You are given a string of length n. For every integer between 1 \ldots n you need to print the number of distinct substrings of that length.

Input

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

Output

For each integer between 1 \ldots n print the number of distinct substrings of that length.

Constraints

• 1 \le n \le 10^5

Example

Input:

abab

Output:

2 2 2 1