You are given a string $S$ of length $N.$ You are also given a string array str of size $M.$

It is give that a string $x$ is beautiful if there is a subsequence concatenation $K$ from the string array str that meets the following conditions:

Theyength of $K$ is equal to the length of $x.$

The concatenation of $K$ and the string $x$ is a palindrome string. $.$ subsequence $"$a$","$dc$"$ from strand concatenate them to get $K=$ "adc". The length of "adc" is equal to the length of $x$ and their concatenation is a palindrome string.

Find the longest prefix length from $S$ that can be divided into beautiful substrings.

Notes:

It is given that a string is a palinidrome string if reading it fr$$m left to right is equal to reading it from right to left.

Input Format

The first line contains an integer ${?}_{5}N,$ denoting the length of stging $S.$ The next line contains an integer, $M,$ denoting the size of the string array str$.$

The next fine contains a string, $S,$ denoting the given string.

Each line $i$ of the $M$ subsequent lines $($where $0i$

Constraints $e$

Sample Test Cases

HandsOn $>$ suibsequence for substring ${?}_e$

You are given a string $S$ of length $N.$ You are also given a string array str of size $M.$

It is given that a string $x$ is beauthiful if there is a subsequencee concatenation $K$ from the string array str that meets the following conditions:

The vength of $K$ is equal to the length of $x.$

The concatenation of $K$ and the string $x$ is a palindrome ${?}^s$ string. subsequience $"a","$dc$"$ from strand concatenate them to get $K=$ "adc". The length of "adc" is equal to the length of $x$ and their concatenation is a palindrome string.

Find the longest prefix length from $S$ that can be divided into beautiful substrings.

Notes:

It is given that a string is a palindrome string if reading it from left to right is equal to reading it from right to left.

Input Format

The first line contains an integer s ${?}_{5}N,$ denoting the length of stoving $S.$ The next line contains an integer, $M,$ denoting the size of the string array str$.$

The next thine contains a string, $S,$ denoting the given string.

Each tine $i$ of the $M$ subsequent lines $($where $0i$

$n=4,m=2S=SSS$