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;
}
}
/**
 * @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.
 */
function mod(uint256 a, uint256 b) internal pure returns (uint256) {
require(b > 0, "SafeMath: modulo 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.
 */