To my boyfriend

Problem Description

Dear Liao I never forget the moment I met with you. You carefully asked me: "I have a very difficult problem. Can you teach me?". I replied with a smile, "of course". You replied:"Given a matrix, I randomly choose a sub-matrix, what is the expectation of the number of different numbers it contains?" Sincerely yours, Guo

Input

The first line of input contains an integer T(T<=8) indicating the number of test cases. Each case contains two integers, n and m (1<=n, m<=100), the number of rows and the number of columns in the grid, respectively. The next n lines each contain m integers. In particular, the j-th integer in the i-th of these rows contains g_i,j (0<=g_i,j <=n*m).

Output

Each case outputs a number that holds 9 decimal places.

Sample Input

1

2 3

1 2 1

2 1 2

Sample Output

1.666666667

Hint

6(size = 1) + 14(size = 2) + 4(size = 3) + 4(size = 4) + 2(size = 6) = 30 / 18 = 6(size = 1) + 7(size = 2) + 2(size = 3) + 2(size = 4) + 1(size = 6)

Source

2017 Multi-University Training Contest - Team 2

https://acm.hdu.edu.cn/showproblem.php?pid=6052