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

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

• $1 \le n \le 2 \cdot 10^5$

Print $n+1$ values as specified above.