One Bit Positions

You are given a binary string of length n. Your task is to calculate, for every k between 1 \ldots n-1, the number of ways we can choose two positions i and j such that i-j=k and there is a one-bit at both positions.

Input

The only input line has a string that consists only of characters 0 and 1.

Output

For every distance k between 1\ldots n-1 print the number of ways we can choose two such positions.

Constraints

$2 \le n \le 2$ \cdot 10^5$

Example

Input

1001011010

Output

1 2 3 0 2 1 0 1 0