题目描述

Sudoku is a popular single player game. The objective is to fill a $9 \times 9$ matrix with digits so that each column, each row, and all $9$ non-overlapping $3 \times 3$ sub-matrices contain all of the digits from $1$ through $9$. Each $9 \times 9$ matrix is partially completed at the start of game play and typically has a unique solution.

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Given a completed ${N^2} \times {N^2}$ Sudoku matrix, your task is to determine whether it is a valid solution. A valid solution must satisfy the following criteria:

• Each row contains each number from $1$ to ${N^2}$, once each.
• Each column contains each number from $1$ to ${N^2}$, once each.
• Divide the ${N^2} \times {N^2}$ matrix into ${N^2}$ non-overlapping ${N} \times {N}$ sub-matrices. Each sub-matrix contains each number from $1$ to ${N^2}$, once each.

You don't need to worry about the uniqueness of the problem. Just check if the given matrix is a valid solution.

输入格式

The first line of the input gives 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 solution, with each line contains exactly $N^2$ integers. All input integers are positive and less than $1000$.

输出格式

For each test case, output one line containing "Case #x: y", where x is the case number (starting from $1$) and y is "Yes" (quotes for clarity only) if it is a valid solution, or "No" (quotes for clarity only) if it is invalid. Note that the judge is case-sensitive, so answers of "yes" and "no" will not be accepted.

3
3
5 3 4 6 7 8 9 1 2
6 7 2 1 9 5 3 4 8
1 9 8 3 4 2 5 6 7
8 5 9 7 6 1 4 2 3
4 2 6 8 5 3 7 9 1
7 1 3 9 2 4 8 5 6
9 6 1 5 3 7 2 8 4
2 8 7 4 1 9 6 3 5
3 4 5 2 8 6 1 7 9
3
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
3
5 3 4 6 7 8 9 1 2
6 7 2 1 9 5 3 4 8
1 9 8 3 4 2 5 6 7
8 5 9 7 6 1 4 2 3
4 2 6 8 999 3 7 9 1
7 1 3 9 2 4 8 5 6
9 6 1 5 3 7 2 8 4
2 8 7 4 1 9 6 3 5
3 4 5 2 8 6 1 7 9

Case #1: Yes
Case #2: No
Case #3: No

提示

Limits

$1 \le T \le 100$.

Test set 1 - Visible

$N = 3$.

Test set 2 - Hidden

$3 \le N \le 6$.