// File @openzeppelin/contracts/utils/math/SafeMath.sol@v4.3.2

// SPDX-License-Identifier: MIT

pragma solidity ^0.8.0;

// CAUTION
// This version of SafeMath should only be used with Solidity 0.8 or later,
// because it relies on the compiler's built in overflow checks.

/**
 * @dev Wrappers over Solidity's arithmetic operations.
 *
 * NOTE: `SafeMath` is no longer needed starting with Solidity 0.8. The compiler
 * now has built in overflow checking.
 */
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) {
        unchecked {
            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) {
        unchecked {
            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) {
        unchecked {
            // Gas optimization: this is cheaper than requiring 'a' not being zero, but the
            // benefit is lost if 'b' is also tested.
            // See: https://github.com/OpenZeppelin/openzeppelin-contracts/pull/522
            if (a == 0) return (true, 0);
            uint256 c = a * b;
            if (c / a != b) return (false, 0);
            return (true, c);
        }
    }

    /**
     * @dev Returns the division of two unsigned integers, with a division by zero flag.
     *
     * _Available since v3.4._
     */
    function tryDiv(uint256 a, uint256 b) internal pure returns (bool, uint256) {
        unchecked {
            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) {
        unchecked {
            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) {
        return a + b;
    }

    /**
     * @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) {
        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) {
        return a * b;
    }

    /**
     * @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.
     *
     * Requirements:
     *
     * - The divisor cannot be zero.
     */
    function div(uint256 a, uint256 b) internal pure returns (uint256) {
        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) {
        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) {
        unchecked {
            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.
     *
     * 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) {
        unchecked {
            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) {
        unchecked {
            require(b > 0, errorMessage);
            return a % b;
        }
    }
}


// File @openzeppelin/contracts/token/ERC20/IERC20.sol@v4.3.2

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/utils/Address.sol@v4.3.2

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);
    }

    /**
     * @dev Tool to verifies that a low level call was successful, and revert if it wasn't, either by bubbling the
     * revert reason using the provided one.
     *
     * _Available since v4.3._
     */
    function verifyCallResult(
        bool success,
        bytes memory returndata,
        string memory errorMessage
    ) internal pure returns (bytes memory) {
        if (success) {
            return returndata;
        } else {
            // 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/token/ERC20/utils/SafeERC20.sol@v4.3.2

pragma solidity ^0.8.0;


/**
 * @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 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'
        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) + value;
        _callOptionalReturn(token, abi.encodeWithSelector(token.approve.selector, spender, newAllowance));
    }

    function safeDecreaseAllowance(
        IERC20 token,
        address spender,
        uint256 value
    ) internal {
        unchecked {
            uint256 oldAllowance = token.allowance(address(this), spender);
            require(oldAllowance >= value, "SafeERC20: decreased allowance below zero");
            uint256 newAllowance = oldAllowance - value;
            _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
            require(abi.decode(returndata, (bool)), "SafeERC20: ERC20 operation did not succeed");
        }
    }
}


// File @openzeppelin/contracts/security/ReentrancyGuard.sol@v4.3.2

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/utils/cryptography/ECDSA.sol@v4.3.2

pragma solidity ^0.8.0;

/**
 * @dev Elliptic Curve Digital Signature Algorithm (ECDSA) operations.
 *
 * These functions can be used to verify that a message was signed by the holder
 * of the private keys of a given address.
 */
library ECDSA {
    enum RecoverError {
        NoError,
        InvalidSignature,
        InvalidSignatureLength,
        InvalidSignatureS,
        InvalidSignatureV
    }

    function _throwError(RecoverError error) private pure {
        if (error == RecoverError.NoError) {
            return; // no error: do nothing
        } else if (error == RecoverError.InvalidSignature) {
            revert("ECDSA: invalid signature");
        } else if (error == RecoverError.InvalidSignatureLength) {
            revert("ECDSA: invalid signature length");
        } else if (error == RecoverError.InvalidSignatureS) {
            revert("ECDSA: invalid signature 's' value");
        } else if (error == RecoverError.InvalidSignatureV) {
            revert("ECDSA: invalid signature 'v' value");
        }
    }

    /**
     * @dev Returns the address that signed a hashed message (`hash`) with
     * `signature` or error string. This address can then be used for verification purposes.
     *
     * The `ecrecover` EVM opcode allows for malleable (non-unique) signatures:
     * this function rejects them by requiring the `s` value to be in the lower
     * half order, and the `v` value to be either 27 or 28.
     *
     * IMPORTANT: `hash` _must_ be the result of a hash operation for the
     * verification to be secure: it is possible to craft signatures that
     * recover to arbitrary addresses for non-hashed data. A safe way to ensure
     * this is by receiving a hash of the original message (which may otherwise
     * be too long), and then calling {toEthSignedMessageHash} on it.
     *
     * Documentation for signature generation:
     * - with https://web3js.readthedocs.io/en/v1.3.4/web3-eth-accounts.html#sign[Web3.js]
     * - with https://docs.ethers.io/v5/api/signer/#Signer-signMessage[ethers]
     *
     * _Available since v4.3._
     */
    function tryRecover(bytes32 hash, bytes memory signature) internal pure returns (address, RecoverError) {
        // Check the signature length
        // - case 65: r,s,v signature (standard)
        // - case 64: r,vs signature (cf https://eips.ethereum.org/EIPS/eip-2098) _Available since v4.1._
        if (signature.length == 65) {
            bytes32 r;
            bytes32 s;
            uint8 v;
            // ecrecover takes the signature parameters, and the only way to get them
            // currently is to use assembly.
            assembly {
                r := mload(add(signature, 0x20))
                s := mload(add(signature, 0x40))
                v := byte(0, mload(add(signature, 0x60)))
            }
            return tryRecover(hash, v, r, s);
        } else if (signature.length == 64) {
            bytes32 r;
            bytes32 vs;
            // ecrecover takes the signature parameters, and the only way to get them
            // currently is to use assembly.
            assembly {
                r := mload(add(signature, 0x20))
                vs := mload(add(signature, 0x40))
            }
            return tryRecover(hash, r, vs);
        } else {
            return (address(0), RecoverError.InvalidSignatureLength);
        }
    }

