Score : $800$ points

Problem Statement

You are given a string $S$ consisting of lowercase English letters. Determine whether we can turn $S$ into a palindrome by repeating the operation of swapping two adjacent characters. If it is possible, find the minimum required number of operations.

Constraints

• $1 \leq |S| \leq 2 \times 10^5$
• $S$ consists of lowercase English letters.

Input

Input is given from Standard Input in the following format:

$S$

Output

If we cannot turn $S$ into a palindrome, print -1. Otherwise, print the minimum required number of operations.

eel

1

We can turn $S$ into a palindrome by the following operation:

• Swap the $2$-nd and $3$-rd characters. $S$ is now ele.

ataatmma

4

We can turn $S$ into a palindrome by the following operation:

• Swap the $5$-th and $6$-th characters. $S$ is now ataamtma.
• Swap the $4$-th and $5$-th characters. $S$ is now atamatma.
• Swap the $3$-rd and $4$-th characters. $S$ is now atmaatma.
• Swap the $2$-nd and $3$-rd characters. $S$ is now amtaatma.

snuke

-1

We cannot turn $S$ into a palindrome.