Festive Shuffling

You are given a binary string $S$ and $k$ distinct indices to perform an operation.

The operation is like below:

You can shuffle the given indices any number of times (possibly zero).

You have to find out the maximum length of a palindromic subsequence of string $S$ after shuffling.

Example of an operation: Say $S$ = “001110”, Let the indices be $[1, 3, 5]$. Then after the operation the string content can be, 100110.

Input

The first line of input contains a string $S$ and an integer $k$

The next line will contain $k$ space separated integers $a_1, a_2, \ldots, a_k$ denoting the indices that you can shuffle, all of them are guaranteed to be distinct.

Constraints

$1\le|S|\le500$

$0 \le k \le |S|$

$1\le a_i\le |S|$

Output

Output one line containing the output, the maximum length of any palindromic subsequence after the operation.

Sample

Input	Output
10010 2 1 2	5