Longest Common Subsequence

Given two strings A and B of lengths N and M respectively, find the length of the longest string that is a subsequence of both A and B.

Input Format

The first line contains two integers N and M.

The second line contains a string of length N, representing string A.

The third line contains a string of length M, representing string B.

The strings consist of lowercase letters.

Output Format

Output an integer representing the maximum length.

Constraints

1 ≤ N, M ≤ 1000

Sample Input

4 5
acbd
abedc

Sample Output

3