// File: 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: IERC20.sol



// SPDX-License-Identifier: MIT

pragma solidity >=0.6.0 <0.8.0;

import "./SafeMath.sol";
import "./Address.sol";

/**
 * @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: Peggy.sol



pragma solidity ^0.6.0;

import "./SafeMath.sol";
import "./IERC20.sol";
import "./SafeERC20.sol";

contract Peggy {
	using SafeMath for uint256;
	using SafeERC20 for IERC20;

	// These are updated often
	bytes32 public state_lastValsetCheckpoint;
	mapping(address => uint256) public state_lastBatchNonces;
	uint256 public state_lastValsetNonce = 0;
	uint256 public state_lastEventNonce = 0;

	// These are set once at initialization
	bytes32 public state_peggyId;
	uint256 public state_powerThreshold;

	bool public halted = false;
	bool public depositsStopped = false;
	address public guardian;

	event TransactionBatchExecutedEvent(
		uint256 indexed _batchNonce,
		address indexed _token,
		address indexed _sender,
		uint256 _eventNonce
	);
	event SendToHubEvent(
		address indexed _tokenContract,
		address indexed _sender,
		bytes32 indexed _destination,
		uint256 _amount,
		uint256 _eventNonce
	);
	event SendToMinterEvent(
		address indexed _tokenContract,
		address indexed _sender,
		bytes32 indexed _destination,
		uint256 _amount,
		uint256 _eventNonce
	);
	event ValsetUpdatedEvent(
		uint256 indexed _newValsetNonce,
		address[] _validators,
		uint256[] _powers
	);

	function lastBatchNonce(address _erc20Address) public view returns (uint256) {
		return state_lastBatchNonces[_erc20Address];
	}

	// Utility function to verify geth style signatures
	function verifySig(
		address _signer,
		bytes32 _theHash,
		uint8 _v,
		bytes32 _r,
		bytes32 _s
	) private pure returns (bool) {
		bytes32 messageDigest = keccak256(
			abi.encodePacked("\x19Ethereum Signed Message:\n32", _theHash)
		);
		return _signer == ecrecover(messageDigest, _v, _r, _s);
	}

	// 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(peggyId, "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(
		address[] memory _validators,
		uint256[] memory _powers,
		uint256 _valsetNonce,
		bytes32 _peggyId
	) private pure returns (bytes32) {
		// bytes32 encoding of the string "checkpoint"
		bytes32 methodName = 0x636865636b706f696e7400000000000000000000000000000000000000000000;

		bytes32 checkpoint = keccak256(
			abi.encode(_peggyId, methodName, _valsetNonce, _validators, _powers)
		);

		return checkpoint;
	}

	function checkValidatorSignatures(
		// The current validator set and their powers
		address[] memory _currentValidators,
		uint256[] memory _currentPowers,
		// The current validator's signatures
		uint8[] memory _v,
		bytes32[] memory _r,
		bytes32[] memory _s,
		// This is what we are checking they have signed
		bytes32 _theHash,
		uint256 _powerThreshold
	) private pure {
		uint256 cumulativePower = 0;

		for (uint256 i = 0; i < _currentValidators.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 (_v[i] != 0) {
				// Check that the current validator has signed off on the hash
				require(
					verifySig(_currentValidators[i], _theHash, _v[i], _r[i], _s[i]),
					"Validator signature does not match."
				);

				// Sum up cumulative power
				cumulativePower = cumulativePower + _currentPowers[i];

				// Break early to avoid wasting gas
				if (cumulativePower > _powerThreshold) {
					break;
				}
			}
		}

		// Check that there was enough power
		require(
			cumulativePower > _powerThreshold,
			"Submitted validator set signatures do not have enough power."
		);
		// 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
		address[] memory _newValidators,
		uint256[] memory _newPowers,
		uint256 _newValsetNonce,
		// The current validators that approve the change
		address[] memory _currentValidators,
		uint256[] memory _currentPowers,
		uint256 _currentValsetNonce,
		// These are arrays of the parts of the current validator's signatures
		uint8[] memory _v,
		bytes32[] memory _r,
		bytes32[] memory _s
	) public {
		// CHECKS

		require(!halted, "contract halted");

		// Check that the valset nonce is greater than the old one
		require(
			_newValsetNonce > _currentValsetNonce,
			"New valset nonce must be greater than the current nonce"
		);

		// Check that new validators and powers set is well-formed
		require(_newValidators.length == _newPowers.length, "Malformed new validator set");

		// Check that current validators, powers, and signatures (v,r,s) set is well-formed
		require(
			_currentValidators.length == _currentPowers.length &&
				_currentValidators.length == _v.length &&
				_currentValidators.length == _r.length &&
				_currentValidators.length == _s.length,
			"Malformed current validator set"
		);

		// Check that the supplied current validator set matches the saved checkpoint
		require(
			makeCheckpoint(
				_currentValidators,
				_currentPowers,
				_currentValsetNonce,
				state_peggyId
			) == state_lastValsetCheckpoint,
			"Supplied current validators and powers do not match checkpoint."
		);

		// Check that enough current validators have signed off on the new validator set
		bytes32 newCheckpoint = makeCheckpoint(
			_newValidators,
			_newPowers,
			_newValsetNonce,
			state_peggyId
		);

		checkValidatorSignatures(
			_currentValidators,
			_currentPowers,
			_v,
			_r,
			_s,
			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 = _newValsetNonce;

