Description
Given an n×n matrix A,
,
its determinant can be defined recursively as follows.
where M1,j is an (n–1)×(n–1) matrix, defined by removing the first row and the jth column of A,
For example,
.
Input
The first line contains an integer t (1 <= t <= 20), which indicates the number of test cases in the input. Each case starts with an integer n (2 <= n <= 8), specifying the size of the square matrix A. Then following next n lines, each line containing n integers, define the entries of the matrix A. The range of values in the entries is from -5 to 5.
Output
For each case, output one line with the determinant of matrix A.