    /**
     * @dev Returns the address that signed a hashed message (`hash`) with
     * `signature`. This address can then be used for verification purposes.
     *
     * The `ecrecover` EVM opcode allows for malleable (non-unique) signatures:
     * this function rejects them by requiring the `s` value to be in the lower
     * half order, and the `v` value to be either 27 or 28.
     *
     * IMPORTANT: `hash` _must_ be the result of a hash operation for the
     * verification to be secure: it is possible to craft signatures that
     * recover to arbitrary addresses for non-hashed data. A safe way to ensure
     * this is by receiving a hash of the original message (which may otherwise
     * be too long), and then calling {toEthSignedMessageHash} on it.
     */
    function recover(bytes32 hash, bytes memory signature) internal pure returns (address) {
        (address recovered, RecoverError error) = tryRecover(hash, signature);
        _throwError(error);
        return recovered;
    }

    /**
     * @dev Overload of {ECDSA-tryRecover} that receives the `r` and `vs` short-signature fields separately.
     *
     * See https://eips.ethereum.org/EIPS/eip-2098[EIP-2098 short signatures]
     *
     * _Available since v4.3._
     */
    function tryRecover(
        bytes32 hash,
        bytes32 r,
        bytes32 vs
    ) internal pure returns (address, RecoverError) {
        bytes32 s;
        uint8 v;
        assembly {
            s := and(vs, 0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff)
            v := add(shr(255, vs), 27)
        }
        return tryRecover(hash, v, r, s);
    }

    /**
     * @dev Overload of {ECDSA-recover} that receives the `r and `vs` short-signature fields separately.
     *
     * _Available since v4.2._
     */
    function recover(
        bytes32 hash,
        bytes32 r,
        bytes32 vs
    ) internal pure returns (address) {
        (address recovered, RecoverError error) = tryRecover(hash, r, vs);
        _throwError(error);
        return recovered;
    }

    /**
     * @dev Overload of {ECDSA-tryRecover} that receives the `v`,
     * `r` and `s` signature fields separately.
     *
     * _Available since v4.3._
     */
    function tryRecover(
        bytes32 hash,
        uint8 v,
        bytes32 r,
        bytes32 s
    ) internal pure returns (address, RecoverError) {
        // EIP-2 still allows signature malleability for ecrecover(). Remove this possibility and make the signature
        // unique. Appendix F in the Ethereum Yellow paper (https://ethereum.github.io/yellowpaper/paper.pdf), defines
        // the valid range for s in (301): 0 < s < secp256k1n ÷ 2 + 1, and for v in (302): v ∈ {27, 28}. Most
        // signatures from current libraries generate a unique signature with an s-value in the lower half order.
        //
        // If your library generates malleable signatures, such as s-values in the upper range, calculate a new s-value
        // with 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141 - s1 and flip v from 27 to 28 or
        // vice versa. If your library also generates signatures with 0/1 for v instead 27/28, add 27 to v to accept
        // these malleable signatures as well.
        if (uint256(s) > 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF5D576E7357A4501DDFE92F46681B20A0) {
            return (address(0), RecoverError.InvalidSignatureS);
        }
        if (v != 27 && v != 28) {
            return (address(0), RecoverError.InvalidSignatureV);
        }

        // If the signature is valid (and not malleable), return the signer address
        address signer = ecrecover(hash, v, r, s);
        if (signer == address(0)) {
            return (address(0), RecoverError.InvalidSignature);
        }

        return (signer, RecoverError.NoError);
    }

    /**
     * @dev Overload of {ECDSA-recover} that receives the `v`,
     * `r` and `s` signature fields separately.
     */
    function recover(
        bytes32 hash,
        uint8 v,
        bytes32 r,
        bytes32 s
    ) internal pure returns (address) {
        (address recovered, RecoverError error) = tryRecover(hash, v, r, s);
        _throwError(error);
        return recovered;
    }

    /**
     * @dev Returns an Ethereum Signed Message, created from a `hash`. This
     * produces hash corresponding to the one signed with the
     * https://eth.wiki/json-rpc/API#eth_sign[`eth_sign`]
     * JSON-RPC method as part of EIP-191.
     *
     * See {recover}.
     */
    function toEthSignedMessageHash(bytes32 hash) internal pure returns (bytes32) {
        // 32 is the length in bytes of hash,
        // enforced by the type signature above
        return keccak256(abi.encodePacked("\x19Ethereum Signed Message:\n32", hash));
    }

    /**
     * @dev Returns an Ethereum Signed Typed Data, created from a
     * `domainSeparator` and a `structHash`. This produces hash corresponding
     * to the one signed with the
     * https://eips.ethereum.org/EIPS/eip-712[`eth_signTypedData`]
     * JSON-RPC method as part of EIP-712.
     *
     * See {recover}.
     */
    function toTypedDataHash(bytes32 domainSeparator, bytes32 structHash) internal pure returns (bytes32) {
        return keccak256(abi.encodePacked("\x19\x01", domainSeparator, structHash));
    }
}


// File @openzeppelin/contracts/token/ERC20/extensions/IERC20Metadata.sol@v4.3.2

pragma solidity ^0.8.0;

/**
 * @dev Interface for the optional metadata functions from the ERC20 standard.
 *
 * _Available since v4.1._
 */
interface IERC20Metadata is IERC20 {
    /**
     * @dev Returns the name of the token.
     */
    function name() external view returns (string memory);

