Score : $300$ points

Problem Statement

You are given a string $S$ of length $N$. Let $S_i\ (1\leq i \leq N)$ be the $i$-th character of $S$ from the left.

You may perform the following two kinds of operations zero or more times in any order:

• Pay $A$ yen (the currency in Japan). Move the leftmost character of $S$ to the right end. In other words, change $S_1S_2\ldots S_N$ to $S_2\ldots S_NS_1$.
• Pay $B$ yen. Choose an integer $i$ between $1$ and $N$, and replace $S_i$ with any lowercase English letter.

How many yen do you need to pay to make $S$ a palindrome?

Constraints

• $1\leq N \leq 5000$
• $1\leq A,B\leq 10^9$
• $S$ is a string of length $N$ consisting of lowercase English letters.
• All values in the input except for $S$ are integers.

Input

The input is given from Standard Input in the following format:

$N$ $A$ $B$

$S$

Output

Print the answer as an integer.

5 1 2
rrefa

3

First, pay $2$ yen to perform the operation of the second kind once: let $i=5$ to replace $S_5$ with e. $S$ is now rrefe.

Then, pay $1$ yen to perform the operation of the first kind once. $S$ is now refer, which is a palindrome.

Thus, you can make $S$ a palindrome for $3$ yen. Since you cannot make $S$ a palindrome for $2$ yen or less, $3$ is the answer.

8 1000000000 1000000000
bcdfcgaa

4000000000

Note that the answer may not fit into a $32$-bit integer type.