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 long long Mod = 1e9 + 7;
const long long MAX_N = 1 << 20;
long long C[MAX_N];
long long A[MAX_N];
long long n;
long long P[MAX_N];
long long popcount(long long x) {
  long long ret = 0;
  while (x > 0) {
    ret++;
    x -= ((x) & (-(x)));
  }
  return ret;
}
signed main() {
  cin >> n;
  for (long long i = 1; i <= n; i++) {
    cin >> A[i];
    C[A[i]]++;
  }
  P[0] = 1;
  for (long long i = 1; i < (1 << 20); i++) P[i] = P[i - 1] * 2 % Mod;
  for (long long j = 0; j < 20; j++) {
    for (long long i = (1 << 20) - 1; i >= 0; i--) {
      if (i >> j & 1) C[i ^ (1 << j)] += C[i];
      assert(C[i] >= 0 && C[i] <= n);
    }
  }
  long long ans = 0;
  for (long long i = 0; i < (1 << 20); i++) {
    if (popcount(i) % 2)
      ans -= P[C[i]];
    else
      ans += P[C[i]];
    ans = (ans + Mod) % Mod;
  }
  cout << ans << endl;
  return 0;
}