    /**
     * @dev Returns the symbol of the token.
     */
    function symbol() external view returns (string memory);

    /**
     * @dev Returns the decimals places of the token.
     */
    function decimals() external view returns (uint8);
}


// File @openzeppelin/contracts/utils/Context.sol@v4.3.2

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/token/ERC20/ERC20.sol@v4.3.2

pragma solidity ^0.8.0;



/**
 * @dev Implementation of the {IERC20} interface.
 *
 * This implementation is agnostic to the way tokens are created. This means
 * that a supply mechanism has to be added in a derived contract using {_mint}.
 * For a generic mechanism see {ERC20PresetMinterPauser}.
 *
 * TIP: For a detailed writeup see our guide
 * https://forum.zeppelin.solutions/t/how-to-implement-erc20-supply-mechanisms/226[How
 * to implement supply mechanisms].
 *
 * We have followed general OpenZeppelin Contracts guidelines: functions revert
 * instead returning `false` on failure. This behavior is nonetheless
 * conventional and does not conflict with the expectations of ERC20
 * applications.
 *
 * Additionally, an {Approval} event is emitted on calls to {transferFrom}.
 * This allows applications to reconstruct the allowance for all accounts just
 * by listening to said events. Other implementations of the EIP may not emit
 * these events, as it isn't required by the specification.
 *
 * Finally, the non-standard {decreaseAllowance} and {increaseAllowance}
 * functions have been added to mitigate the well-known issues around setting
 * allowances. See {IERC20-approve}.
 */
contract ERC20 is Context, IERC20, IERC20Metadata {
    mapping(address => uint256) private _balances;

    mapping(address => mapping(address => uint256)) private _allowances;

    uint256 private _totalSupply;

    string private _name;
    string private _symbol;

    /**
     * @dev Sets the values for {name} and {symbol}.
     *
     * The default value of {decimals} is 18. To select a different value for
     * {decimals} you should overload it.
     *
     * All two of these values are immutable: they can only be set once during
     * construction.
     */
    constructor(string memory name_, string memory symbol_) {
        _name = name_;
        _symbol = symbol_;
    }

    /**
     * @dev Returns the name of the token.
     */
    function name() public view virtual override returns (string memory) {
        return _name;
    }

    /**
     * @dev Returns the symbol of the token, usually a shorter version of the
     * name.
     */
    function symbol() public view virtual override returns (string memory) {
        return _symbol;
    }

    /**
     * @dev Returns the number of decimals used to get its user representation.
     * For example, if `decimals` equals `2`, a balance of `505` tokens should
     * be displayed to a user as `5.05` (`505 / 10 ** 2`).
     *
     * Tokens usually opt for a value of 18, imitating the relationship between
     * Ether and Wei. This is the value {ERC20} uses, unless this function is
     * overridden;
     *
     * NOTE: This information is only used for _display_ purposes: it in
     * no way affects any of the arithmetic of the contract, including
     * {IERC20-balanceOf} and {IERC20-transfer}.
     */
    function decimals() public view virtual override returns (uint8) {
        return 18;
    }

    /**
     * @dev See {IERC20-totalSupply}.
     */
    function totalSupply() public view virtual override returns (uint256) {
        return _totalSupply;
    }

    /**
     * @dev See {IERC20-balanceOf}.
     */
    function balanceOf(address account) public view virtual override returns (uint256) {
        return _balances[account];
    }

    /**
     * @dev See {IERC20-transfer}.
     *
     * Requirements:
     *
     * - `recipient` cannot be the zero address.
     * - the caller must have a balance of at least `amount`.
     */
    function transfer(address recipient, uint256 amount) public virtual override returns (bool) {
        _transfer(_msgSender(), recipient, amount);
        return true;
    }

    /**
     * @dev See {IERC20-allowance}.
     */
    function allowance(address owner, address spender) public view virtual override returns (uint256) {
        return _allowances[owner][spender];
    }

    /**
     * @dev See {IERC20-approve}.
     *
     * Requirements:
     *
     * - `spender` cannot be the zero address.
     */
    function approve(address spender, uint256 amount) public virtual override returns (bool) {
        _approve(_msgSender(), spender, amount);
        return true;
    }

    /**
     * @dev See {IERC20-transferFrom}.
     *
     * Emits an {Approval} event indicating the updated allowance. This is not
     * required by the EIP. See the note at the beginning of {ERC20}.
     *
     * Requirements:
     *
     * - `sender` and `recipient` cannot be the zero address.
     * - `sender` must have a balance of at least `amount`.
     * - the caller must have allowance for ``sender``'s tokens of at least
     * `amount`.
     */
    function transferFrom(
        address sender,
        address recipient,
        uint256 amount
    ) public virtual override returns (bool) {
        _transfer(sender, recipient, amount);

        uint256 currentAllowance = _allowances[sender][_msgSender()];
        require(currentAllowance >= amount, "ERC20: transfer amount exceeds allowance");
        unchecked {
            _approve(sender, _msgSender(), currentAllowance - amount);
        }

        return true;
    }

    /**
     * @dev Atomically increases the allowance granted to `spender` by the caller.
     *
     * This is an alternative to {approve} that can be used as a mitigation for
     * problems described in {IERC20-approve}.
     *
     * Emits an {Approval} event indicating the updated allowance.
     *
     * Requirements:
     *
     * - `spender` cannot be the zero address.
     */
    function increaseAllowance(address spender, uint256 addedValue) public virtual returns (bool) {
        _approve(_msgSender(), spender, _allowances[_msgSender()][spender] + addedValue);
        return true;
    }