		// LOGS

		emit ValsetUpdatedEvent(_newValsetNonce, _newValidators, _newPowers);
	}

	// submitBatch processes a batch of Hub -> Ethereum transactions by sending the tokens in the transactions
	// to the destination addresses. It is approved by the current Hub 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
		address[] memory _currentValidators,
		uint256[] memory _currentPowers,
		uint256 _currentValsetNonce,
		// These are arrays of the parts of the validators signatures
		uint8[] memory _v,
		bytes32[] memory _r,
		bytes32[] memory _s,
		// The batch of transactions
		uint256[] memory _amounts,
		address[] memory _destinations,
		uint256 _batchNonce,
		address _tokenContract
	) public {
		// CHECKS scoped to reduce stack depth
		{
			require(!halted, "contract halted");

			// Check that the batch nonce is higher than the last nonce for this token
			require(
				state_lastBatchNonces[_tokenContract] < _batchNonce,
				"New batch nonce must be greater than the current nonce"
			);

			// Check that current validators, powers, and signatures (v,r,s) set is well-formed
			require(
				_currentValidators.length == _currentPowers.length &&
					_currentValidators.length == _v.length &&
					_currentValidators.length == _r.length &&
					_currentValidators.length == _s.length,
				"Malformed current validator set"
			);

			// Check that the supplied current validator set matches the saved checkpoint
			require(
				makeCheckpoint(
					_currentValidators,
					_currentPowers,
					_currentValsetNonce,
					state_peggyId
				) == state_lastValsetCheckpoint,
				"Supplied current validators and powers do not match checkpoint."
			);

			// Check that the transaction batch is well-formed
			require(
				_amounts.length == _destinations.length,
				"Malformed batch of transactions"
			);

			// Check that enough current validators have signed off on the transaction batch and valset
			checkValidatorSignatures(
				_currentValidators,
				_currentPowers,
				_v,
				_r,
				_s,
				// Get hash of the transaction batch and checkpoint
				keccak256(
					abi.encode(
						state_peggyId,
						// bytes32 encoding of "transactionBatch"
						0x7472616e73616374696f6e426174636800000000000000000000000000000000,
						_amounts,
						_destinations,
						_batchNonce,
						_tokenContract
					)
				),
				state_powerThreshold
			);

			// ACTIONS

			// Store batch nonce
			state_lastBatchNonces[_tokenContract] = _batchNonce;

			{
				// Send transaction amounts to destinations
				for (uint256 i = 0; i < _amounts.length; i++) {
					IERC20(_tokenContract).safeTransfer(_destinations[i], _amounts[i]);
				}
			}
		}

		// LOGS scoped to reduce stack depth
		{
			state_lastEventNonce = state_lastEventNonce.add(1);
			emit TransactionBatchExecutedEvent(_batchNonce, _tokenContract, msg.sender, state_lastEventNonce);
		}
	}

	function sendToHub(
		address _tokenContract,
		bytes32 _destination,
		uint256 _amount
	) public {
		require(!halted, "contract halted");
		require(!depositsStopped, "deposits stopped");

		IERC20(_tokenContract).safeTransferFrom(msg.sender, address(this), _amount);
		state_lastEventNonce = state_lastEventNonce.add(1);
		emit SendToHubEvent(
			_tokenContract,
			msg.sender,
			_destination,
			_amount,
			state_lastEventNonce
		);
	}

	function sendToMinter(
		address _tokenContract,
		bytes32 _destination,
		uint256 _amount
	) public {
		IERC20(_tokenContract).safeTransferFrom(msg.sender, address(this), _amount);
		state_lastEventNonce = state_lastEventNonce.add(1);
		emit SendToMinterEvent(
			_tokenContract,
			msg.sender,
			_destination,
			_amount,
			state_lastEventNonce
		);
	}

	function toggleHalt() public {
		require(msg.sender == guardian, "permission denied");

		halted = !halted;
	}

	function toggleDeposits() public {
		require(msg.sender == guardian, "permission denied");

		depositsStopped = !depositsStopped;
	}

	function changeGuardian(address _guardian) public {
		require(msg.sender == guardian, "permission denied");

		guardian = _guardian;
	}

	function panicHalt(address[] memory _tokenContracts, address _safeAddress) public {
		require(msg.sender == guardian, "permission denied");

		halted = true;
		depositsStopped = true;

		for (uint256 i = 0; i < _tokenContracts.length; i++) {
			IERC20 token = IERC20(_tokenContracts[i]);
			token.safeTransfer(_safeAddress, token.balanceOf(address(this)));
		}
	}

	constructor(
		// A unique identifier for this peggy instance to use in signatures
		bytes32 _peggyId,
		// How much voting power is needed to approve operations
		uint256 _powerThreshold,
		// The validator set
		address[] memory _validators,
		uint256[] memory _powers,
		address _guardian
	) public {
		// CHECKS

		// Check that validators, powers, and signatures (v,r,s) set is well-formed
		require(_validators.length == _powers.length, "Malformed current validator set");

		// 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;
			}
		}
		require(
			cumulativePower > _powerThreshold,
			"Submitted validator set signatures do not have enough power."
		);

		bytes32 newCheckpoint = makeCheckpoint(_validators, _powers, 0, _peggyId);

		// ACTIONS

		state_peggyId = _peggyId;
		state_powerThreshold = _powerThreshold;
		state_lastValsetCheckpoint = newCheckpoint;

		guardian = _guardian;

		// LOGS

		emit ValsetUpdatedEvent(0, _validators, _powers);
	}
}
// File: SafeERC20.sol



// SPDX-License-Identifier: MIT

pragma solidity >=0.6.0 <0.8.0;

import "./SafeMath.sol";
import "./Address.sol";
import "./IERC20.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: 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;
    }
}