// File: @openzeppelin/contracts/math/SafeMath.sol



// SPDX-License-Identifier: MIT

pragma solidity >=0.6.0 <0.8.0;

/**
 * @dev Wrappers over Solidity's arithmetic operations with added overflow
 * checks.
 *
 * Arithmetic operations in Solidity wrap on overflow. This can easily result
 * in bugs, because programmers usually assume that an overflow raises an
 * error, which is the standard behavior in high level programming languages.
 * `SafeMath` restores this intuition by reverting the transaction when an
 * operation overflows.
 *
 * Using this library instead of the unchecked operations eliminates an entire
 * class of bugs, so it's recommended to use it always.
 */
library SafeMath {
    /**
     * @dev Returns the addition of two unsigned integers, with an overflow flag.
     *
     * _Available since v3.4._
     */
    function tryAdd(uint256 a, uint256 b) internal pure returns (bool, uint256) {
        uint256 c = a + b;
        if (c < a) return (false, 0);
        return (true, c);
    }

    /**
     * @dev Returns the substraction of two unsigned integers, with an overflow flag.
     *
     * _Available since v3.4._
     */
    function trySub(uint256 a, uint256 b) internal pure returns (bool, uint256) {
        if (b > a) return (false, 0);
        return (true, a - b);
    }

    /**
     * @dev Returns the multiplication of two unsigned integers, with an overflow flag.
     *
     * _Available since v3.4._
     */
    function tryMul(uint256 a, uint256 b) internal pure returns (bool, uint256) {
        // Gas optimization: this is cheaper than requiring 'a' not being zero, but the
        // benefit is lost if 'b' is also tested.
        // See: https://github.com/OpenZeppelin/openzeppelin-contracts/pull/522
        if (a == 0) return (true, 0);
        uint256 c = a * b;
        if (c / a != b) return (false, 0);
        return (true, c);
    }

    /**
     * @dev Returns the division of two unsigned integers, with a division by zero flag.
     *
     * _Available since v3.4._
     */
    function tryDiv(uint256 a, uint256 b) internal pure returns (bool, uint256) {
        if (b == 0) return (false, 0);
        return (true, a / b);
    }

    /**
     * @dev Returns the remainder of dividing two unsigned integers, with a division by zero flag.
     *
     * _Available since v3.4._
     */
    function tryMod(uint256 a, uint256 b) internal pure returns (bool, uint256) {
        if (b == 0) return (false, 0);
        return (true, a % b);
    }

    /**
     * @dev Returns the addition of two unsigned integers, reverting on
     * overflow.
     *
     * Counterpart to Solidity's `+` operator.
     *
     * Requirements:
     *
     * - Addition cannot overflow.
     */
    function add(uint256 a, uint256 b) internal pure returns (uint256) {
        uint256 c = a + b;
        require(c >= a, "SafeMath: addition overflow");
        return c;
    }

    /**
     * @dev Returns the subtraction of two unsigned integers, reverting on
     * overflow (when the result is negative).
     *
     * Counterpart to Solidity's `-` operator.
     *
     * Requirements:
     *
     * - Subtraction cannot overflow.
     */
    function sub(uint256 a, uint256 b) internal pure returns (uint256) {
        require(b <= a, "SafeMath: subtraction overflow");
        return a - b;
    }

    /**
     * @dev Returns the multiplication of two unsigned integers, reverting on
     * overflow.
     *
     * Counterpart to Solidity's `*` operator.
     *
     * Requirements:
     *
     * - Multiplication cannot overflow.
     */
    function mul(uint256 a, uint256 b) internal pure returns (uint256) {
        if (a == 0) return 0;
        uint256 c = a * b;
        require(c / a == b, "SafeMath: multiplication overflow");
        return c;
    }

    /**
     * @dev Returns the integer division of two unsigned integers, reverting on
     * division by zero. The result is rounded towards zero.
     *
     * Counterpart to Solidity's `/` operator. Note: this function uses a
     * `revert` opcode (which leaves remaining gas untouched) while Solidity
     * uses an invalid opcode to revert (consuming all remaining gas).
     *
     * Requirements:
     *
     * - The divisor cannot be zero.
     */
    function div(uint256 a, uint256 b) internal pure returns (uint256) {
        require(b > 0, "SafeMath: division by zero");
        return a / b;
    }

    /**
     * @dev Returns the remainder of dividing two unsigned integers. (unsigned integer modulo),
     * reverting when dividing by zero.
     *
     * Counterpart to Solidity's `%` operator. This function uses a `revert`
     * opcode (which leaves remaining gas untouched) while Solidity uses an
     * invalid opcode to revert (consuming all remaining gas).
     *
     * Requirements:
     *
     * - The divisor cannot be zero.
     */
    function mod(uint256 a, uint256 b) internal pure returns (uint256) {
        require(b > 0, "SafeMath: modulo by zero");
        return a % b;
    }