    /**
     * @dev Atomically decreases the allowance granted to `spender` by the caller.
     *
     * This is an alternative to {approve} that can be used as a mitigation for
     * problems described in {IERC20-approve}.
     *
     * Emits an {Approval} event indicating the updated allowance.
     *
     * Requirements:
     *
     * - `spender` cannot be the zero address.
     * - `spender` must have allowance for the caller of at least
     * `subtractedValue`.
     */
    function decreaseAllowance(address spender, uint256 subtractedValue) public virtual returns (bool) {
        uint256 currentAllowance = _allowances[_msgSender()][spender];
        require(currentAllowance >= subtractedValue, "ERC20: decreased allowance below zero");
        unchecked {
            _approve(_msgSender(), spender, currentAllowance - subtractedValue);
        }

        return true;
    }

    /**
     * @dev Moves `amount` of tokens from `sender` to `recipient`.
     *
     * This internal function is equivalent to {transfer}, and can be used to
     * e.g. implement automatic token fees, slashing mechanisms, etc.
     *
     * Emits a {Transfer} event.
     *
     * Requirements:
     *
     * - `sender` cannot be the zero address.
     * - `recipient` cannot be the zero address.
     * - `sender` must have a balance of at least `amount`.
     */
    function _transfer(
        address sender,
        address recipient,
        uint256 amount
    ) internal virtual {
        require(sender != address(0), "ERC20: transfer from the zero address");
        require(recipient != address(0), "ERC20: transfer to the zero address");

        _beforeTokenTransfer(sender, recipient, amount);

        uint256 senderBalance = _balances[sender];
        require(senderBalance >= amount, "ERC20: transfer amount exceeds balance");
        unchecked {
            _balances[sender] = senderBalance - amount;
        }
        _balances[recipient] += amount;

        emit Transfer(sender, recipient, amount);

        _afterTokenTransfer(sender, recipient, amount);
    }

    /** @dev Creates `amount` tokens and assigns them to `account`, increasing
     * the total supply.
     *
     * Emits a {Transfer} event with `from` set to the zero address.
     *
     * Requirements:
     *
     * - `account` cannot be the zero address.
     */
    function _mint(address account, uint256 amount) internal virtual {
        require(account != address(0), "ERC20: mint to the zero address");

        _beforeTokenTransfer(address(0), account, amount);

        _totalSupply += amount;
        _balances[account] += amount;
        emit Transfer(address(0), account, amount);

        _afterTokenTransfer(address(0), account, amount);
    }

    /**
     * @dev Destroys `amount` tokens from `account`, reducing the
     * total supply.
     *
     * Emits a {Transfer} event with `to` set to the zero address.
     *
     * Requirements:
     *
     * - `account` cannot be the zero address.
     * - `account` must have at least `amount` tokens.
     */
    function _burn(address account, uint256 amount) internal virtual {
        require(account != address(0), "ERC20: burn from the zero address");

        _beforeTokenTransfer(account, address(0), amount);

        uint256 accountBalance = _balances[account];
        require(accountBalance >= amount, "ERC20: burn amount exceeds balance");
        unchecked {
            _balances[account] = accountBalance - amount;
        }
        _totalSupply -= amount;

        emit Transfer(account, address(0), amount);

        _afterTokenTransfer(account, address(0), amount);
    }

    /**
     * @dev Sets `amount` as the allowance of `spender` over the `owner` s tokens.
     *
     * This internal function is equivalent to `approve`, and can be used to
     * e.g. set automatic allowances for certain subsystems, etc.
     *
     * Emits an {Approval} event.
     *
     * Requirements:
     *
     * - `owner` cannot be the zero address.
     * - `spender` cannot be the zero address.
     */
    function _approve(
        address owner,
        address spender,
        uint256 amount
    ) internal virtual {
        require(owner != address(0), "ERC20: approve from the zero address");
        require(spender != address(0), "ERC20: approve to the zero address");

        _allowances[owner][spender] = amount;
        emit Approval(owner, spender, amount);
    }

    /**
     * @dev Hook that is called before any transfer of tokens. This includes
     * minting and burning.
     *
     * Calling conditions:
     *
     * - when `from` and `to` are both non-zero, `amount` of ``from``'s tokens
     * will be transferred to `to`.
     * - when `from` is zero, `amount` tokens will be minted for `to`.
     * - when `to` is zero, `amount` of ``from``'s tokens will be burned.
     * - `from` and `to` are never both zero.
     *
     * To learn more about hooks, head to xref:ROOT:extending-contracts.adoc#using-hooks[Using Hooks].
     */
    function _beforeTokenTransfer(
        address from,
        address to,
        uint256 amount
    ) internal virtual {}

    /**
     * @dev Hook that is called after any transfer of tokens. This includes
     * minting and burning.
     *
     * Calling conditions:
     *
     * - when `from` and `to` are both non-zero, `amount` of ``from``'s tokens
     * has been transferred to `to`.
     * - when `from` is zero, `amount` tokens have been minted for `to`.
     * - when `to` is zero, `amount` of ``from``'s tokens have been burned.
     * - `from` and `to` are never both zero.
     *
     * To learn more about hooks, head to xref:ROOT:extending-contracts.adoc#using-hooks[Using Hooks].
     */
    function _afterTokenTransfer(
        address from,
        address to,
        uint256 amount
    ) internal virtual {}
}


// File contracts/CosmosToken.sol

pragma solidity ^0.8.10;

contract CosmosERC20 is ERC20 {
	uint256 private MAX_UINT = 2**256 - 1;

	address public gravity;

	uint8 private cosmosDecimals;

	mapping(address => mapping(address => uint256)) private _allowances;


	modifier onlyGravity() {
		require(msg.sender == gravity, "Not gravity");
		_;
	}

	constructor(
		address _gravityAddress,
		string memory _name,
		string memory _symbol,
		uint8 _decimals
	) public ERC20(_name, _symbol)  {
		cosmosDecimals = _decimals;
		gravity = _gravityAddress;
		_mint(_gravityAddress, MAX_UINT);

	}


	// This is not an accurate total supply. Instead this is the total supply
	// of the given cosmos asset on Ethereum at this moment in time. Keeping
	// a totally accurate supply would require constant updates from the Cosmos
	// side, while in theory this could be piggy-backed on some existing bridge
	// operation it's a lot of complextiy to add so we chose to forgoe it.
	
