You are given a 2D matrix named $A$ with all slots are integers.

Each element can be represented as: $A(i,j)$, while $i, j$ indicate the line number of row and column, respectively.

Now, we define a rectangle sum $S(x_1,y_1,x_2,y_2)$ as follows:

And we define mean of rectangle sum $M(x_1,y_1,x_2,y_2)$ as follows:

You're going to calculate the minimum mean of rectangle sum in a 2D matrix.

That is, you need to find:

while $n,\ m$ indicate the number or row and column of matrix $A$, respectively.

Take sample I/O as example, the matrix $A$ should be:

$A(1,1)=-1,\ A(1,3)=8$

$S(1,2,2,3)=(-1)+8+0+2=9$

$M(1,2,2,3)=\dfrac{9}{(2-1+1)(3-2+1)}=\dfrac{9}{4}=2.25$

For the minimum choice, you may choose $M(1,1,1,2)$ or $M(1,1,2,1)$, while the answer of both of them are $-1$.

The first contains 2 integers $n,\ m$, indicate the number or row and column of matrix $A$, respectively.

The next $n$ lines contain the whole matrix $A$. The $i$-th line contains the $i$-th row of the matrix.

$1\le n,\ m\le 10^3$, All elements in $A$ will be in range $[-10^9,\ 10^9]$.

The output should contains only the value of minimum mean of rectangle sum.

That is, find out:

and output its value.

Remember the print a '\n' at the end of the output.