    /**
     * @dev Returns the subtraction of two unsigned integers, reverting with custom message on
     * overflow (when the result is negative).
     *
     * CAUTION: This function is deprecated because it requires allocating memory for the error
     * message unnecessarily. For custom revert reasons use {trySub}.
     *
     * Counterpart to Solidity's `-` operator.
     *
     * Requirements:
     *
     * - Subtraction cannot overflow.
     */
    function sub(uint256 a, uint256 b, string memory errorMessage) internal pure returns (uint256) {
        require(b <= a, errorMessage);
        return a - b;
    }

    /**
     * @dev Returns the integer division of two unsigned integers, reverting with custom message on
     * division by zero. The result is rounded towards zero.
     *
     * CAUTION: This function is deprecated because it requires allocating memory for the error
     * message unnecessarily. For custom revert reasons use {tryDiv}.
     *
     * Counterpart to Solidity's `/` operator. Note: this function uses a
     * `revert` opcode (which leaves remaining gas untouched) while Solidity
     * uses an invalid opcode to revert (consuming all remaining gas).
     *
     * Requirements:
     *
     * - The divisor cannot be zero.
     */
    function div(uint256 a, uint256 b, string memory errorMessage) internal pure returns (uint256) {
        require(b > 0, errorMessage);
        return a / b;
    }

    /**
     * @dev Returns the remainder of dividing two unsigned integers. (unsigned integer modulo),
     * reverting with custom message when dividing by zero.
     *
     * CAUTION: This function is deprecated because it requires allocating memory for the error
     * message unnecessarily. For custom revert reasons use {tryMod}.
     *
     * Counterpart to Solidity's `%` operator. This function uses a `revert`
     * opcode (which leaves remaining gas untouched) while Solidity uses an
     * invalid opcode to revert (consuming all remaining gas).
     *
     * Requirements:
     *
     * - The divisor cannot be zero.
     */
    function mod(uint256 a, uint256 b, string memory errorMessage) internal pure returns (uint256) {
        require(b > 0, errorMessage);
        return a % b;
    }
}

// File: @openzeppelin/contracts/proxy/Clones.sol



// SPDX-License-Identifier: MIT

pragma solidity >=0.6.0 <0.8.0;

/**
 * @dev https://eips.ethereum.org/EIPS/eip-1167[EIP 1167] is a standard for
 * deploying minimal proxy contracts, also known as "clones".
 *
 * > To simply and cheaply clone contract functionality in an immutable way, this standard specifies
 * > a minimal bytecode implementation that delegates all calls to a known, fixed address.
 *
 * The library includes functions to deploy a proxy using either `create` (traditional deployment) or `create2`
 * (salted deterministic deployment). It also includes functions to predict the addresses of clones deployed using the
 * deterministic method.
 *
 * _Available since v3.4._
 */
library Clones {
    /**
     * @dev Deploys and returns the address of a clone that mimics the behaviour of `master`.
     *
     * This function uses the create opcode, which should never revert.
     */
    function clone(address master) internal returns (address instance) {
        // solhint-disable-next-line no-inline-assembly
        assembly {
            let ptr := mload(0x40)
            mstore(ptr, 0x3d602d80600a3d3981f3363d3d373d3d3d363d73000000000000000000000000)
            mstore(add(ptr, 0x14), shl(0x60, master))
            mstore(add(ptr, 0x28), 0x5af43d82803e903d91602b57fd5bf30000000000000000000000000000000000)
            instance := create(0, ptr, 0x37)
        }
        require(instance != address(0), "ERC1167: create failed");
    }

    /**
     * @dev Deploys and returns the address of a clone that mimics the behaviour of `master`.
     *
     * This function uses the create2 opcode and a `salt` to deterministically deploy
     * the clone. Using the same `master` and `salt` multiple time will revert, since
     * the clones cannot be deployed twice at the same address.
     */
    function cloneDeterministic(address master, bytes32 salt) internal returns (address instance) {
        // solhint-disable-next-line no-inline-assembly
        assembly {
            let ptr := mload(0x40)
            mstore(ptr, 0x3d602d80600a3d3981f3363d3d373d3d3d363d73000000000000000000000000)
            mstore(add(ptr, 0x14), shl(0x60, master))
            mstore(add(ptr, 0x28), 0x5af43d82803e903d91602b57fd5bf30000000000000000000000000000000000)
            instance := create2(0, ptr, 0x37, salt)
        }
        require(instance != address(0), "ERC1167: create2 failed");
    }

    /**
     * @dev Computes the address of a clone deployed using {Clones-cloneDeterministic}.
     */
    function predictDeterministicAddress(address master, bytes32 salt, address deployer) internal pure returns (address predicted) {
        // solhint-disable-next-line no-inline-assembly
        assembly {
            let ptr := mload(0x40)
            mstore(ptr, 0x3d602d80600a3d3981f3363d3d373d3d3d363d73000000000000000000000000)
            mstore(add(ptr, 0x14), shl(0x60, master))
            mstore(add(ptr, 0x28), 0x5af43d82803e903d91602b57fd5bf3ff00000000000000000000000000000000)
            mstore(add(ptr, 0x38), shl(0x60, deployer))
            mstore(add(ptr, 0x4c), salt)
            mstore(add(ptr, 0x6c), keccak256(ptr, 0x37))
            predicted := keccak256(add(ptr, 0x37), 0x55)
        }
    }

