On the plane, located the N (3 ≤ N) points. Of these, randomly selected three points, which are then connected by segments. Required to determine the expectation of the perimeter of a triangle, provided that each set of three points can be chosen with equal probability, and the resulting triangle can be degenerate.
The first line of the input file contains two numbers H and W (1 ≤ H, W ≤ 700). This is followed by lines of H characters. j-th symbol of the i-th row is equal to '1' if there is a point with coordinates (i, j), otherwise the corresponding position is a symbol of '0'. It is guaranteed that the input data are presented as at least three points.
The output file output a single number - the expectation of the perimeter of a triangle. The answer must differ from the correct no more than 10^{-6}.