Given a list of $n$ integers, your task is to calculate for each element $x$:

1. the number of elements $y$ such that $x \mid y = x$
2. the number of elements $y$ such that $x \mathrel{\&} y = x$
3. the number of elements $y$ such that $x \mathrel{\&} y \neq 0$

Input

The first line has an integer $n$: the size of the list.

The next line has $n$ integers $x_1,x_2,\dots,x_n$: the elements of the list.

Output

Print $n$ lines: for each element the required values.

Constraints

• $1 \le n \le 2 \cdot 10^5$
• $1 \le x_i \le 10^6$

Example

Input:

5
3 7 2 9 2

Output:

3 2 5
4 1 5
2 4 4
1 1 3
2 4 4