B. Beautiful Words
time limit per test
1 s
memory limit per test
1024 megabytes
input
standard input
output
standard output

You are given a string $$$A$$$ of length $$$N$$$ and a set $$$S$$$, containing $$$M$$$ strings.

A cyclic permutation $$$B_i$$$ of $$$A$$$, in which $$$i$$$ is between $$$1$$$ and $$$N$$$, is the string

$$$B_i = A_{i}A_{i+1} \dotsm A_{N-1}A_NA_1A_2 \dotsm A_{i-2}A_{i-1}$$$

and its score is defined as the maximum length of a substring of $$$B_i$$$ that is also a substring of some string in $$$S$$$.

A substring is defined as a contiguous sequence of letters. For example, ab and dc are substrings of abfdc, but ad and fc aren't substrings of abfdc.

Your task is to calculate the minimum score over all cyclic permutations of string $$$A$$$.

Input

The first line contains two positive integers $$$N$$$ and $$$M$$$, ($$$1 \leq N \leq 10^5$$$, $$$1 \leq M \leq 10^4$$$), representing the length of the string $$$A$$$ and the size of the set $$$S$$$, respectively.

The second line contains the string $$$A$$$.

Each of the next $$$M$$$ lines contains one string $$$s_i$$$, representing the $$$i$$$-th string in $$$S$$$.

All strings contain only lowercase English letters and it's guaranteed that the sum of lengths of all strings in $$$S$$$ never exceeds $$$10^5$$$ characters.

Output

Output an integer representing the minimum score over all cyclic permutations of string $$$A$$$.

Examples
Input
7 3
acmicpc
acm
icpc
maratona
Output
3
Input
11 4
competition
oncom
petition
ztxvu
fmwper
Output
5
Input
12 4
latinamerica
zyvu
okp
wsgh
kqpdb
Output
0