GCD Subsets

You are given an array of n integers. Your task is to calculate the number of non-empty subsets whose elements' greatest common divisor is equal to k for each k = 1,\dots, n.

Input

The first line has an integer n: the size of the array. The next line has n integers x_1, x_2,\dots, x_n: the contents of the array.

Output

Print n integers as specified above modulo 10^9 + 7.

Constraints

$1 \le n \le 2$ \cdot 10^5$

$1 \le x_i \le n$

Example

Input

5
5 4 4 2 3

Output

22 4 1 3 1