    /**
     * @dev Computes the address of a clone deployed using {Clones-cloneDeterministic}.
     */
    function predictDeterministicAddress(address master, bytes32 salt) internal view returns (address predicted) {
        return predictDeterministicAddress(master, salt, address(this));
    }
}

// File: @openzeppelin/contracts/proxy/Initializable.sol



// SPDX-License-Identifier: MIT

// solhint-disable-next-line compiler-version
pragma solidity >=0.4.24 <0.8.0;

import "../utils/Address.sol";

/**
 * @dev This is a base contract to aid in writing upgradeable contracts, or any kind of contract that will be deployed
 * behind a proxy. Since a proxied contract can't have a constructor, it's common to move constructor logic to an
 * external initializer function, usually called `initialize`. It then becomes necessary to protect this initializer
 * function so it can only be called once. The {initializer} modifier provided by this contract will have this effect.
 *
 * TIP: To avoid leaving the proxy in an uninitialized state, the initializer function should be called as early as
 * possible by providing the encoded function call as the `_data` argument to {UpgradeableProxy-constructor}.
 *
 * CAUTION: When used with inheritance, manual care must be taken to not invoke a parent initializer twice, or to ensure
 * that all initializers are idempotent. This is not verified automatically as constructors are by Solidity.
 */
abstract contract Initializable {

    /**
     * @dev Indicates that the contract has been initialized.
     */
    bool private _initialized;

    /**
     * @dev Indicates that the contract is in the process of being initialized.
     */
    bool private _initializing;

    /**
     * @dev Modifier to protect an initializer function from being invoked twice.
     */
    modifier initializer() {
        require(_initializing || _isConstructor() || !_initialized, "Initializable: contract is already initialized");

        bool isTopLevelCall = !_initializing;
        if (isTopLevelCall) {
            _initializing = true;
            _initialized = true;
        }

        _;

        if (isTopLevelCall) {
            _initializing = false;
        }
    }

    /// @dev Returns true if and only if the function is running in the constructor
    function _isConstructor() private view returns (bool) {
        return !Address.isContract(address(this));
    }
}

// File: @openzeppelin/contracts/token/ERC20/IERC20.sol



// SPDX-License-Identifier: MIT

pragma solidity >=0.6.0 <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/ERC20/SafeERC20.sol



// SPDX-License-Identifier: MIT

pragma solidity >=0.6.0 <0.8.0;

import "./IERC20.sol";
import "../../math/SafeMath.sol";
import "../../utils/Address.sol";

/**
 * @title SafeERC20
 * @dev Wrappers around ERC20 operations that throw on failure (when the token
 * contract returns false). Tokens that return no value (and instead revert or
 * throw on failure) are also supported, non-reverting calls are assumed to be
 * successful.
 * To use this library you can add a `using SafeERC20 for IERC20;` statement to your contract,
 * which allows you to call the safe operations as `token.safeTransfer(...)`, etc.
 */
library SafeERC20 {
    using SafeMath for uint256;
    using Address for address;

    function safeTransfer(IERC20 token, address to, uint256 value) internal {
        _callOptionalReturn(token, abi.encodeWithSelector(token.transfer.selector, to, value));
    }

    function safeTransferFrom(IERC20 token, address from, address to, uint256 value) internal {
        _callOptionalReturn(token, abi.encodeWithSelector(token.transferFrom.selector, from, to, value));
    }

    /**
     * @dev Deprecated. This function has issues similar to the ones found in
     * {IERC20-approve}, and its usage is discouraged.
     *
     * Whenever possible, use {safeIncreaseAllowance} and
     * {safeDecreaseAllowance} instead.
     */
    function safeApprove(IERC20 token, address spender, uint256 value) internal {
        // safeApprove should only be called when setting an initial allowance,
        // or when resetting it to zero. To increase and decrease it, use
        // 'safeIncreaseAllowance' and 'safeDecreaseAllowance'
        // solhint-disable-next-line max-line-length
        require((value == 0) || (token.allowance(address(this), spender) == 0),
            "SafeERC20: approve from non-zero to non-zero allowance"
        );
        _callOptionalReturn(token, abi.encodeWithSelector(token.approve.selector, spender, value));
    }

    function safeIncreaseAllowance(IERC20 token, address spender, uint256 value) internal {
        uint256 newAllowance = token.allowance(address(this), spender).add(value);
        _callOptionalReturn(token, abi.encodeWithSelector(token.approve.selector, spender, newAllowance));
    }

    function safeDecreaseAllowance(IERC20 token, address spender, uint256 value) internal {
        uint256 newAllowance = token.allowance(address(this), spender).sub(value, "SafeERC20: decreased allowance below zero");
        _callOptionalReturn(token, abi.encodeWithSelector(token.approve.selector, spender, newAllowance));
    }

    /**
     * @dev Imitates a Solidity high-level call (i.e. a regular function call to a contract), relaxing the requirement
     * on the return value: the return value is optional (but if data is returned, it must not be false).
     * @param token The token targeted by the call.
     * @param data The call data (encoded using abi.encode or one of its variants).
     */
    function _callOptionalReturn(IERC20 token, bytes memory data) private {
        // We need to perform a low level call here, to bypass Solidity's return data size checking mechanism, since
        // we're implementing it ourselves. We use {Address.functionCall} to perform this call, which verifies that
        // the target address contains contract code and also asserts for success in the low-level call.

