balls

Time Limit: 6000/3000 MS (Java/Others)

Memory Limit: 65536/65536 K (Java/Others)

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.

Sample Input

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

Sample Output

3.00 2.96 3.20

Hint

hujie

Source

BestCoder Round #63 (div.2)

提交代码