You are given an array of n integers. Your task is to calculate the number of non-empty subsets whose elements' bitwise and is equal to k for each k = 0, 1,\dots, n.

Input

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

The next line has n integers a_1, a_2,\dots, a_n: the contents of the array.

Output

Print n + 1 integers as specified above modulo 10^9 + 7.

Constraints

• 1 \le n \le 2 \cdot 10^5
• 0 \le a_i \le n

Example

Input:

4
3 1 3 4

Output:

7 4 0 3 1