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.Array

main = do
  s <- getLine
  let ans = compute s
  print ans

{-
sを両側から突き合わせる。
両方同じ文字なら、消費する。
両方違う非x文字なら、失敗する。
片方がxでもう片方が違うなら、x入れたことにして消費する。
同じ文字にたどり着くか行きすぎたら成功。
-}

compute :: String -> Int
compute s = loop 0 1 n
  where
    n = length s
    arr = listArray (1,n) s
    loop cnt i j
      | i >= j = cnt
      | c == d = loop cnt (succ i) (pred j)
      | c == 'x' = loop (succ cnt) (succ i) j
      | d == 'x' = loop (succ cnt) i (pred j)
      | True   = -1
      where
        c = arr ! i
        d = arr ! j