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
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).
Each case outputs a number that holds 9 decimal places.