Time Limit: 2000/1000MS (Java/Others) Memory Limit: 128000/64000KB (Java/Others)

#### Problem Description

Sudoku is a popular single player game. The objective is to fill a 9x9 matrix with digits so that each column, each row, and all 9 non-overlapping 3x3 sub-matrices contain all of the digits from 1 through 9. Each 9x9 matrix is partially completed at the start of game play and typically has a unique solution.

Given a completed *N*^{2}×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}×N^{2} matrix into *N*^{2} non-overlapping *N×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.**

#### Input

The first line of the input gives the number of test cases, *T(**1 ≤ T ≤ 100)*.

*T* test cases follow. Each test case starts with an integer *N(**3 ≤ N ≤ 6)*.

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*.

#### Output

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.

#### Sample Input

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

#### Sample Output

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

#### Source

codejam

#### Manager