Let $s$ be a given string of up to $10^6$ digits. Find the maximal $k$ for which it is possible to partition $s$ into $k$ consecutive contiguous substrings, such that the $k$ parts form a palindrome. More precisely, we say that strings $s_0, s_1, \dots , s_{k-1}$ form a palindrome if $s_ i = s_{k-1-i}$ for all $0\leq i < k$.

In the first sample case, we can split the string 652526 into $4$ parts as 6|52|52|6, and these parts together form a palindrome. It turns out that it is impossible to split this input into more than $4$ parts while still making sure the parts form a palindrome.

-----Input-----
 - A nonempty string of up to $10^6$ digits.

-----Output-----
 - Print the maximal value of $k$ on a single line.

-----Examples-----
Sample Input 1:
652526
Sample Output 1:
4

Sample Input 2:
12121131221
Sample Output 2:
7

Sample Input 3:
123456789
Sample Output 3:
1

Source: kattis | Difficulty: HARD


Solutions: