Jzzhu have n non-negative integers a1,a2,...,an. We will call a sequence of indexes i1,i2,...,ik (1 \le i1 \lt i2 \lt ... \lt ik \le n) a group of size k.

Jzzhu wonders, how many groups exists such that ai1 & ai2 & ... & aik=0 (1 \le k \le 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 \le n \le 106). The second line contains n integers a1,a2,...,an (0 \le ai \le 106).

Output a single integer representing the number of required groups modulo 1000000007 (109+7).