Jzzhu and Numbers
说明
D. Jzzhu and Numbers
time limit per test
2 secondsmemory limit per test
256 megabytesinput
standard inputoutput
standard outputJzzhu 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
样例
