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#1884. [Ipsc2008]Discover All Sets

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Description

Input

The first line of the input file contains an integer T specifying the number of test cases. Each test case is preceded by a blank line. Each test case looks as follows: The first line contains three positive integer N, M and K giving the number of different properties of the cards, the number of different values of a single property, and the number of cards drawn. Each of the next K lines describes one of these cards. The i-th of these lines (1 ≤ i ≤ K) contains exactly N numbers pi,j (1 ≤ j ≤ N), 1 ≤ pi,j ≤ M. Value pi,j is the value of the j-th property of the i-the card.

Output

Sample Input

1
4 3 12
1 1 1 2
2 3 3 3
2 2 3 1
1 3 1 3
3 3 3 3
1 2 1 1
2 1 3 2
1 1 3 2
2 3 2 3
1 3 2 3
3 2 1 1
3 1 2 2

Sample Output

11

Hint

Source