Monk's best friend Micro, who happen to be an awesome programmer, got him an integer matrix M of size \(N \times N\) for his birthday. Monk is taking coding classes from Micro. They have just completed array inversions and Monk was successful in writing a program to count the number of inversions in an array. Now, Micro has asked Monk to find out the number of inversion in the matrix M. Number of inversions, in a matrix is defined as the number of unordered pairs of cells \(\{(i, j), (p, q)\}\) such that \(M[i][j] \gt M[p][q]\space \&\space i \le p\space \& \space j \le q\).
Monk is facing a little trouble with this task and since you did not got him any birthday gift, you need to help him with this task.

Video approach to solve this question: here

Input:
First line consists of a single integer T denoting the number of test cases.
First line of each test case consists of one integer denoting N. Following N lines consists of N space separated integers denoting the matrix M.

Output:
Print the answer to each test case in a new line.

Constraints:
\(1 \le T \le 100\)
\(1 \le N \le 20\)
\(1 \le M[i][j] \le 1000\)