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11349 Symmetric Matrix

You‘re given a square matrix M . Elements of this matrix are M

ij

: {0 < i < n, 0 < j < n}. In this problem you’ll have to find out whether the given matrix is symmetric or not.

Definition: Symmetric matrix is such a matrix that all elements of it are non-negative and symmetric with relation to the center of this matrix. Any other matrix is considered to be non-symmetric. For example:

M =

 5 1 3 2 0 2 3 1 5

 is symmetric

M =

 5 1 3 2 0 2 0 1 5

 is not symmetric, because 3 ̸= 0

All you have to do is to find whether the matrix is symmetric or not. Elements of a matrix given in the input are −2

32

≤ M

ij

≤ 2

32

and 0 < n ≤ 100.

Input

First line of input contains number of test cases T ≤ 300. Then T test cases follow each described in the following way. The first line of each test case contains n – the dimension of square matrix. Then n lines follow each of then containing row i. Row contains exactly n elements separated by a space character. j-th number in row i is the element M

ij

of matrix you have to process.

Output

For each test case output one line ‘Test #t: S’. Where t is the test number starting from 1. Line S is equal to ‘Symmetric’ if matrix is symmetric and ‘Non-symmetric’ in any other case.

Sample Input 2

N = 3 5 1 3 2 0 2 3 1 5 N = 3 5 1 3 2 0 2 0 1 5

Sample Output Test #1: Symmetric.

Test #2: Non-symmetric.

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