#D7620. Jzzhu and Numbers
Jzzhu and Numbers
Jzzhu and Numbers
Jzzhu have n non-negative integers a1, a2, ..., an. We will call a sequence of indexes i1, i2, ..., ik (1 ≤ i1 < i2 < ... < ik ≤ n) a group of size k.
Jzzhu wonders, how many groups exists such that ai1 & ai2 & ... & aik = 0 (1 ≤ k ≤ n)? Help him and print this number modulo 1000000007 (109 + 7). Operation x & y denotes bitwise AND operation of two numbers.
Input
The first line contains a single integer n (1 ≤ n ≤ 106). The second line contains n integers a1, a2, ..., an (0 ≤ ai ≤ 106).
Output
Output a single integer representing the number of required groups modulo 1000000007 (109 + 7).
Examples
Input
3 2 3 3
Output
0
Input
4 0 1 2 3
Output
10
Input
6 5 2 0 5 2 1
Output
53
inputFormat
Input
The first line contains a single integer n (1 ≤ n ≤ 106). The second line contains n integers a1, a2, ..., an (0 ≤ ai ≤ 106).
outputFormat
Output
Output a single integer representing the number of required groups modulo 1000000007 (109 + 7).
Examples
Input
3 2 3 3
Output
0
Input
4 0 1 2 3
Output
10
Input
6 5 2 0 5 2 1
Output
53
样例
3
2 3 3
0