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 (3.8.2) (judge verdict: Runtime Error)

#!/usr/bin/env python3

import sys
from typing import Any, Callable, Deque, Dict, List, Mapping, Optional, Sequence, Set, Tuple, TypeVar, Union
# import time
# import math, cmath
# import numpy as np
# import scipy.sparse.csgraph as cs            # csgraph_from_dense(ndarray, null_value=inf), bellman_ford(G, return_predecessors=True), dijkstra, floyd_warshall
# import random                                # random, uniform, randint, randrange, shuffle, sample
# import string                                # ascii_lowercase, ascii_uppercase, ascii_letters, digits, hexdigits
# import re                                    # re.compile(pattern) => ptn obj; p.search(s), p.match(s), p.finditer(s) => match obj; p.sub(after, s)
# from bisect import bisect_left, bisect_right # bisect_left(a, x, lo=0, hi=len(a)) returns i such that all(val<x for val in a[lo:i]) and all(val>-=x for val in a[i:hi]).
# from collections import deque                # deque class. deque(L): dq.append(x), dq.appendleft(x), dq.pop(), dq.popleft(), dq.rotate()
# from collections import defaultdict          # subclass of dict. defaultdict(facroty)
# from collections import Counter              # subclass of dict. Counter(iter): c.elements(), c.most_common(n), c.subtract(iter)
# from datetime import date, datetime          # date.today(), date(year,month,day) => date obj; datetime.now(), datetime(year,month,day,hour,second,microsecond) => datetime obj; subtraction => timedelta obj
# from datetime.datetime import strptime       # strptime('2019/01/01 10:05:20', '%Y/%m/%d/ %H:%M:%S') returns datetime obj
# from datetime import timedelta               # td.days, td.seconds, td.microseconds, td.total_seconds(). abs function is also available.
# from copy import copy, deepcopy              # use deepcopy to copy multi-dimentional matrix without reference
# from functools import reduce                 # reduce(f, iter[, init])
# from functools import lru_cache              # @lrucache ...arguments of functions should be able to be keys of dict (e.g. list is not allowed)
# from heapq import heapify, heappush, heappop # built-in list. heapify(L) changes list in-place to min-heap in O(n), heappush(heapL, x) and heappop(heapL) in O(lgn).
# from heapq import _heapify_max, _heappop_max, _siftdown_max
# from heapq import nlargest, nsmallest        # nlargest(n, iter[, key]) returns k-largest-list in O(n+klgn).
# from itertools import count, cycle, repeat   # count(start[,step]), cycle(iter), repeat(elm[,n])
# from itertools import groupby                # [(k, list(g)) for k, g in groupby('000112')] returns [('0',['0','0','0']), ('1',['1','1']), ('2',['2'])]
# from itertools import starmap                # starmap(pow, [[2,5], [3,2]]) returns [32, 9]
# from itertools import product, permutations  # product(iter, repeat=n), permutations(iter[,r])
# from itertools import combinations, combinations_with_replacement
# from itertools import accumulate             # accumulate(iter[, f])
# from operator import itemgetter              # itemgetter(1), itemgetter('key')
# from fractions import Fraction               # Fraction(a, b) => a / b ∈ Q. note: Fraction(0.1) do not returns Fraciton(1, 10). Fraction('0.1') returns Fraction(1, 10)



def main():
    Num = Union[int, float]
    mod = 1000000007                # 10^9+7
    inf = float('inf')              # sys.float_info.max = 1.79e+308
    # inf = 2 ** 63 - 1             # (for fast JIT compile in PyPy) 9.22e+18
    sys.setrecursionlimit(10**6)    # 1000 -> 1000000
    def input(): return sys.stdin.readline().rstrip()
    def ii():    return int(input())
    def isp():   return input().split()
    def mi():    return map(int, input().split())
    def mi_0():  return map(lambda x: int(x)-1, input().split())
    def lmi():   return list(map(int, input().split()))
    def lmi_0(): return list(map(lambda x: int(x)-1, input().split()))
    def li():    return list(input())
    # def _heappush_max(h, item): h.append(item); _siftdown_max(h, 0, len(h)-1)
    
    def check_palindrome(s):
        n = len(s)
        for i in range(n//2):
            if s[i] != s[n-1-i]:
                return False
        return True
    
    def find_center(s, cnt):
        num = 0
        n = len(s)
        for i in range(n):
            if s[i] != 'x':
                num += 1
            if num == cnt:
                return i

    def find_center_even(s, cnt):
        num = 0
        n = len(s)
        left, right = -1, -1
        for i in range(n):
            if s[i] != 'x':
                num += 1     
            if num == cnt:
                if left == -1:
                    left = i
                    print(f"left {left}")
            if num == cnt + 1:
                right = i
                print(f"right {right}")
                return (left + right) / 2
    
    def not_x_split(s):
        buf = []
        s += 'E'
        n = len(s)
        x_cnt = 0
        for i in range(n):
            if s[i] != 'x':
                buf.append(x_cnt)
                x_cnt = 0
            else:
                x_cnt += 1
        return buf



    def solve(s, buf):
        bufsize = len(buf)
        if bufsize % 2 == 0:
            cnt = bufsize // 2
            ind = find_center_even(s, cnt)
        else:
            cnt = (bufsize + 1) // 2
            ind = find_center(s, cnt)
        
        if ind % 1 == 0:
            left_s = s[0:ind][::-1]
            right_s = s[ind+1:]
        else:
            left_s = s[0:int(ind)+1][::-1]
            right_s = s[int(ind)+1:]

        # print(f"ind {ind}")
        # print(left_s)
        # print(right_s)
        left = not_x_split(left_s)
        right = not_x_split(right_s)
        # print(left)
        # print(right)
        assert len(left) == len(right)
        ans = 0
        for i in range(len(left)):
            ans += max(left[i], right[i]) - min(left[i], right[i])
        return ans

    
    s = input()
    if check_palindrome(s):
        print(0)
    else:
        buf = [char for char in s if char != 'x']
        if not check_palindrome(buf):
            print(-1)
        else:
            # print('solve')
            print(solve(s, buf))



if __name__ == "__main__":
    main()