	/**
	 * @dev Returns the number of tokens not currently held by the gravity address
	 *

	 */	
	function totalSupply() public view virtual override returns (uint256) {
		return MAX_UINT - balanceOf(gravity);
	}


	/**
	 * @dev Sets the gravity contract to a new address.
	 *
	 * Requirements:
	 *
	 * - `msg.sender` must be the current gravity contract
	 */
	function setGravityContract(address _gravityAddress) external onlyGravity {

		gravity = _gravityAddress;
	 }

	/**
	 * @dev Overrides the decimal function in the base ERC20 contract. 
	 * This override is needed to Ethereum wallets display tokens consistently
	 * with how Cosmos wallets display the native version of the token.
	 */

   function decimals()public view override returns (uint8){
	   return cosmosDecimals;
   }

}


// File contracts/Gravity.sol

pragma solidity 0.8.10;







error InvalidSignature();
error InvalidValsetNonce(uint256 newNonce, uint256 currentNonce);
error InvalidBatchNonce(uint256 newNonce, uint256 currentNonce);
error InvalidLogicCallNonce(uint256 newNonce, uint256 currentNonce);
error InvalidLogicCallTransfers();
error InvalidLogicCallFees();
error InvalidSendToCosmos();
error IncorrectCheckpoint();
error MalformedNewValidatorSet();
error MalformedCurrentValidatorSet();
error MalformedBatch();
error InsufficientPower(uint256 cumulativePower, uint256 powerThreshold);
error BatchTimedOut();
error LogicCallTimedOut();

// This is being used purely to avoid stack too deep errors
struct LogicCallArgs {
	// Transfers out to the logic contract
	uint256[] transferAmounts;
	address[] transferTokenContracts;
	// The fees (transferred to msg.sender)
	uint256[] feeAmounts;
	address[] feeTokenContracts;
	// The arbitrary logic call
	address logicContractAddress;
	bytes payload;
	// Invalidation metadata
	uint256 timeOut;
	bytes32 invalidationId;
	uint256 invalidationNonce;
}

// This is used purely to avoid stack too deep errors
// represents everything about a given validator set
struct ValsetArgs {
	// the validators in this set, represented by an Ethereum address
	address[] validators;
	// the powers of the given validators in the same order as above
	uint256[] powers;
	// the nonce of this validator set
	uint256 valsetNonce;
	// the reward amount denominated in the below reward token, can be
	// set to zero
	uint256 rewardAmount;
	// the reward token, should be set to the zero address if not being used
	address rewardToken;
}

struct ValSignature {
	uint8 v;
	bytes32 r;
	bytes32 s;
}

contract Gravity is ReentrancyGuard {
	using SafeMath for uint256;
	using SafeERC20 for IERC20;

	// These are updated often
	bytes32 public state_lastValsetCheckpoint;
	mapping(address => uint256) public state_lastBatchNonces;
	mapping(bytes32 => uint256) public state_invalidationMapping;
	uint256 public state_lastValsetNonce = 0;
	// event nonce zero is reserved by the Cosmos module as a special
	// value indicating that no events have yet been submitted
	uint256 public state_lastEventNonce = 1;

	// These are set once at initialization
	uint256 public state_powerThreshold;
	// This is set once at initialization
	bytes32 public immutable state_gravityId;

	// TransactionBatchExecutedEvent and SendToCosmosEvent both include the field _eventNonce.
	// This is incremented every time one of these events is emitted. It is checked by the
	// Cosmos module to ensure that all events are received in order, and that none are lost.
	//
	// ValsetUpdatedEvent does not include the field _eventNonce because it is never submitted to the Cosmos
	// module. It is purely for the use of relayers to allow them to successfully submit batches.
	event TransactionBatchExecutedEvent(
		uint256 indexed _batchNonce,
		address indexed _token,
		uint256 _eventNonce
	);
	event SendToCosmosEvent(
		address indexed _tokenContract,
		address indexed _sender,
		bytes32 indexed _destination,
		uint256 _amount,
		uint256 _eventNonce
	);
	event ERC20DeployedEvent(
		// FYI: Can't index on a string without doing a bunch of weird stuff
		string _cosmosDenom,
		address indexed _tokenContract,
		string _name,
		string _symbol,
		uint8 _decimals,
		uint256 _eventNonce
	);
	event ValsetUpdatedEvent(
		uint256 indexed _newValsetNonce,
		uint256 _eventNonce,
		uint256 _rewardAmount,
		address _rewardToken,
		address[] _validators,
		uint256[] _powers
	);
	event LogicCallEvent(
		bytes32 _invalidationId,
		uint256 _invalidationNonce,
		bytes _returnData,
		uint256 _eventNonce
	);

	// TEST FIXTURES
	// These are here to make it easier to measure gas usage. They should be removed before production
	function testMakeCheckpoint(ValsetArgs calldata _valsetArgs, bytes32 _gravityId) external pure {
		makeCheckpoint(_valsetArgs, _gravityId);
	}

	function testCheckValidatorSignatures(
		ValsetArgs calldata _currentValset,
		ValSignature[] calldata _sigs,
		bytes32 _theHash,
		uint256 _powerThreshold
	) external pure {
		checkValidatorSignatures(_currentValset, _sigs, _theHash, _powerThreshold);
	}

