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 Python (3.4.3) (judge verdict: Runtime Error)

import math as mt
import numpy as np

string = input()
use = string.split('x')
word =''
for x in use:
    word += x
i = 0
n = len(word) - 1
while i < n:
    if word[i] != word[n]:
        print(-1)
        exit()
    i += 1
    n -= 1
if len(word) % 2 == 0:
    fh = []
    i = 0
    mid = int(len(word)/2)
    count = 0
    n = len(string) - 1
    for x in string:
        if x == word[i]:
            i += 1
            fh.append(count)
            count = 0
            if i == mid:
                break
        else:
            count += 1
    i = len(word) - 1
    lh = []
    count = 0
    while i != mid - 1:
        if string[n] == word[i]:
            i -= 1
            lh.append(count)
            count = 0
        else:
            count += 1
        n -= 1
    if len(lh) != len(fh):
        print(12222)
        exit()
    print(np.sum(np.abs(np.array(fh)-np.array(lh))))

else:
    fh = []
    i = 0
    mid = int((len(word) - 1)/2)
    count = 0
    n = len(string) - 1
    for x in string:
        if x == word[i]:
            i += 1
            fh.append(count)
            count = 0
            if i > mid:
                break
        else:
            count += 1
    i = len(word) - 1
    lh = []
    count = 0
    while i != mid - 1:
        if string[n] == word[i]:
            i -= 1
            lh.append(count)
            count = 0
        else:
            count += 1
        n -= 1
    if len(lh) != len(fh):
        print(12222)
        exit()
    print(np.sum(np.abs(np.array(fh)-np.array(lh))))