{"raw_statement":[{"iden":"problem statement","content":"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.\nYou may perform the following two kinds of operations zero or more times in any order:\n\n*   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 $S_2\\ldots S_NS_1$.\n    \n*   Pay $B$ yen. Choose an integer $i$ between $1$ and $N$, and replace $S_i$ with any lowercase English letter.\n    \n\nHow many yen do you need to pay to make $S$ a palindrome?\nWhat is a palindrome? A string $T$ is a palindrome if and only if the $i$\\-th character from the left and the $i$\\-th character from the right are the same for all integers $i$ ($1 \\le i \\le |T|$), where $|T|$ is the length of $T$."},{"iden":"constraints","content":"*   $1\\leq N \\leq 5000$\n*   $1\\leq A,B\\leq 10^9$\n*   $S$ is a string of length $N$ consisting of lowercase English letters.\n*   All values in the input except for $S$ are integers."},{"iden":"input","content":"The input is given from Standard Input in the following format:\n\n$N$ $A$ $B$\n$S$"},{"iden":"sample input 1","content":"5 1 2\nrrefa"},{"iden":"sample output 1","content":"3\n\nFirst, 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`.\nThen, pay $1$ yen to perform the operation of the first kind once. $S$ is now `refer`, which is a palindrome.\nThus, 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."},{"iden":"sample input 2","content":"8 1000000000 1000000000\nbcdfcgaa"},{"iden":"sample output 2","content":"4000000000\n\nNote that the answer may not fit into a $32$\\-bit integer type."}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}