Sudoku Solution Checker

Sudoku is a single player number puzzle. You fill a 9x9 grid with digits so that every row, every column, and each of the nine non-overlapping 3x3 sub-matrices holds each digit from 1 to 9 exactly once. The grid starts out partially filled and usually has one solution.

You are given a completed Sudoku grid of size $N^2 \times N^2$. Decide whether it is a valid solution. A valid solution meets all three rules below.

• Every row holds each number from 1 to $N^2$ exactly once.
• Every column holds each number from 1 to $N^2$ exactly once.
• Split the $N^2 \times N^2$ grid into $N^2$ non-overlapping $N \times N$ sub-matrices. Every sub-matrix holds each number from 1 to $N^2$ exactly once.

Uniqueness of the puzzle does not matter here. Only check whether the given grid is a valid solution.

The first line holds the number of test cases $T$. $T$ test cases follow. Each test case starts with an integer $N$. The next $N^2$ lines describe a completed Sudoku grid, and each line holds exactly $N^2$ integers. Every integer in the input is positive and smaller than 1000.

Limits

• $1 \le T \le 100$
• $3 \le N \le 6$

For each test case print one line in the form Case #x: y, where x is the test case number starting from 1 and y is Yes if the grid is a valid solution or No if it is not. The judge is case sensitive, so yes and no are not accepted.