Bob has an matrix .

This matrix is very special, It's calculated by two sequences , ,

Now Bob wants to find a submatrix of with the largest average value.

Bob doesn't want the size of submatrix to be too small, so the submatrix you find must satisfy that the height(the first dimension of matrix) of it is at least and the width(the second dimension of matrix) of it is at least .

Now you need to calculate the largest average value.

The first line has four integers .

The second line has  integers .

The third line has  integers .

Output the largest average value.

Your answer will be considered correct if the absolute or relative error is less than 

3 4 2 2
3 1 2
4 1 3 2

4.6666666667