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;
int dp[21][(1 << 20)], pw[1000005];
int main() {
  int n, i, x, mask, cnt;
  cin >> n;
  for (i = 1; i <= n; i++) {
    cin >> x;
    dp[0][x]++;
  }
  for (i = 1; i <= 20; i++) {
    for (mask = 0; mask < (1 << 20); ++mask) {
      if (mask & (1 << (i - 1)))
        dp[i][mask] = dp[i - 1][mask];
      else {
        dp[i][mask] = dp[i - 1][mask] + dp[i - 1][mask + (1 << (i - 1))];
      }
    }
  }
  pw[0] = 1;
  for (i = 1; i < 1000005; i++) pw[i] = (pw[i - 1] * 2LL) % 1000000007;
  long long ans = 0;
  for (mask = 0; mask < (1 << 20); mask++) {
    cnt = 0;
    for (i = 0; i < 20; i++) {
      if (mask & (1 << i)) cnt ^= 1;
    }
    if (cnt) {
      ans -= pw[dp[20][mask]];
      if (ans < 0) ans += 1000000007;
    } else {
      ans += pw[dp[20][mask]];
      if (ans >= 1000000007) ans -= 1000000007;
    }
  }
  cout << ans << endl;
  return 0;
}