C - Inserting 'x' /

問題文

• s の任意の位置 (先頭および末尾を含む) をひとつ選び、英小文字 x をひとつ挿入する。

すぬけ君の目標は、s を回文にすることです。 すぬけ君の目標が達成可能か判定し、達成可能ならば必要な操作回数の最小値を求めてください。

制約

• 1 \leq |s| \leq 10^5
• s は英小文字のみからなる。

入力

s


出力

すぬけ君の目標が達成可能ならば、必要な操作回数の最小値を出力せよ。 達成不可能ならば、代わりに -1 を出力せよ。

入力例 1

xabxa


出力例 1

2


xabxa → xaxbxa → xaxbxax

入力例 2

ab


出力例 2

-1


どのように操作を行っても、s を回文にできません。

入力例 3

a


出力例 3

0


s は最初から回文です。

入力例 4

oxxx


出力例 4

3


oxxx → xoxxx → xxoxxx → xxxoxxx

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