	// END TEST FIXTURES

	function lastBatchNonce(address _erc20Address) external view returns (uint256) {
		return state_lastBatchNonces[_erc20Address];
	}

	function lastLogicCallNonce(bytes32 _invalidation_id) external view returns (uint256) {
		return state_invalidationMapping[_invalidation_id];
	}

	// Utility function to verify geth style signatures
	function verifySig(
		address _signer,
		bytes32 _theHash,
		ValSignature calldata _sig
	) private pure returns (bool) {
		bytes32 messageDigest = keccak256(
			abi.encodePacked("\x19Ethereum Signed Message:\n32", _theHash)
		);
		return _signer == ECDSA.recover(messageDigest, _sig.v, _sig.r, _sig.s);
	}


	// Utility function to determine that a validator set and signatures are well formed
	function validateValset(ValsetArgs calldata _valset, ValSignature[] calldata _sigs) private pure {
		// Check that current validators, powers, and signatures (v,r,s) set is well-formed
		if (
			_valset.validators.length != _valset.powers.length ||
			_valset.validators.length != _sigs.length
		) {
			revert MalformedCurrentValidatorSet();
		}
	}



	// Make a new checkpoint from the supplied validator set
	// A checkpoint is a hash of all relevant information about the valset. This is stored by the contract,
	// instead of storing the information directly. This saves on storage and gas.
	// The format of the checkpoint is:
	// h(gravityId, "checkpoint", valsetNonce, validators[], powers[])
	// Where h is the keccak256 hash function.
	// The validator powers must be decreasing or equal. This is important for checking the signatures on the
	// next valset, since it allows the caller to stop verifying signatures once a quorum of signatures have been verified.
	function makeCheckpoint(ValsetArgs memory _valsetArgs, bytes32 _gravityId)
		private
		pure
		returns (bytes32)
	{
		// bytes32 encoding of the string "checkpoint"
		bytes32 methodName = 0x636865636b706f696e7400000000000000000000000000000000000000000000;

		bytes32 checkpoint = keccak256(
			abi.encode(
				_gravityId,
				methodName,
				_valsetArgs.valsetNonce,
				_valsetArgs.validators,
				_valsetArgs.powers,
				_valsetArgs.rewardAmount,
				_valsetArgs.rewardToken
			)
		);

		return checkpoint;
	}


	function checkValidatorSignatures(
		// The current validator set and their powers
		ValsetArgs calldata _currentValset,
		// The current validator's signatures
		ValSignature[] calldata _sigs,
		// This is what we are checking they have signed
		bytes32 _theHash,
		uint256 _powerThreshold
	) private pure {
		uint256 cumulativePower = 0;

		for (uint256 i = 0; i < _currentValset.validators.length; i++) {
			// If v is set to 0, this signifies that it was not possible to get a signature from this validator and we skip evaluation
			// (In a valid signature, it is either 27 or 28)
			if (_sigs[i].v != 0) {
				// Check that the current validator has signed off on the hash
				if (!verifySig(_currentValset.validators[i], _theHash, _sigs[i])) {
					revert InvalidSignature();
				}

				// Sum up cumulative power
				cumulativePower = cumulativePower + _currentValset.powers[i];

				// Break early to avoid wasting gas
				if (cumulativePower > _powerThreshold) {
					break;
				}
			}
		}

		// Check that there was enough power
		if (cumulativePower <= _powerThreshold) {
			revert InsufficientPower(cumulativePower, _powerThreshold);
		}
		// Success
	}
	// This updates the valset by checking that the validators in the current valset have signed off on the
	// new valset. The signatures supplied are the signatures of the current valset over the checkpoint hash
	// generated from the new valset.
	// Anyone can call this function, but they must supply valid signatures of state_powerThreshold of the current valset over
	// the new valset.
function updateValset(
		// The new version of the validator set
		ValsetArgs calldata _newValset,
		// The current validators that approve the change
		ValsetArgs calldata _currentValset,
		// These are arrays of the parts of the current validator's signatures
		ValSignature[] calldata _sigs
	) external {
		// CHECKS

		// Check that the valset nonce is greater than the old one
		if (_newValset.valsetNonce <= _currentValset.valsetNonce) {
			revert InvalidValsetNonce({
				newNonce: _newValset.valsetNonce,
				currentNonce: _currentValset.valsetNonce
			});
		}

		// Check that the valset nonce is less than a million nonces forward from the old one
		// this makes it difficult for an attacker to lock out the contract by getting a single
		// bad validator set through with uint256 max nonce
		if (_newValset.valsetNonce > _currentValset.valsetNonce + 1000000) {
			revert InvalidValsetNonce({
				newNonce: _newValset.valsetNonce,
				currentNonce: _currentValset.valsetNonce
			});
		}

		// Check that new validators and powers set is well-formed
		if (
			_newValset.validators.length != _newValset.powers.length ||
			_newValset.validators.length == 0
		) {
			revert MalformedNewValidatorSet();
		}

		// Check that current validators, powers, and signatures (v,r,s) set is well-formed
		validateValset(_currentValset, _sigs);

		// Check cumulative power to ensure the contract has sufficient power to actually
		// pass a vote
		uint256 cumulativePower = 0;
		for (uint256 i = 0; i < _newValset.powers.length; i++) {
			cumulativePower = cumulativePower + _newValset.powers[i];
			if (cumulativePower > state_powerThreshold) {
				break;
			}
		}
		if (cumulativePower <= state_powerThreshold) {
			revert InsufficientPower({
				cumulativePower: cumulativePower,
				powerThreshold: state_powerThreshold
			});
		}

		// Check that the supplied current validator set matches the saved checkpoint
		if (makeCheckpoint(_currentValset, state_gravityId) != state_lastValsetCheckpoint) {
			revert IncorrectCheckpoint();
		}

		// Check that enough current validators have signed off on the new validator set
		bytes32 newCheckpoint = makeCheckpoint(_newValset, state_gravityId);

		checkValidatorSignatures(_currentValset, _sigs, newCheckpoint, state_powerThreshold);

