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### Strange Square

Time Limit: 1000 ms
Memory Limit: 65536 KiB

#### Problem Description

Small Jan and Rain are playing an interesting game: Strange Square. A stranger square is a square of numbers that is arranged such that every row and column has the same sum. For example:

1 2 3

3 2 1

2 2 2

Now, there are 9 numbers (-100000 <= xi <= 100000) and they want to know the number of distinct ways those numbers can be arranged in a strange square. Two squares are distinct if they differ in value at one or more positions.

#### Input

The input contains multiple test cases. The first line is the number of cases T (0 < T <= 100).

Each case contains a line with 9 numbers.

Each case contains a line with 9 numbers.

#### Output

You should output one line for each test case. The line contains the case number first, and then one integer indicating the number of distinct ways.

#### Sample Input

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

#### Sample Output

Case 1: 1 Case 2: 72

#### Hint

#### Source

2012年"浪潮杯"山东省第三届ACM大学生程序设计竞赛(热身赛)