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.
The first line contains a single integer n (1≤n≤106). The second line contains n integers a1,a2,...,an (0≤ai≤106).
Output a single integer representing the number of required groups modulo 1000000007 (109+7).
3
2 3 3
0
4
0 1 2 3
10
6
5 2 0 5 2 1
53