Sudoku?

Given a 9X9 2-D matrix, with some cells filled with digits(1-9), and some empty cells(denoted by 0), you need to find whether there exists a way to fill all the empty cells with some digit(1-9) such that the final matrix is a valid Sudoku Solution.

A Sudoku solution must satisfy all the following conditions-

1. Each of the digits 1-9 must occur exactly once in each row.
2. Each of the digits 1-9 must occur exactly once in each column.
3. Each of the digits 1-9 must occur exactly once in each of the 9, 3x3 sub-matrices of the matrix.

Note

1. There will always be a cell in the matrix which is empty.
2. The given initial matrix will always be consistent according to the rules mentioned in the problem statement.

Input Format:

The first line contains a single integer t -  the number of test cases. The next 9t lines contains the description of each test case.
There will be 9 lines for each test case with each line containing 9 space separated digits, (0, if the cell is empty, digit(1-9) otherwise.

Output Format:

Print “yes”(without quotes), if there is way or “no” (without quotes) otherwise. Note the lowercase format of the output.

Note:

You do not need to print anything, it has already been taken care of. Just implement the given function.

Constraints:

1 <= T <= 5
N=9
0 <= Matrix[i][j] <= 9

Time Limit: 1sec

Sample Input 1:

1
9 0 0 0 2 0 7 5 0 
6 0 0 0 5 0 0 4 0 
0 2 0 4 0 0 0 1 0 
2 0 8 0 0 0 0 0 0 
0 7 0 5 0 9 0 6 0 
0 0 0 0 0 0 4 0 1 
0 1 0 0 0 5 0 8 0 
0 9 0 0 7 0 0 0 4 
0 8 2 0 4 0 0 0 6

Sample Output 1:

yes

Explanation of the Sample Input1:

One of the possible solutions is:
9 4 1 3 2 6 7 5 8
6 3 7 1 5 8 2 4 9
8 2 5 4 9 7 6 1 3
2 6 8 7 1 4 3 9 5
1 7 4 5 3 9 8 6 2
3 5 9 6 8 2 4 7 1
4 1 3 2 6 5 9 8 7
5 9 6 8 7 3 1 2 4
7 8 2 9 4 1 5 3 6

Sample Input 2:

1
1 5 9 0 0 6 0 3 2
2 7 4 0 0 0 0 0 0
3 8 6 2 0 0 0 0 5
4 9 2 5 0 1 0 8 0
6 3 7 0 4 0 0 0 0
5 1 0 8 2 0 0 0 0
8 2 1 0 0 0 0 0 0
7 6 0 1 0 0 4 2 0
9 4 3 0 7 0 0 6 1

Sample Output 2:

no

Explanation of the Sample Input2:

In the third column from the left, there are two empty cells out of which one has to be filled with ‘8’, but we can’t put 8 in any of those two cells.