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 Control.Applicative
import Data.Maybe
import qualified Data.Sequence as S
import Data.Sequence (Seq, fromList, (<|), (|>), viewl, viewr, ViewL(..), ViewR(..))
 
main = getLine >>= print . fromMaybe (-1) . solve . fromList
 
solve :: Seq Char -> Maybe Int
solve q
  | S.length q <= 1 = Just 0
  | l == r    = solve ms
  | l == 'x'  = succ <$> solve (q |> 'x')
  | r == 'x'  = succ <$> solve ('x' <| q)
  | otherwise = Nothing
  where
    (l :< rs) = viewl q
    (ms :> r) = viewr rs