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 MAXN = 20, MOD = 1e9 + 7;
int p[1 << MAXN], dp[1 << MAXN];
int main() {
  ios::sync_with_stdio(false);
  int n;
  cin >> n;
  for (int i = 0; i < n; i++) {
    int x;
    cin >> x;
    dp[x]++;
  }
  for (int i = 0; i < MAXN; i++)
    for (int mask = 0; mask < (1 << MAXN); mask++)
      dp[mask] += (mask >> i & 1 ? 0 : dp[mask ^ (1 << i)]);
  p[0] = 1;
  for (int i = 1; i < (1 << MAXN); i++) p[i] = (p[i - 1] * 2) % MOD;
  int ans = 0;
  for (int mask = 0; mask < (1 << MAXN); mask++) {
    int cur = p[dp[mask]];
    if (__builtin_popcount(mask) & 1)
      ans -= cur;
    else
      ans += cur;
    ans %= MOD;
  }
  ans = (ans + MOD) % MOD;
  cout << ans << endl;
  return 0;
}