-point number.
    /// @return result The result as an unsigned 60.18-decimal fixed-point number.
    function exp2(uint256 x) internal pure returns (uint256 result) {
        // 2^192 doesn't fit within the 192.64-bit format used internally in this function.
        if (x >= 192e18) {
            revert PRBMathUD60x18__Exp2InputTooBig(x);
        }

        unchecked {
            // Convert x to the 192.64-bit fixed-point format.
            uint256 x192x64 = (x << 64) / SCALE;

            // Pass x to the PRBMath.exp2 function, which uses the 192.64-bit fixed-point number representation.
            result = PRBMath.exp2(x192x64);
        }
    }

    /// @notice Yields the greatest unsigned 60.18 decimal fixed-point number less than or equal to x.
    /// @dev Optimised for fractional value inputs, because for every whole value there are (1e18 - 1) fractional counterparts.
    /// See https://en.wikipedia.org/wiki/Floor_and_ceiling_functions.
    /// @param x The unsigned 60.18-decimal fixed-point number to floor.
    /// @param result The greatest integer less than or equal to x, as an unsigned 60.18-decimal fixed-point number.
    function floor(uint256 x) internal pure returns (uint256 result) {
        assembly {
            // Equivalent to "x % SCALE" but faster.
            let remainder := mod(x, SCALE)

            // Equivalent to "x - remainder * (remainder > 0 ? 1 : 0)" but faster.
            result := sub(x, mul(remainder, gt(remainder, 0)))
        }
    }

    /// @notice Yields the excess beyond the floor of x.
    /// @dev Based on the odd function definition https://en.wikipedia.org/wiki/Fractional_part.
    /// @param x The unsigned 60.18-decimal fixed-point number to get the fractional part of.
    /// @param result The fractional part of x as an unsigned 60.18-decimal fixed-point number.
    function frac(uint256 x) internal pure returns (uint256 result) {
        assembly {
            result := mod(x, SCALE)
        }
    }

    /// @notice Converts a number from basic integer form to unsigned 60.18-decimal fixed-point representation.
    ///
    /// @dev Requirements:
    /// - x must be less than or equal to MAX_UD60x18 divided by SCALE.
    ///
    /// @param x The basic integer to convert.
    /// @param result The same number in unsigned 60.18-decimal fixed-point representation.
    function fromUint(uint256 x) internal pure returns (uint256 result) {
        unchecked {
            if (x > MAX_UD60x18 / SCALE) {
                revert PRBMathUD60x18__FromUintOverflow(x);
            }
            result = x * SCALE;
        }
    }

    /// @notice Calculates geometric mean of x and y, i.e. sqrt(x * y), rounding down.
    ///
    /// @dev Requirements:
    /// - x * y must fit within MAX_UD60x18, lest it overflows.
    ///
    /// @param x The first operand as an unsigned 60.18-decimal fixed-point number.
    /// @param y The second operand as an unsigned 60.18-decimal fixed-point number.
    /// @return result The result as an unsigned 60.18-decimal fixed-point number.
    function gm(uint256 x, uint256 y) internal pure returns (uint256 result) {
        if (x == 0) {
            return 0;
        }

        unchecked {
            // Checking for overflow this way is faster than letting Solidity do it.
            uint256 xy = x * y;
            if (xy / x != y) {
                revert PRBMathUD60x18__GmOverflow(x, y);
            }

            // We don't need to multiply by the SCALE here because the x*y product had already picked up a factor of SCALE
            // during multiplication. See the comments within the "sqrt" function.
            result = PRBMath.sqrt(xy);
        }
    }

    /// @notice Calculates 1 / x, rounding towards zero.
    ///
    /// @dev Requirements:
    /// - x cannot be zero.
    ///
    /// @param x The unsigned 60.18-decimal fixed-point number for which to calculate the inverse.
    /// @return result The inverse as an unsigned 60.18-decimal fixed-point number.
    function inv(uint256 x) internal pure returns (uint256 result) {
        unchecked {
            // 1e36 is SCALE * SCALE.
            result = 1e36 / x;
        }
    }