		// ACTIONS

		// Stored to be used next time to validate that the valset
		// supplied by the caller is correct.
		state_lastValsetCheckpoint = newCheckpoint;

		// Store new nonce
		state_lastValsetNonce = _newValset.valsetNonce;

		// Send submission reward to msg.sender if reward token is a valid value
		if (_newValset.rewardToken != address(0) && _newValset.rewardAmount != 0) {
			IERC20(_newValset.rewardToken).safeTransfer(msg.sender, _newValset.rewardAmount);
		}

		// LOGS

		state_lastEventNonce = state_lastEventNonce + 1;
		emit ValsetUpdatedEvent(
			_newValset.valsetNonce,
			state_lastEventNonce,
			_newValset.rewardAmount,
			_newValset.rewardToken,
			_newValset.validators,
			_newValset.powers
		);
	}

	// submitBatch processes a batch of Cosmos -> Ethereum transactions by sending the tokens in the transactions
	// to the destination addresses. It is approved by the current Cosmos validator set.
	// Anyone can call this function, but they must supply valid signatures of state_powerThreshold of the current valset over
	// the batch.
	function submitBatch(
		// The validators that approve the batch
		ValsetArgs calldata _currentValset,
		// These are arrays of the parts of the validators signatures
		ValSignature[] calldata _sigs,
		// The batch of transactions
		uint256[] calldata _amounts,
		address[] calldata _destinations,
		uint256[] calldata _fees,
		uint256 _batchNonce,
		address _tokenContract,
		// a block height beyond which this batch is not valid
		// used to provide a fee-free timeout
		uint256 _batchTimeout
	) external nonReentrant {
		// CHECKS scoped to reduce stack depth
		{
			// Check that the batch nonce is higher than the last nonce for this token
			if (_batchNonce <= state_lastBatchNonces[_tokenContract]) {
				revert InvalidBatchNonce({
					newNonce: _batchNonce,
					currentNonce: state_lastBatchNonces[_tokenContract]
				});
			}

			// Check that the batch nonce is less than one million nonces forward from the old one
			// this makes it difficult for an attacker to lock out the contract by getting a single
			// bad batch through with uint256 max nonce
			if (_batchNonce > state_lastBatchNonces[_tokenContract] + 1000000) {
				revert InvalidBatchNonce({
					newNonce: _batchNonce,
					currentNonce: state_lastBatchNonces[_tokenContract]
				});
			}

			// Check that the block height is less than the timeout height
			if (block.number >= _batchTimeout) {
				revert BatchTimedOut();
			}

			// Check that current validators, powers, and signatures (v,r,s) set is well-formed
			validateValset(_currentValset, _sigs);

			// Check that the supplied current validator set matches the saved checkpoint
			if (makeCheckpoint(_currentValset, state_gravityId) != state_lastValsetCheckpoint) {
				revert IncorrectCheckpoint();
			}

			// Check that the transaction batch is well-formed
			if (_amounts.length != _destinations.length || _amounts.length != _fees.length) {
				revert MalformedBatch();
			}

			// Check that enough current validators have signed off on the transaction batch and valset
			checkValidatorSignatures(
				_currentValset,
				_sigs,
				// Get hash of the transaction batch and checkpoint
				keccak256(
					abi.encode(
						state_gravityId,
						// bytes32 encoding of "transactionBatch"
						0x7472616e73616374696f6e426174636800000000000000000000000000000000,
						_amounts,
						_destinations,
						_fees,
						_batchNonce,
						_tokenContract,
						_batchTimeout
					)
				),
				state_powerThreshold
			);

			// ACTIONS

			// Store batch nonce
			state_lastBatchNonces[_tokenContract] = _batchNonce;

			{
				// Send transaction amounts to destinations
				uint256 totalFee;
				for (uint256 i = 0; i < _amounts.length; i++) {
					IERC20(_tokenContract).safeTransfer(_destinations[i], _amounts[i]);
					totalFee = totalFee + _fees[i];
				}

				// Send transaction fees to msg.sender
				IERC20(_tokenContract).safeTransfer(msg.sender, totalFee);
			}
		}

		// LOGS scoped to reduce stack depth
		{
			state_lastEventNonce = state_lastEventNonce + 1;
			emit TransactionBatchExecutedEvent(_batchNonce, _tokenContract, state_lastEventNonce);
		}
	}	

	// This makes calls to contracts that execute arbitrary logic
	// First, it gives the logic contract some tokens
	// Then, it gives msg.senders tokens for fees
	// Then, it calls an arbitrary function on the logic contract
	// invalidationId and invalidationNonce are used for replay prevention.
	// They can be used to implement a per-token nonce by setting the token
	// address as the invalidationId and incrementing the nonce each call.
	// They can be used for nonce-free replay prevention by using a different invalidationId
	// for each call.
	function submitLogicCall(
		// The validators that approve the call
		ValsetArgs calldata _currentValset,
		// These are arrays of the parts of the validators signatures
		ValSignature[] calldata _sigs,
		LogicCallArgs memory _args
	) external nonReentrant {
		// CHECKS scoped to reduce stack depth
		{
			// Check that the call has not timed out
			if (block.number >= _args.timeOut) {
				revert LogicCallTimedOut();
			}

			// Check that the invalidation nonce is higher than the last nonce for this invalidation Id
			if (state_invalidationMapping[_args.invalidationId] >= _args.invalidationNonce) {
				revert InvalidLogicCallNonce({
					newNonce: _args.invalidationNonce,
					currentNonce: state_invalidationMapping[_args.invalidationId]
				});
			}

			// note the lack of nonce skipping check, it's not needed here since an attacker
			// will never be able to fill the invalidationId space, therefore a nonce lockout
			// is simply not possible

