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>
#pragma GCC optimize("Ofast")
using namespace std;
const long double eps = 1e-7;
const int inf = 1000000010;
const long long INF = 10000000000000010LL;
const int mod = 1000000007;
const int MAXN = 1000010;
long long n, m, k, u, v, x, y, t, a, b, ans;
int A[MAXN];
long long cnt[MAXN];
long long tav[MAXN];
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  for (int i = 1; i < MAXN; i++) tav[i] = (tav[i - 1] * 2 + 1) % mod;
  cin >> n;
  for (int i = 0; i < n; i++) {
    cin >> A[i];
    cnt[A[i]]++;
  }
  for (int j = 0; j < 20; j++)
    for (int i = 0; i < MAXN; i++)
      if (i & (1 << j)) cnt[i ^ (1 << j)] += cnt[i];
  for (int i = 0; i < MAXN; i++) {
    if (__builtin_popcount(i) & 1)
      ans = (ans - tav[cnt[i]]) % mod;
    else
      ans = (ans + tav[cnt[i]]) % mod;
  }
  cout << (ans + mod) % mod << endl;
  return 0;
}