    /// @notice Calculates the natural logarithm of x.
    ///
    /// @dev Based on the insight that ln(x) = log2(x) / log2(e).
    ///
    /// Requirements:
    /// - All from "log2".
    ///
    /// Caveats:
    /// - All from "log2".
    /// - This doesn't return exactly 1 for 2.718281828459045235, for that we would need more fine-grained precision.
    ///
    /// @param x The unsigned 60.18-decimal fixed-point number for which to calculate the natural logarithm.
    /// @return result The natural logarithm as an unsigned 60.18-decimal fixed-point number.
    function ln(uint256 x) internal pure returns (uint256 result) {
        // Do the fixed-point multiplication inline to save gas. This is overflow-safe because the maximum value that log2(x)
        // can return is 196205294292027477728.
        unchecked {
            result = (log2(x) * SCALE) / LOG2_E;
        }
    }

    /// @notice Calculates the common logarithm of x.
    ///
    /// @dev First checks if x is an exact power of ten and it stops if yes. If it's not, calculates the common
    /// logarithm based on the insight that log10(x) = log2(x) / log2(10).
    ///
    /// Requirements:
    /// - All from "log2".
    ///
    /// Caveats:
    /// - All from "log2".
    ///
    /// @param x The unsigned 60.18-decimal fixed-point number for which to calculate the common logarithm.
    /// @return result The common logarithm as an unsigned 60.18-decimal fixed-point number.
    function log10(uint256 x) internal pure returns (uint256 result) {
        if (x < SCALE) {
            revert PRBMathUD60x18__LogInputTooSmall(x);
        }

        // Note that the "mul" in this block is the assembly multiplication operation, not the "mul" function defined
        // in this contract.
        // prettier-ignore
        assembly {
            switch x
            case 1 { result := mul(SCALE, sub(0, 18)) }
            case 10 { result := mul(SCALE, sub(1, 18)) }
            case 100 { result := mul(SCALE, sub(2, 18)) }
            case 1000 { result := mul(SCALE, sub(3, 18)) }
            case 10000 { result := mul(SCALE, sub(4, 18)) }
            case 100000 { result := mul(SCALE, sub(5, 18)) }
            case 1000000 { result := mul(SCALE, sub(6, 18)) }
            case 10000000 { result := mul(SCALE, sub(7, 18)) }
            case 100000000 { result := mul(SCALE, sub(8, 18)) }
            case 1000000000 { result := mul(SCALE, sub(9, 18)) }
            case 10000000000 { result := mul(SCALE, sub(10, 18)) }
            case 100000000000 { result := mul(SCALE, sub(11, 18)) }
            case 1000000000000 { result := mul(SCALE, sub(12, 18)) }
            case 10000000000000 { result := mul(SCALE, sub(13, 18)) }
            case 100000000000000 { result := mul(SCALE, sub(14, 18)) }
            case 1000000000000000 { result := mul(SCALE, sub(15, 18)) }
            case 10000000000000000 { result := mul(SCALE, sub(16, 18)) }
            case 100000000000000000 { result := mul(SCALE, sub(17, 18)) }
            case 1000000000000000000 { result := 0 }
            case 10000000000000000000 { result := SCALE }
            case 100000000000000000000 { result := mul(SCALE, 2) }
            case 1000000000000000000000 { result := mul(SCALE, 3) }
            case 10000000000000000000000 { result := mul(SCALE, 4) }
            case 100000000000000000000000 { result := mul(SCALE, 5) }
            case 1000000000000000000000000 { result := mul(SCALE, 6) }
            case 10000000000000000000000000 { result := mul(SCALE, 7) }
            case 100000000000000000000000000 { result := mul(SCALE, 8) }
            case 1000000000000000000000000000 { result := mul(SCALE, 9) }
            case 10000000000000000000000000000 { result := mul(SCALE, 10) }
            case 100000000000000000000000000000 { result := mul(SCALE, 11) }
            case 1000000000000000000000000000000 { result := mul(SCALE, 12) }
            case 10000000000000000000000000000000 { result := mul(SCALE, 13) }
            case 100000000000000000000000000000000 { result := mul(SCALE, 14) }
            case 1000000000000000000000000000000000 { result := mul(SCALE, 15) }
            case 10000000000000000000000000000000000 { result := mul(SCALE, 16) }
            case 100000000000000000000000000000000000 { result := mul(SCALE, 17) }
            case 1000000000000000000000000000000000000 { result := mul(SCALE, 18) }
            case 10000000000000000000000000000000000000 { result := mul(SCALE, 19) }
            case 100000000000000000000000000000000000000 { result := mul(SCALE, 20) }
            case 1000000000000000000000000000000000000000 { result := mul(SCALE, 21) }
            case 10000000000000000000000000000000000000000 { result := mul(SCALE, 22) }
            case 100000000000000000000000000000000000000000 { result := mul(SCALE, 23) }
            case 1000000000000000000000000000000000000000000 { result := mul(SCALE, 24) }
            case 10000000000000000000000000000000000000000000 { result := mul(SCALE, 25) }
            case 100000000000000000000000000000000000000000000 { result := mul(SCALE, 26) }
            case 1000000000000000000000000000000000000000000000 { result := mul(SCALE, 27) }
            case 10000000000000000000000000000000000000000000000 { result := mul(SCALE, 28) }
            case 100000000000000000000000000000000000000000000000 { result := mul(SCALE, 29) }
            case 1000000000000000000000000000000000000000000000000 { result := mul(SCALE, 30) }
            case 10000000000000000000000000000000000000000000000000 { result := mul(SCALE, 31) }
            case 100000000000000000000000000000000000000000000000000 { result := mul(SCALE, 32) }
            case 1000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 33) }
            case 10000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 34) }
            case 100000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 35) }
            case 1000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 36) }
            case 10000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 37) }
            case 100000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 38) }
            case 1000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 39) }
            case 10000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 40) }
            case 100000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 41) }
            case 1000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 42) }
            case 10000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 43) }
            case 100000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 44) }
            case 1000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 45) }
            case 10000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 46) }
            case 100000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 47) }
            case 1000000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 48) }
            case 10000000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 49) }
            case 100000000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 50) }
            case 1000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 51) }
            case 10000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 52) }
            case 100000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 53) }
            case 1000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 54) }
            case 10000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 55) }
            case 100000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 56) }
            case 1000000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 57) }
            case 10000000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 58) }
            case 100000000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 59) }
            default {
                result := MAX_UD60x18
            }
        }

