1663 - To my boyfriend

1663. To my boyfriend

时间限制 1000 ms 内存限制 32 MB

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

输入数据

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).

输出数据

Each case outputs a number that holds 9 decimal places.

样例输入

复制

1
2 3
1 2 1
2 1 2 \n
 · \n
 · · \n
 · · \n

样例输出

复制

1.666666667           \n

样例说明

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)

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Source

2017 Multi-University Training Contest - Team 2