Problem: 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

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const int N = 2e6 + 5;
const int mod = 1e9 + 7;
int n, a[N], pw[N];
long long ans;
int main() {
  pw[0] = 1;
  for (int i = 1; i < N; i++) {
    pw[i] = (pw[i - 1] * 2ll) % mod;
  }
  cin >> n;
  for (int i = 1; i <= n; i++) {
    int x;
    cin >> x;
    a[x]++;
  }
  for (int j = 0; j < 20; j++) {
    for (int i = (1 << 20) - 1; i >= 0; i--) {
      if (i & (1 << j)) {
        a[i - (1 << j)] += a[i];
      }
    }
  }
  for (int i = 0; i < pw[20]; i++) {
    int bit = __builtin_popcount(i);
    if (bit & 1)
      ans -= pw[a[i]], ans = (ans + mod) % mod;
    else
      ans += pw[a[i]], ans = (ans + mod) % mod;
  }
  cout << ans << endl;
}