# Jzzhu and Numbers

## 题目描述

Jzzhu have \$ n \$ non-negative integers \$ a_{1},a_{2},...,a_{n} \$ . We will call a sequence of indexes \$ i_{1},i_{2},...,i_{k} \$ \$ (1<=i_{1}<i_{2}<...<i_{k}<=n) \$ a group of size \$ k \$ . Jzzhu wonders, how many groups exists such that \$ a_{i1} \$ & \$ a_{i2} \$ & ... & \$ a_{ik}=0 \$ \$ (1<=k<=n) \$ ? Help him and print this number modulo \$ 1000000007 \$ \$ (10^{9}+7) \$ . Operation \$ x \$ & \$ y \$ denotes bitwise AND operation of two numbers.

## 输入输出格式

### 输入格式

The first line contains a single integer \$ n \$ \$ (1<=n<=10^{6}) \$ . The second line contains \$ n \$ integers \$ a_{1},a_{2},...,a_{n} \$ \$ (0<=a_{i}<=10^{6}) \$ .

### 输出格式

Output a single integer representing the number of required groups modulo \$ 1000000007 \$ \$ (10^{9}+7) \$ .

## 输入输出样例

### 输入样例 #1

``````3
2 3 3
``````

### 输出样例 #1

``````0
``````

### 输入样例 #2

``````4
0 1 2 3
``````

### 输出样例 #2

``````10
``````

### 输入样例 #3

``````6
5 2 0 5 2 1
``````

### 输出样例 #3

``````53
``````