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;
 }
 }
}
/**
 * @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.
 */
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 remainder of dividing two unsigned integers, with a division by zero flag.
 *
 * _Available since v3.4._
 */