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.
Note
The answer for the first test sample is subsequence [1, 2, 3].
样例
4 3
1 4 2 3
4 1 2 3
1 2 4 3
3
题面与样例版权归 Codeforces 及出题人所有；中文翻译由 AI 生成（CI 管线），如有出入请以原文为准。