Sudoku Validity Problem Statement

You are provided with a 9 x 9 2D matrix MATRIX containing digits (1-9) and empty cells indicated by 0.

Your task is to determine if there exists a method to fill all empty cells with digits (1-9) such that the resulting matrix is a valid Sudoku solution.

A valid Sudoku solution must meet the following criteria:

• Each digit from 1 to 9 must appear exactly once in each row.
• Each digit from 1 to 9 must appear exactly once in each column.
• Each digit from 1 to 9 must appear exactly once in each of the nine 3 x 3 sub-matrices within the main matrix.

Input:

The first line contains an integer 'T', the number of test cases. For each test case, 9 lines follow, each containing 9 space-separated integers representing a row in the matrix.

Output:

For each test case, output "yes" if a valid Sudoku solution exists, or "no" if it does not. Outputs should be in lowercase.

Example:

Input:

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

Output:

yes
no

• The matrix always contains at least one empty cell.
• The initial matrix is consistent with Sudoku rules.

Constraints:

• 1 ≤ T ≤ 5
• N = 9
• 0 ≤ MATRIX[i][j] ≤ 9
• Time Limit: 1 sec