Isomorphic Inversion
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 $s_0, s_1, \dots , s_{k1}$ form a palindrome if $s_ i = s_{k1i}$ for all $0\leq i < k$.
In the first sample case, we can split the string 652526 into $4$ parts as 652526, 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.
Sample Input 1  Sample Output 1 

652526 
4 
Sample Input 2  Sample Output 2 

12121131221 
7 
Sample Input 3  Sample Output 3 

123456789 
1 
Sample Input 4  Sample Output 4 

132594414896459441321 
9 