One Bit Positions

• Time limit: 1.00 s
• Memory limit: 512 MB

You are given a binary string of length $n$ and 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