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