You are given a bit string of length n. Your task is to calculate for each k between 0 \ldots n the number of non-empty substrings that contain exactly k ones.

For example, if the string is 101, there are:

• 1 substring that contains 0 ones: 0
• 4 substrings that contain 1 one: 01, 1, 1, 10
• 1 substring that contains 2 ones: 101
• 0 substrings that contain 3 ones

Input

The only input line contains a binary string of length n.

Output

Print n+1 values as specified above.

Constraints

• 1 \le n \le 2 \cdot 10^5

Example

Input:

101

Output:

1 4 1 0