Score : $400$ points

Problem Statement

We have a string $s$ consisting of lowercase English letters. Snuke can perform the following operation repeatedly:

• Insert a letter x to any position in $s$ of his choice, including the beginning and end of $s$.

Snuke's objective is to turn $s$ into a palindrome. Determine whether the objective is achievable. If it is achievable, find the minimum number of operations required.

Notes

A palindrome is a string that reads the same forward and backward. For example, a, aa, abba and abcba are palindromes, while ab, abab and abcda are not.

Constraints

• $1 \leq |s| \leq 10^5$
• $s$ consists of lowercase English letters.

Input

Input is given from Standard Input in the following format:

$s$

Output

If the objective is achievable, print the number of operations required. If it is not, print -1 instead.

xabxa

2

One solution is as follows (newly inserted x are shown in bold):

xabxa → xaxbxa → xaxbxax

ab

-1

No sequence of operations can turn $s$ into a palindrome.

a

0

$s$ is a palindrome already at the beginning.

oxxx

3

One solution is as follows:

oxxx → xoxxx → xxoxxx → xxxoxxx