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D. Gargari and Permutations
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

Gargari 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].