Difference

A graph is a difference if every vertex vi can be assigned a real number ai and there exists a positive real number T such that
(a) |a_i| < T for all i and
(b) (v_i, v_j) in E <=> |a_i - a_j| >= T,
where E is the set of the edges.
Now given a graph, please recognize it whether it is a difference.

The first line of input contains one integer TC(1<=TC<=25), the number of test cases.
Then TC test cases follow. For each test case, the first line contains one integer N(1<=N<=300), the number of vertexes in the graph. Then N lines follow, each of the N line contains a string of length N. The j-th character in the i-th line is "1" if (v_i, v_j) in E, and it is "0" otherwise. The i-th character in the i-th line will be always "0". It is guaranteed that the j-th character in the i-th line will be the same as the i-th character in the j-th line.

For each test case, output a string in one line. Output "Yes" if the graph is a difference, and "No" if it is not a difference.

3 
4 
0011 
0001 
1000 
1100 
4 
0111 
1001 
1001 
1110 
3 
000
000 
000

Yes 
No 
Yes

In sample 1, it can let T=3 and a₁=-2, a₂=-1, a₃=1, a₄=2.

2013 ACM-ICPC吉林通化全国邀请赛——题目重现