You are given a string of n bits. Your task is to calculate for each k = 0, 1, \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 ones: 01, 1, 1, 10
• 1 substring that contains 2 ones: 101
• 0 substrings that contain 3 ones

Input

The first input line contains an integer t: the number of test cases.

After this, t lines follow. Each line contains a string of length n.

Output

For each test case, output n+1 values as specified above.

Constraints

• 1 \le t \le 20
• 1 \le n \le 10^5
• the sum of all n values is at most 10^5

Example

Input:

3
101
1111
01

Output:

1 4 1 0
0 4 3 2 1
1 2 0