Given a sequence of integers A consisting of n elements. For each integer i from 1 to n, count how many pairs of integers in sequence A have the greatest common divisor (GCD) equal to i.
### Input
- The first line contains an integer n.
- The second line contains n integers Ai.
### Output
- Output n integers, where the ith integer is the number of pairs of integers with the smallest GCD equal to i.
### Constraints
- 1≤n≤106.
- 1≤Ai≤n
### Example
Input:
851568835
Output:
212103001