        if (result == MAX_UD60x18) {
            // Do the fixed-point division inline to save gas. The denominator is log2(10).
            unchecked {
                result = (log2(x) * SCALE) / 3321928094887362347;
            }
        }
    }

    /// @notice Calculates the binary logarithm of x.
    ///
    /// @dev Based on the iterative approximation algorithm.
    /// https://en.wikipedia.org/wiki/Binary_logarithm#Iterative_approximation
    ///
    /// Requirements:
    /// - x must be greater than or equal to SCALE, otherwise the result would be negative.
    ///
    /// Caveats:
    /// - The results are nor perfectly accurate to the last decimal, due to the lossy precision of the iterative approximation.
    ///
    /// @param x The unsigned 60.18-decimal fixed-point number for which to calculate the binary logarithm.
    /// @return result The binary logarithm as an unsigned 60.18-decimal fixed-point number.
    function log2(uint256 x) internal pure returns (uint256 result) {
        if (x < SCALE) {
            revert PRBMathUD60x18__LogInputTooSmall(x);
        }
        unchecked {
            // Calculate the integer part of the logarithm and add it to the result and finally calculate y = x * 2^(-n).
            uint256 n = PRBMath.mostSignificantBit(x / SCALE);

            // The integer part of the logarithm as an unsigned 60.18-decimal fixed-point number. The operation can't overflow
            // because n is maximum 255 and SCALE is 1e18.
            result = n * SCALE;

            // This is y = x * 2^(-n).
            uint256 y = x >> n;

            // If y = 1, the fractional part is zero.
            if (y == SCALE) {
                return result;
            }

            // Calculate the fractional part via the iterative approximation.
            // The "delta >>= 1" part is equivalent to "delta /= 2", but shifting bits is faster.
            for (uint256 delta = HALF_SCALE; delta > 0; delta >>= 1) {
                y = (y * y) / SCALE;

                // Is y^2 > 2 and so in the range [2,4)?
                if (y >= 2 * SCALE) {
                    // Add the 2^(-m) factor to the logarithm.
                    result += delta;

                    // Corresponds to z/2 on Wikipedia.
                    y >>= 1;
                }
            }
        }
    }

