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.orgwikiLongest_common_subsequence_problem

输入描述:

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.

输出描述:

Print the length of the longest common subsequence.

备注:

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