        bytes memory returndata = address(token).functionCall(data, "SafeERC20: low-level call failed");
        if (returndata.length > 0) { // Return data is optional
            // solhint-disable-next-line max-line-length
            require(abi.decode(returndata, (bool)), "SafeERC20: ERC20 operation did not succeed");
        }
    }
}

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



// SPDX-License-Identifier: MIT

pragma solidity >=0.6.2 <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;
        // solhint-disable-next-line no-inline-assembly
        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");

        // solhint-disable-next-line avoid-low-level-calls, avoid-call-value
        (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");

        // solhint-disable-next-line avoid-low-level-calls
        (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");

        // solhint-disable-next-line avoid-low-level-calls
        (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");

        // solhint-disable-next-line avoid-low-level-calls
        (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

                // solhint-disable-next-line no-inline-assembly
                assembly {
                    let returndata_size := mload(returndata)
                    revert(add(32, returndata), returndata_size)
                }
            } else {
                revert(errorMessage);
            }
        }
    }
}

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



// SPDX-License-Identifier: MIT

pragma solidity >=0.6.0 <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 () internal {
        _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: contracts/instances/ERC20TornadoCloneable.sol



// SPDX-License-Identifier: MIT

pragma solidity 0.7.6;
pragma abicoder v2;

import "tornado-core/contracts/ERC20Tornado.sol";

contract ERC20TornadoCloneable is ERC20Tornado {
  constructor(address verifier, address hasher) ERC20Tornado(IVerifier(verifier), IHasher(hasher), 1, 1, IERC20(address(0))) {}

  function init(uint256 _denomination, uint32 _merkleTreeHeight, address _token) external {
    require(denomination == 0 && levels == 0, "already initialized");

    token = IERC20(_token);
    require(_denomination > 0, "denomination should be greater than 0");
    denomination = _denomination;
    require(_merkleTreeHeight > 0, "_levels should be greater than zero");
    require(_merkleTreeHeight < 32, "_levels should be less than 32");
    levels = _merkleTreeHeight;

    for (uint32 i = 0; i < _merkleTreeHeight; i++) {
      filledSubtrees[i] = zeros(i);
    }

    roots[0] = zeros(_merkleTreeHeight - 1);
  }
}

// File: contracts/instances/ETHTornadoCloneable.sol



// SPDX-License-Identifier: MIT

pragma solidity 0.7.6;
pragma abicoder v2;

import "tornado-core/contracts/ETHTornado.sol";

contract ETHTornadoCloneable is ETHTornado {
  constructor(address verifier, address hasher) ETHTornado(IVerifier(verifier), IHasher(hasher), 1, 1) {}

  function init(uint256 _denomination, uint32 _merkleTreeHeight) external {
    require(denomination == 0 && levels == 0, "already initialized");

    require(_denomination > 0, "denomination should be greater than 0");
    denomination = _denomination;
    require(_merkleTreeHeight > 0, "_levels should be greater than zero");
    require(_merkleTreeHeight < 32, "_levels should be less than 32");
    levels = _merkleTreeHeight;

    for (uint32 i = 0; i < _merkleTreeHeight; i++) {
      filledSubtrees[i] = zeros(i);
    }

    roots[0] = zeros(_merkleTreeHeight - 1);
  }
}

// File: contracts/MinimalInstanceFactory.sol



// SPDX-License-Identifier: MIT

pragma solidity 0.7.6;
pragma abicoder v2;

import { Address } from "@openzeppelin/contracts/utils/Address.sol";
import { Initializable } from "@openzeppelin/contracts/proxy/Initializable.sol";
import "@openzeppelin/contracts/proxy/Clones.sol";
import "./instances/ERC20TornadoCloneable.sol";
import "./instances/ETHTornadoCloneable.sol";

contract MinimalInstanceFactory {
  using Clones for address;
  using Address for address;

  address public immutable ERC20Impl;
  address public immutable nativeCurImpl;
  address public immutable verifier;
  address public immutable hasher;
  uint32 public immutable merkleTreeHeight;

  event NewTreeHeightSet(uint32 indexed newTreeHeight);
  event NewImplementationSet(address indexed ERC20Impl, address indexed nativeCurImpl, address verifier, address hasher);
  event NewInstanceCloneCreated(address indexed clone);

  /**
   * @notice This instance factory is NOT permissioned. It is designed to always be able to print
   * new Tornado Instances if necessary.
   * @dev Creates new Tornado instance.
   */
  constructor(address _verifier, address _hasher, uint32 _merkleTreeHeight) public {
    verifier = _verifier;
    hasher = _hasher;
    merkleTreeHeight = _merkleTreeHeight;

    ERC20TornadoCloneable ERC20ImplContract = new ERC20TornadoCloneable(_verifier, _hasher);
    ERC20Impl = address(ERC20ImplContract);
    ETHTornadoCloneable nativeCurImplContract = new ETHTornadoCloneable(_verifier, _hasher);
    nativeCurImpl = address(nativeCurImplContract);
  }