			// Check that current validators, powers, and signatures (v,r,s) set is well-formed
			validateValset(_currentValset, _sigs);

			// Check that the supplied current validator set matches the saved checkpoint
			if (makeCheckpoint(_currentValset, state_gravityId) != state_lastValsetCheckpoint) {
				revert IncorrectCheckpoint();
			}

			if (_args.transferAmounts.length != _args.transferTokenContracts.length) {
				revert InvalidLogicCallTransfers();
			}

			if (_args.feeAmounts.length != _args.feeTokenContracts.length) {
				revert InvalidLogicCallFees();
			}
		}
		{
			bytes32 argsHash = keccak256(
				abi.encode(
					state_gravityId,
					// bytes32 encoding of "logicCall"
					0x6c6f67696343616c6c0000000000000000000000000000000000000000000000,
					_args.transferAmounts,
					_args.transferTokenContracts,
					_args.feeAmounts,
					_args.feeTokenContracts,
					_args.logicContractAddress,
					_args.payload,
					_args.timeOut,
					_args.invalidationId,
					_args.invalidationNonce
				)
			);

			// Check that enough current validators have signed off on the transaction batch and valset
			checkValidatorSignatures(
				_currentValset,
				_sigs,
				// Get hash of the transaction batch and checkpoint
				argsHash,
				state_powerThreshold
			);
		}

		// ACTIONS

		// Update invaldiation nonce
		state_invalidationMapping[_args.invalidationId] = _args.invalidationNonce;

		// Send tokens to the logic contract
		for (uint256 i = 0; i < _args.transferAmounts.length; i++) {
			IERC20(_args.transferTokenContracts[i]).safeTransfer(
				_args.logicContractAddress,
				_args.transferAmounts[i]
			);
		}

		// Make call to logic contract
		bytes memory returnData = Address.functionCall(_args.logicContractAddress, _args.payload);

		// Send fees to msg.sender
		for (uint256 i = 0; i < _args.feeAmounts.length; i++) {
			IERC20(_args.feeTokenContracts[i]).safeTransfer(msg.sender, _args.feeAmounts[i]);
		}

		// LOGS scoped to reduce stack depth
		{
			state_lastEventNonce = state_lastEventNonce + 1;
			emit LogicCallEvent(
				_args.invalidationId,
				_args.invalidationNonce,
				returnData,
				state_lastEventNonce
			);
		}
	}

	function sendToCosmos(
		address _tokenContract,
		bytes32 _destination,
		uint256 _amount
	) public nonReentrant {
		// we snapshot our current balance of this token
		uint256 ourStartingBalance = IERC20(_tokenContract).balanceOf(address(this));

		// attempt to transfer the user specified amount
		IERC20(_tokenContract).safeTransferFrom(msg.sender, address(this), _amount);

		// check what this particular ERC20 implementation actually gave us, since it doesn't
		// have to be at all related to the _amount
		uint256 ourEndingBalance = IERC20(_tokenContract).balanceOf(address(this));

		// a very strange ERC20 may trigger this condition, if we didn't have this we would
		// underflow, so it's mostly just an error message printer
		if (ourEndingBalance <= ourStartingBalance) {
			revert InvalidSendToCosmos();
		}

		state_lastEventNonce = state_lastEventNonce + 1;

		// emit to Cosmos the actual amount our balance has changed, rather than the user
		// provided amount. This protects against a small set of wonky ERC20 behavior, like
		// burning on send but not tokens that for example change every users balance every day.
		emit SendToCosmosEvent(
			_tokenContract,
			msg.sender,
			_destination,
			ourEndingBalance - ourStartingBalance,
			state_lastEventNonce
		);
	}

	function deployERC20(
		string calldata _cosmosDenom,
		string calldata _name,
		string calldata _symbol,
		uint8 _decimals
	) external {
		// Deploy an ERC20 with entire supply granted to Gravity.sol
		CosmosERC20 erc20 = new CosmosERC20(address(this), _name, _symbol, _decimals);

		// Fire an event to let the Cosmos module know
		state_lastEventNonce = state_lastEventNonce.add(1);
		emit ERC20DeployedEvent(
			_cosmosDenom,
			address(erc20),
			_name,
			_symbol,
			_decimals,
			state_lastEventNonce
		);
	}

	constructor(
		// A unique identifier for this gravity instance to use in signatures
		bytes32 _gravityId,
		// How much voting power is needed to approve operations
		uint256 _powerThreshold,
		// The validator set
		address[] memory _validators,
		uint256[] memory _powers
	) public {
		// CHECKS

		// Check that validators, powers, and signatures (v,r,s) set is well-formed
		if (_validators.length != _powers.length) {
			revert MalformedCurrentValidatorSet();
		}

		// Check cumulative power to ensure the contract has sufficient power to actually
		// pass a vote
		uint256 cumulativePower = 0;
		for (uint256 i = 0; i < _powers.length; i++) {
			cumulativePower = cumulativePower + _powers[i];
			if (cumulativePower > _powerThreshold) {
				break;
			}
		}

		if (cumulativePower <= _powerThreshold) {
			revert InsufficientPower({
				cumulativePower: cumulativePower,
				powerThreshold: _powerThreshold
			});
		}

		ValsetArgs memory _valset;
		_valset = ValsetArgs(_validators, _powers, 0, 0, address(0));

		bytes32 newCheckpoint = makeCheckpoint(_valset, _gravityId);

		// ACTIONS

		state_gravityId = _gravityId;
		state_powerThreshold = _powerThreshold;
		state_lastValsetCheckpoint = newCheckpoint;

		// LOGS

		emit ValsetUpdatedEvent(
			state_lastValsetNonce,
			state_lastEventNonce,
			0,
			address(0),
			_validators,
			_powers
		);
	}
}