Problem Description

There are $n$ balls with $m$ colors. The possibility of that the color of the $i$-th ball is color $j$ is $\frac{a_{i,j}}{a_{i,1}+a_{i,2}+...+a_{i,m}}$. If the number of balls with the $j$-th is $x$, then you should pay $x^2$ as the cost. Please calculate the expectation of the cost.

Input

Several test cases(about $5$)

For each cases, first come 2 integers, $n,m(1 \leq n \leq 1000,1 \leq m \leq 1000)$

Then follows $n$ lines with $m$ numbers $a_{i,j} ( 1 \leq a_i \leq 100)$

Output

For each cases, please output the answer with two decimal places.

2 2
1 1
3 5
2 2
4 5
4 2
2 2
2 4
1 4

3.00
2.96
3.20