### 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.

#### 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


#### 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)