  /**
   * @notice Creates new Tornado instance.
   * @param _denomination denomination of new Tornado instance
   * @param _token address of ERC20 token for a new instance, if zero address, then it will be ETH
   */
  function createInstanceClone(uint256 _denomination, address _token) public virtual returns (address clone) {
    bytes32 salt = keccak256(abi.encodePacked(_denomination, _token));

    if (_token == address(0)) {
      clone = nativeCurImpl.predictDeterministicAddress(salt);
      if (!clone.isContract()) {
        nativeCurImpl.cloneDeterministic(salt);
        emit NewInstanceCloneCreated(clone);
        ETHTornadoCloneable(clone).init(_denomination, merkleTreeHeight);
      }
    } else {
      clone = ERC20Impl.predictDeterministicAddress(salt);
      if (!clone.isContract()) {
        ERC20Impl.cloneDeterministic(salt);
        emit NewInstanceCloneCreated(clone);
        ERC20TornadoCloneable(clone).init(_denomination, merkleTreeHeight, _token);
      }
    }
    return clone;
  }

  function getInstanceAddress(uint256 _denomination, address _token) public view returns (address) {
    bytes32 salt = keccak256(abi.encodePacked(_denomination, _token));
    if (_token == address(0)) {
      return nativeCurImpl.predictDeterministicAddress(salt);
    } else {
      return ERC20Impl.predictDeterministicAddress(salt);
    }
  }
}

// File: tornado-core/contracts/ERC20Tornado.sol



// https://tornado.cash
/*
 * d888888P                                           dP              a88888b.                   dP
 *    88                                              88             d8'   `88                   88
 *    88    .d8888b. 88d888b. 88d888b. .d8888b. .d888b88 .d8888b.    88        .d8888b. .d8888b. 88d888b.
 *    88    88'  `88 88'  `88 88'  `88 88'  `88 88'  `88 88'  `88    88        88'  `88 Y8ooooo. 88'  `88
 *    88    88.  .88 88       88    88 88.  .88 88.  .88 88.  .88 dP Y8.   .88 88.  .88       88 88    88
 *    dP    `88888P' dP       dP    dP `88888P8 `88888P8 `88888P' 88  Y88888P' `88888P8 `88888P' dP    dP
 * ooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
 */

// SPDX-License-Identifier: MIT
pragma solidity ^0.7.0;

import "./Tornado.sol";
import "@openzeppelin/contracts/token/ERC20/IERC20.sol";
import "@openzeppelin/contracts/token/ERC20/SafeERC20.sol";

contract ERC20Tornado is Tornado {
  using SafeERC20 for IERC20;
  IERC20 public token;

  constructor(
    IVerifier _verifier,
    IHasher _hasher,
    uint256 _denomination,
    uint32 _merkleTreeHeight,
    IERC20 _token
  ) Tornado(_verifier, _hasher, _denomination, _merkleTreeHeight) {
    token = _token;
  }

  function _processDeposit() internal override {
    require(msg.value == 0, "ETH value is supposed to be 0 for ERC20 instance");
    token.safeTransferFrom(msg.sender, address(this), denomination);
  }

  function _processWithdraw(
    address payable _recipient,
    address payable _relayer,
    uint256 _fee,
    uint256 _refund
  ) internal override {
    require(msg.value == _refund, "Incorrect refund amount received by the contract");

    token.safeTransfer(_recipient, denomination - _fee);
    if (_fee > 0) {
      token.safeTransfer(_relayer, _fee);
    }

    if (_refund > 0) {
      (bool success, ) = _recipient.call{ value: _refund }("");
      if (!success) {
        // let's return _refund back to the relayer
        _relayer.transfer(_refund);
      }
    }
  }
}

// File: tornado-core/contracts/ETHTornado.sol



// https://tornado.cash
/*
 * d888888P                                           dP              a88888b.                   dP
 *    88                                              88             d8'   `88                   88
 *    88    .d8888b. 88d888b. 88d888b. .d8888b. .d888b88 .d8888b.    88        .d8888b. .d8888b. 88d888b.
 *    88    88'  `88 88'  `88 88'  `88 88'  `88 88'  `88 88'  `88    88        88'  `88 Y8ooooo. 88'  `88
 *    88    88.  .88 88       88    88 88.  .88 88.  .88 88.  .88 dP Y8.   .88 88.  .88       88 88    88
 *    dP    `88888P' dP       dP    dP `88888P8 `88888P8 `88888P' 88  Y88888P' `88888P8 `88888P' dP    dP
 * ooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
 */

// SPDX-License-Identifier: MIT
pragma solidity ^0.7.0;

import "./Tornado.sol";

contract ETHTornado is Tornado {
  constructor(
    IVerifier _verifier,
    IHasher _hasher,
    uint256 _denomination,
    uint32 _merkleTreeHeight
  ) Tornado(_verifier, _hasher, _denomination, _merkleTreeHeight) {}

  function _processDeposit() internal override {
    require(msg.value == denomination, "Please send `mixDenomination` ETH along with transaction");
  }

  function _processWithdraw(
    address payable _recipient,
    address payable _relayer,
    uint256 _fee,
    uint256 _refund
  ) internal override {
    // sanity checks
    require(msg.value == 0, "Message value is supposed to be zero for ETH instance");
    require(_refund == 0, "Refund value is supposed to be zero for ETH instance");

