Problem10322--CF EDU - Suffix Array - Step 5 - F. Periodic Substring

10322: CF EDU - Suffix Array - Step 5 - F. Periodic Substring

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Time Limit : 1.000 sec  Memory Limit : 512 MiB

Description

Given the string $s$. Find a maximum integer $k$ such that there is a non-empty substring in the string $s$ that is a concatenation of $k$ equal strings.

Input

The first line of input contains the string $s\ (1≤|s|≤400,000)$. The string consists of lowercase English letters.

Output

Print the desired value $k$.

Sample 1 Input

aabaaabaaabaaabaab

Sample 1 Output

4

Sample 2 Input

aabaabb

Sample 2 Output

2

Sample 3 Input

aaaa

Sample 3 Output

4

ppppplppp

5

Sample 4 Input

nn

Sample 4 Output

2

HINT

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