    /// @notice Multiplies two unsigned 60.18-decimal fixed-point numbers together, returning a new unsigned 60.18-decimal
    /// fixed-point number.
    /// @dev See the documentation for the "PRBMath.mulDivFixedPoint" function.
    /// @param x The multiplicand as an unsigned 60.18-decimal fixed-point number.
    /// @param y The multiplier as an unsigned 60.18-decimal fixed-point number.
    /// @return result The product as an unsigned 60.18-decimal fixed-point number.
    function mul(uint256 x, uint256 y) internal pure returns (uint256 result) {
        result = PRBMath.mulDivFixedPoint(x, y);
    }

    /// @notice Returns PI as an unsigned 60.18-decimal fixed-point number.
    function pi() internal pure returns (uint256 result) {
        result = 3141592653589793238;
    }

    /// @notice Raises x to the power of y.
    ///
    /// @dev Based on the insight that x^y = 2^(log2(x) * y).
    ///
    /// Requirements:
    /// - All from "exp2", "log2" and "mul".
    ///
    /// Caveats:
    /// - All from "exp2", "log2" and "mul".
    /// - Assumes 0^0 is 1.
    ///
    /// @param x Number to raise to given power y, as an unsigned 60.18-decimal fixed-point number.
    /// @param y Exponent to raise x to, as an unsigned 60.18-decimal fixed-point number.
    /// @return result x raised to power y, as an unsigned 60.18-decimal fixed-point number.
    function pow(uint256 x, uint256 y) internal pure returns (uint256 result) {
        if (x == 0) {
            result = y == 0 ? SCALE : uint256(0);
        } else {
            result = exp2(mul(log2(x), y));
        }
    }

    /// @notice Raises x (unsigned 60.18-decimal fixed-point number) to the power of y (basic unsigned integer) using the
    /// famous algorithm "exponentiation by squaring".
    ///
    /// @dev See https://en.wikipedia.org/wiki/Exponentiation_by_squaring
    ///
    /// Requirements:
    /// - The result must fit within MAX_UD60x18.
    ///
    /// Caveats:
    /// - All from "mul".
    /// - Assumes 0^0 is 1.
    ///
    /// @param x The base as an unsigned 60.18-decimal fixed-point number.
    /// @param y The exponent as an uint256.
    /// @return result The result as an unsigned 60.18-decimal fixed-point number.
    function powu(uint256 x, uint256 y) internal pure returns (uint256 result) {
        // Calculate the first iteration of the loop in advance.
        result = y & 1 > 0 ? x : SCALE;

        // Equivalent to "for(y /= 2; y > 0; y /= 2)" but faster.
        for (y >>= 1; y > 0; y >>= 1) {
            x = PRBMath.mulDivFixedPoint(x, x);

            // Equivalent to "y % 2 == 1" but faster.
            if (y & 1 > 0) {
                result = PRBMath.mulDivFixedPoint(result, x);
            }
        }
    }

    /// @notice Returns 1 as an unsigned 60.18-decimal fixed-point number.
    function scale() internal pure returns (uint256 result) {
        result = SCALE;
    }

    /// @notice Calculates the square root of x, rounding down.
    /// @dev Uses the Babylonian method https://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Babylonian_method.
    ///
    /// Requirements:
    /// - x must be less than MAX_UD60x18 / SCALE.
    ///
    /// @param x The unsigned 60.18-decimal fixed-point number for which to calculate the square root.
    /// @return result The result as an unsigned 60.18-decimal fixed-point .
    function sqrt(uint256 x) internal pure returns (uint256 result) {
        unchecked {
            if (x > MAX_UD60x18 / SCALE) {
                revert PRBMathUD60x18__SqrtOverflow(x);
            }
            // Multiply x by the SCALE to account for the factor of SCALE that is picked up when multiplying two unsigned
            // 60.18-decimal fixed-point numbers together (in this case, those two numbers are both the square root).
            result = PRBMath.sqrt(x * SCALE);
        }
    }

    /// @notice Converts a unsigned 60.18-decimal fixed-point number to basic integer form, rounding down in the process.
    /// @param x The unsigned 60.18-decimal fixed-point number to convert.
    /// @return result The same number in basic integer form.
    function toUint(uint256 x) internal pure returns (uint256 result) {
        unchecked {
            result = x / SCALE;
        }
    }
}