    (bool success, ) = _recipient.call{ value: denomination - _fee }("");
    require(success, "payment to _recipient did not go thru");
    if (_fee > 0) {
      (success, ) = _relayer.call{ value: _fee }("");
      require(success, "payment to _relayer did not go thru");
    }
  }
}

// File: tornado-core/contracts/MerkleTreeWithHistory.sol



// https://tornado.cash
/*
 * d888888P                                           dP              a88888b.                   dP
 *    88                                              88             d8'   `88                   88
 *    88    .d8888b. 88d888b. 88d888b. .d8888b. .d888b88 .d8888b.    88        .d8888b. .d8888b. 88d888b.
 *    88    88'  `88 88'  `88 88'  `88 88'  `88 88'  `88 88'  `88    88        88'  `88 Y8ooooo. 88'  `88
 *    88    88.  .88 88       88    88 88.  .88 88.  .88 88.  .88 dP Y8.   .88 88.  .88       88 88    88
 *    dP    `88888P' dP       dP    dP `88888P8 `88888P8 `88888P' 88  Y88888P' `88888P8 `88888P' dP    dP
 * ooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
 */

// SPDX-License-Identifier: MIT
pragma solidity ^0.7.0;

interface IHasher {
  function MiMCSponge(uint256 in_xL, uint256 in_xR) external pure returns (uint256 xL, uint256 xR);
}

contract MerkleTreeWithHistory {
  uint256 public constant FIELD_SIZE = 21888242871839275222246405745257275088548364400416034343698204186575808495617;
  uint256 public constant ZERO_VALUE = 21663839004416932945382355908790599225266501822907911457504978515578255421292; // = keccak256("tornado") % FIELD_SIZE
  IHasher public immutable hasher;

  uint32 public levels;

  // the following variables are made public for easier testing and debugging and
  // are not supposed to be accessed in regular code

  // filledSubtrees and roots could be bytes32[size], but using mappings makes it cheaper because
  // it removes index range check on every interaction
  mapping(uint256 => bytes32) public filledSubtrees;
  mapping(uint256 => bytes32) public roots;
  uint32 public constant ROOT_HISTORY_SIZE = 30;
  uint32 public currentRootIndex = 0;
  uint32 public nextIndex = 0;

  constructor(uint32 _levels, IHasher _hasher) {
    require(_levels > 0, "_levels should be greater than zero");
    require(_levels < 32, "_levels should be less than 32");
    levels = _levels;
    hasher = _hasher;

    for (uint32 i = 0; i < _levels; i++) {
      filledSubtrees[i] = zeros(i);
    }

    roots[0] = zeros(_levels - 1);
  }

  /**
    @dev Hash 2 tree leaves, returns MiMC(_left, _right)
  */
  function hashLeftRight(
    IHasher _hasher,
    bytes32 _left,
    bytes32 _right
  ) public pure returns (bytes32) {
    require(uint256(_left) < FIELD_SIZE, "_left should be inside the field");
    require(uint256(_right) < FIELD_SIZE, "_right should be inside the field");
    uint256 R = uint256(_left);
    uint256 C = 0;
    (R, C) = _hasher.MiMCSponge(R, C);
    R = addmod(R, uint256(_right), FIELD_SIZE);
    (R, C) = _hasher.MiMCSponge(R, C);
    return bytes32(R);
  }

  function _insert(bytes32 _leaf) internal returns (uint32 index) {
    uint32 _nextIndex = nextIndex;
    require(_nextIndex != uint32(2)**levels, "Merkle tree is full. No more leaves can be added");
    uint32 currentIndex = _nextIndex;
    bytes32 currentLevelHash = _leaf;
    bytes32 left;
    bytes32 right;

    for (uint32 i = 0; i < levels; i++) {
      if (currentIndex % 2 == 0) {
        left = currentLevelHash;
        right = zeros(i);
        filledSubtrees[i] = currentLevelHash;
      } else {
        left = filledSubtrees[i];
        right = currentLevelHash;
      }
      currentLevelHash = hashLeftRight(hasher, left, right);
      currentIndex /= 2;
    }

    uint32 newRootIndex = (currentRootIndex + 1) % ROOT_HISTORY_SIZE;
    currentRootIndex = newRootIndex;
    roots[newRootIndex] = currentLevelHash;
    nextIndex = _nextIndex + 1;
    return _nextIndex;
  }

  /**
    @dev Whether the root is present in the root history
  */
  function isKnownRoot(bytes32 _root) public view returns (bool) {
    if (_root == 0) {
      return false;
    }
    uint32 _currentRootIndex = currentRootIndex;
    uint32 i = _currentRootIndex;
    do {
      if (_root == roots[i]) {
        return true;
      }
      if (i == 0) {
        i = ROOT_HISTORY_SIZE;
      }
      i--;
    } while (i != _currentRootIndex);
    return false;
  }

