Finding Borders

A border of a string is a prefix that is also a suffix of the string but not the whole string. For example, the borders of abcababcab are ab and abcab. Your task is to find all border lengths of a given string.

Input

The only input line has a string of length n consisting of characters a–z.

Output

Print all border lengths of the string in increasing order.

Constraints

$1 \le n \le 10^6$

Example

Input

abcababcab

Output

2 5