Roy likes Symmetric Logos.
How to check whether a logo is symmetric?
Align the center of logo with the origin of Cartesian plane. Now if the colored pixels of the logo are symmetric about both X-axis and Y-axis, then the logo is symmetric.
You are given a binary matrix of size N x N which represents the pixels of a logo.
1 indicates that the pixel is colored and 0 indicates no color.
For instance: Take a 5x5 matrix as follows:
01110
01010
10001
01010
01110
Graphically it is represented as follows:
Observe that it is symmetric about both X-axis and Y-axis.
Let's take another example of 5x5 matrix:
00100
01010
10001
01010
01110
Graphically it is represented as follows:
Now this logo is symmetric about Y-axis but it is not symmetric about X-axis.
Your task is to output YES if the logo is symmetric else output NO.
Input:
First line contains T - number of test cases.
T test cases follow.
First line of each test case contains the N - size of matrix.
Next N lines contains binary strings of length N.
Output:
Print YES or NO in a new line for each test case
Constraints:
1 ≤ T ≤ 10
2 ≤ N ≤ 32
Note: There will always be atleast 1 colored pixel in input data.