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5574: Jzzhu and Numbers

内存限制：256 MB 时间限制：2 S 标准输入输出
题目类型：传统 评测方式：文本比较 上传者：
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题目描述

time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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