  /**
    @dev Returns the last root
  */
  function getLastRoot() public view returns (bytes32) {
    return roots[currentRootIndex];
  }

  /// @dev provides Zero (Empty) elements for a MiMC MerkleTree. Up to 32 levels
  function zeros(uint256 i) public pure returns (bytes32) {
    if (i == 0) return bytes32(0x2fe54c60d3acabf3343a35b6eba15db4821b340f76e741e2249685ed4899af6c);
    else if (i == 1) return bytes32(0x256a6135777eee2fd26f54b8b7037a25439d5235caee224154186d2b8a52e31d);
    else if (i == 2) return bytes32(0x1151949895e82ab19924de92c40a3d6f7bcb60d92b00504b8199613683f0c200);
    else if (i == 3) return bytes32(0x20121ee811489ff8d61f09fb89e313f14959a0f28bb428a20dba6b0b068b3bdb);
    else if (i == 4) return bytes32(0x0a89ca6ffa14cc462cfedb842c30ed221a50a3d6bf022a6a57dc82ab24c157c9);
    else if (i == 5) return bytes32(0x24ca05c2b5cd42e890d6be94c68d0689f4f21c9cec9c0f13fe41d566dfb54959);
    else if (i == 6) return bytes32(0x1ccb97c932565a92c60156bdba2d08f3bf1377464e025cee765679e604a7315c);
    else if (i == 7) return bytes32(0x19156fbd7d1a8bf5cba8909367de1b624534ebab4f0f79e003bccdd1b182bdb4);
    else if (i == 8) return bytes32(0x261af8c1f0912e465744641409f622d466c3920ac6e5ff37e36604cb11dfff80);
    else if (i == 9) return bytes32(0x0058459724ff6ca5a1652fcbc3e82b93895cf08e975b19beab3f54c217d1c007);
    else if (i == 10) return bytes32(0x1f04ef20dee48d39984d8eabe768a70eafa6310ad20849d4573c3c40c2ad1e30);
    else if (i == 11) return bytes32(0x1bea3dec5dab51567ce7e200a30f7ba6d4276aeaa53e2686f962a46c66d511e5);
    else if (i == 12) return bytes32(0x0ee0f941e2da4b9e31c3ca97a40d8fa9ce68d97c084177071b3cb46cd3372f0f);
    else if (i == 13) return bytes32(0x1ca9503e8935884501bbaf20be14eb4c46b89772c97b96e3b2ebf3a36a948bbd);
    else if (i == 14) return bytes32(0x133a80e30697cd55d8f7d4b0965b7be24057ba5dc3da898ee2187232446cb108);
    else if (i == 15) return bytes32(0x13e6d8fc88839ed76e182c2a779af5b2c0da9dd18c90427a644f7e148a6253b6);
    else if (i == 16) return bytes32(0x1eb16b057a477f4bc8f572ea6bee39561098f78f15bfb3699dcbb7bd8db61854);
    else if (i == 17) return bytes32(0x0da2cb16a1ceaabf1c16b838f7a9e3f2a3a3088d9e0a6debaa748114620696ea);
    else if (i == 18) return bytes32(0x24a3b3d822420b14b5d8cb6c28a574f01e98ea9e940551d2ebd75cee12649f9d);
    else if (i == 19) return bytes32(0x198622acbd783d1b0d9064105b1fc8e4d8889de95c4c519b3f635809fe6afc05);
    else if (i == 20) return bytes32(0x29d7ed391256ccc3ea596c86e933b89ff339d25ea8ddced975ae2fe30b5296d4);
    else if (i == 21) return bytes32(0x19be59f2f0413ce78c0c3703a3a5451b1d7f39629fa33abd11548a76065b2967);
    else if (i == 22) return bytes32(0x1ff3f61797e538b70e619310d33f2a063e7eb59104e112e95738da1254dc3453);
    else if (i == 23) return bytes32(0x10c16ae9959cf8358980d9dd9616e48228737310a10e2b6b731c1a548f036c48);
    else if (i == 24) return bytes32(0x0ba433a63174a90ac20992e75e3095496812b652685b5e1a2eae0b1bf4e8fcd1);
    else if (i == 25) return bytes32(0x019ddb9df2bc98d987d0dfeca9d2b643deafab8f7036562e627c3667266a044c);
    else if (i == 26) return bytes32(0x2d3c88b23175c5a5565db928414c66d1912b11acf974b2e644caaac04739ce99);
    else if (i == 27) return bytes32(0x2eab55f6ae4e66e32c5189eed5c470840863445760f5ed7e7b69b2a62600f354);
    else if (i == 28) return bytes32(0x002df37a2642621802383cf952bf4dd1f32e05433beeb1fd41031fb7eace979d);
    else if (i == 29) return bytes32(0x104aeb41435db66c3e62feccc1d6f5d98d0a0ed75d1374db457cf462e3a1f427);
    else if (i == 30) return bytes32(0x1f3c6fd858e9a7d4b0d1f38e256a09d81d5a5e3c963987e2d4b814cfab7c6ebb);
    else if (i == 31) return bytes32(0x2c7a07d20dff79d01fecedc1134284a8d08436606c93693b67e333f671bf69cc);
    else revert("Index out of bounds");
  }
}

