Problem:
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.

Sample Input 1

xabxa

Sample Output 1

2

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

xabxa → xaxbxa → xaxbxax

Sample Input 2

ab

Sample Output 2

-1

No sequence of operations can turn s into a palindrome.

Sample Input 3

a

Sample Output 3

0

s is a palindrome already at the beginning.

Sample Input 4

oxxx

Sample Output 4

3

One solution is as follows:

oxxx → xoxxx → xxoxxx → xxxoxxx

Solution in Haskell (GHC 7.10.3) (judge verdict: Accepted)

import Data.List

main = do
  s <- getLine

  let
    a = filter (/= 'x') s
    b = countX s

  if isPalindrome a then
    print $ aux b
    else
    print $ -1

  where
    isPalindrome xs = xs == (reverse xs)

    countX xs = length a : (if null b then [] else countX $ tail b)
      where (a,b) = span (=='x') xs

    aux xs
      | even len  = sum $ (\(x,y) -> zipWith (\a b -> abs $ a - b) (reverse x) y) $ splitAt (len`div`2) xs
      | otherwise = sum $ (\(x,y) -> zipWith (\a b -> abs $ a - b) (reverse x) (tail y)) $ splitAt (len`div`2) xs 
        where len = length xs