library SafeMath {
   /**
    * @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) {
       return sub(a, b, "SafeMath: subtraction overflow");
   }

   /**
    * @dev Returns the subtraction of two unsigned integers, reverting with custom message on
    * overflow (when the result is negative).
    *
    * Counterpart to Solidity's `-` operator.
    *
    * Requirements:
    * - Subtraction cannot overflow.
    *
    * NOTE: This is a feature of the next version of OpenZeppelin Contracts.
    * @dev Get it via `npm install @openzeppelin/contracts@next`.
    */
   function sub(uint256 a, uint256 b, string memory errorMessage) internal pure returns (uint256) {
       require(b <= a, errorMessage);
       uint256 c = a - b;

       return c;
   }

   /**
    * @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) {
       // 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 0;
       }

       uint256 c = a * b;
       require(c / a == b, "SafeMath: multiplication overflow");

       return c;
   }

   /**
    * @dev Returns the integer division of two unsigned integers. Reverts 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) {
       return div(a, b, "SafeMath: division by zero");
   }

   /**
    * @dev Returns the integer division of two unsigned integers. Reverts 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.
    * NOTE: This is a feature of the next version of OpenZeppelin Contracts.
    * @dev Get it via `npm install @openzeppelin/contracts@next`.
    */
   function div(uint256 a, uint256 b, string memory errorMessage) internal pure returns (uint256) {
       // Solidity only automatically asserts when dividing by 0
       require(b > 0, errorMessage);
       uint256 c = a / b;
       // assert(a == b * c + a % b); // There is no case in which this doesn't hold

       return c;
   }

   /**
    * @dev Returns the remainder of dividing two unsigned integers. (unsigned integer modulo),
    * Reverts 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 mod(a, b, "SafeMath: modulo by zero");
   }

   /**
    * @dev Returns the remainder of dividing two unsigned integers. (unsigned integer modulo),
    * Reverts with custom message 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.
    *
    * NOTE: This is a feature of the next version of OpenZeppelin Contracts.
    * @dev Get it via `npm install @openzeppelin/contracts@next`.
    */
   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 add(uint256 a, uint256 b) internal pure returns (uint256) {
       uint256 c = a + b;
       require(c >= a, "SafeMath: addition overflow");

       return c;
   }
/**
 * @dev Returns the addition of two unsigned integers, reverting on
 * overflow.
 *
 * Counterpart to Solidity's `+` operator.
 *
 * Requirements:
 * - Addition cannot overflow.
 */