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;
long long n, a[1000005], sos[(1 << 20) + 100], mod = 1e9 + 7;
long long bigmod(long long a, long long b) {
  if (b == 0) return 1;
  long long x = bigmod(a, b / 2);
  x = (x * x) % mod;
  if (b % 2 == 1) x *= a;
  return x % mod;
}
int main() {
  ios::sync_with_stdio(0);
  cin >> n;
  int nn = (1 << 20);
  for (int i = 0; i < n; i++) {
    cin >> a[i];
    sos[a[i]]++;
  }
  for (int i = 0; i < 20; ++i)
    for (int mask = 0; mask < (1 << 20); ++mask) {
      if (!(mask & (1 << i))) sos[mask] += sos[mask ^ (1 << i)];
    }
  for (int i = 0; i < 8; i++) {
  }
  long long ans = 0;
  for (int mask = 1; mask < (1 << 20); mask++) {
    int p = __builtin_popcount(mask);
    if (p % 2 == 1) {
      ans += bigmod(2, sos[mask]) - 1;
      ans += mod;
      ans %= mod;
    } else {
      ans -= (bigmod(2, sos[mask]) - 1);
      ans += mod;
      ans %= mod;
    }
  }
  long long ans2 = 0;
  ans2 = bigmod(2, n) - 1;
  ans2 += mod;
  ans2 %= mod;
  ans2 -= ans;
  ans2 += mod;
  ans2 %= mod;
  cout << ans2 << endl;
  return 0;
}