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D. Gargari and Permutations

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputGargari got bored to play with the bishops and now, after solving the problem about them, he is trying to do math homework. In a math book he have found *k* permutations. Each of them consists of numbers 1, 2, ..., *n* in some order. Now he should find the length of the longest common subsequence of these permutations. Can you help Gargari?

You can read about longest common subsequence there: https://en.wikipedia.org/wiki/Longest_common_subsequence_problem

Input

The first line contains two integers *n* and *k* (1 ≤ *n* ≤ 1000; 2 ≤ *k* ≤ 5). Each of the next *k* lines contains integers 1, 2, ..., *n* in some order — description of the current permutation.

Output

Print the length of the longest common subsequence.

Examples

Input

4 3

1 4 2 3

4 1 2 3

1 2 4 3

Output

3

Note

The answer for the first test sample is subsequence [1, 2, 3].

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