nt j, determine if the distance matrix is "a metric" or not.

A distance matrix a[i][j] is a metric if and only if

1. a[i][i] = 0

2. a[i][j]> 0 if i != j

3. a[i][j] = a[j][i]

4. a[i][j] + a[j][k] >= a[i][k]i¹j¹k

The first line of input gives a single integer, 1 ≤ N ≤5, the number of test cases. Then follow, for each test case,

* Line 1: One integer, N, the rows and number of columns, 2 <= N <= 30

* Line 2..N+1: N lines, each with N space-separated integers

(-32000 <=each integer <= 32000).

Output for each test case, asingle line with a single digit, which is the lowest digit of the possible facts on this list:

* 0: The matrix is a metric

* 1: The matrix is not a metric, it violates rule 1 above

* 2: The matrix is not a metric, it violates rule 2 above

* 3: The matrix is not a metric, it violates rule 3 above

* 4: The matrix is not a metric, it violates rule 4 above

第五届河南省大学生程序设计竞赛