// File: tornado-core/contracts/Tornado.sol



// https://tornado.cash
/*
 * d888888P                                           dP              a88888b.                   dP
 *    88                                              88             d8'   `88                   88
 *    88    .d8888b. 88d888b. 88d888b. .d8888b. .d888b88 .d8888b.    88        .d8888b. .d8888b. 88d888b.
 *    88    88'  `88 88'  `88 88'  `88 88'  `88 88'  `88 88'  `88    88        88'  `88 Y8ooooo. 88'  `88
 *    88    88.  .88 88       88    88 88.  .88 88.  .88 88.  .88 dP Y8.   .88 88.  .88       88 88    88
 *    dP    `88888P' dP       dP    dP `88888P8 `88888P8 `88888P' 88  Y88888P' `88888P8 `88888P' dP    dP
 * ooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
 */

// SPDX-License-Identifier: MIT
pragma solidity ^0.7.0;

import "./MerkleTreeWithHistory.sol";
import "@openzeppelin/contracts/utils/ReentrancyGuard.sol";

interface IVerifier {
  function verifyProof(bytes memory _proof, uint256[6] memory _input) external returns (bool);
}

abstract contract Tornado is MerkleTreeWithHistory, ReentrancyGuard {
  IVerifier public immutable verifier;
  uint256 public denomination;

  mapping(bytes32 => bool) public nullifierHashes;
  // we store all commitments just to prevent accidental deposits with the same commitment
  mapping(bytes32 => bool) public commitments;

  event Deposit(bytes32 indexed commitment, uint32 leafIndex, uint256 timestamp);
  event Withdrawal(address to, bytes32 nullifierHash, address indexed relayer, uint256 fee);

  /**
    @dev The constructor
    @param _verifier the address of SNARK verifier for this contract
    @param _hasher the address of MiMC hash contract
    @param _denomination transfer amount for each deposit
    @param _merkleTreeHeight the height of deposits' Merkle Tree
  */
  constructor(
    IVerifier _verifier,
    IHasher _hasher,
    uint256 _denomination,
    uint32 _merkleTreeHeight
  ) MerkleTreeWithHistory(_merkleTreeHeight, _hasher) {
    require(_denomination > 0, "denomination should be greater than 0");
    verifier = _verifier;
    denomination = _denomination;
  }

  /**
    @dev Deposit funds into the contract. The caller must send (for ETH) or approve (for ERC20) value equal to or `denomination` of this instance.
    @param _commitment the note commitment, which is PedersenHash(nullifier + secret)
  */
  function deposit(bytes32 _commitment) external payable nonReentrant {
    require(!commitments[_commitment], "The commitment has been submitted");

    uint32 insertedIndex = _insert(_commitment);
    commitments[_commitment] = true;
    _processDeposit();

    emit Deposit(_commitment, insertedIndex, block.timestamp);
  }

  /** @dev this function is defined in a child contract */
  function _processDeposit() internal virtual;

  /**
    @dev Withdraw a deposit from the contract. `proof` is a zkSNARK proof data, and input is an array of circuit public inputs
    `input` array consists of:
      - merkle root of all deposits in the contract
      - hash of unique deposit nullifier to prevent double spends
      - the recipient of funds
      - optional fee that goes to the transaction sender (usually a relay)
  */
  function withdraw(
    bytes calldata _proof,
    bytes32 _root,
    bytes32 _nullifierHash,
    address payable _recipient,
    address payable _relayer,
    uint256 _fee,
    uint256 _refund
  ) external payable nonReentrant {
    require(_fee <= denomination, "Fee exceeds transfer value");
    require(!nullifierHashes[_nullifierHash], "The note has been already spent");
    require(isKnownRoot(_root), "Cannot find your merkle root"); // Make sure to use a recent one
    require(
      verifier.verifyProof(
        _proof,
        [uint256(_root), uint256(_nullifierHash), uint256(_recipient), uint256(_relayer), _fee, _refund]
      ),
      "Invalid withdraw proof"
    );

    nullifierHashes[_nullifierHash] = true;
    _processWithdraw(_recipient, _relayer, _fee, _refund);
    emit Withdrawal(_recipient, _nullifierHash, _relayer, _fee);
  }

  /** @dev this function is defined in a child contract */
  function _processWithdraw(
    address payable _recipient,
    address payable _relayer,
    uint256 _fee,
    uint256 _refund
  ) internal virtual;

  /** @dev whether a note is already spent */
  function isSpent(bytes32 _nullifierHash) public view returns (bool) {
    return nullifierHashes[_nullifierHash];
  }

  /** @dev whether an array of notes is already spent */
  function isSpentArray(bytes32[] calldata _nullifierHashes) external view returns (bool[] memory spent) {
    spent = new bool[](_nullifierHashes.length);
    for (uint256 i = 0; i < _nullifierHashes.length; i++) {
      if (isSpent(_nullifierHashes[i])) {
        spent[i] = true;
      }
    }
  }
}