library Math {
  function min(uint x, uint y) internal pure returns (uint z) {
    z = x < y ? x : y;
  }

  // babylonian method (https://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Babylonian_method)
  function sqrt(uint y) internal pure returns (uint z) {
    if (y > 3) {
      z = y;
      uint x = y / 2 + 1;
      while (x < z) {
        z = x;
        x = (y / x + x) / 2;
      }
    } else if (y != 0) {
      z = 1;
    }
  }
}
// a library for performing various math operations
function sqrt(uint y) internal pure returns (uint z) {
    if (y > 3) {
      z = y;
      uint x = y / 2 + 1;
      while (x < z) {
        z = x;
        x = (y / x + x) / 2;
      }
    } else if (y != 0) {
      z = 1;
    }
  }
// babylonian method (https://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Babylonian_method)