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: Accepted)

import numpy as np

S = np.array(list(input()))
num_x = np.count_nonzero(S == 'x')
# print(f'{num_x=}')
A = [s for s in S if s != 'x']
# print(f'{S=}, {A=}')

if len(A) % 2 == 0:
    L = A[:len(A) // 2]
    R = A[len(A) // 2:][::-1]
else:
    L = A[:len(A) // 2]
    R = A[len(A) // 2 + 1:][::-1]
# print(f'{L=}, {R=}')
if not np.all(L == R):
    print(-1)
    exit()

# 真ん中までSとreverse_Sを進めていってXの数が足りない分それぞれ足す
# x以外の文字でsplitをする？'x' '' 'x' ''

T = []
subset = ''
for s in S:
    # print(f'{subset=}')
    if s == 'x':
        subset += 'x'
    else:
        T.append(subset)
        subset = ''
T.append(subset)
len_T = np.array([len(t) for t in T])
# print(f'{T=}, {len_T=}, {len_T - len_T[::-1]}')
ans = np.abs(len_T - len_T[::-1]).sum() // 2
print(ans)