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 = (1 << 21) + 5;
const int mod = 1e9 + 7;
int dp[22][maxn];
int ted[maxn], n;
long long t2[maxn], ans;
int main() {
  t2[0] = 1;
  for (int i = 1; i < (1 << 21); i++) t2[i] = (t2[i - 1] * 2) % mod;
  cin >> n;
  for (int i = 1; i <= n; i++) {
    int a;
    cin >> a;
    ted[a]++;
  }
  for (int i = 0; i < (1 << 21); i++) dp[0][i] = ted[i];
  for (long long k = 1; k <= 20; k++)
    for (long long i = 0; i < (1 << 21); i++) {
      if ((i >> (k - 1)) & 1)
        dp[k][i] = dp[k - 1][i];
      else
        dp[k][i] = dp[k - 1][i] + dp[k - 1][i + (1 << (k - 1))];
    }
  for (int i = 0; i < (1 << 21); i++) {
    if ((__builtin_popcount(i)) % 2)
      ans = (ans - t2[dp[20][i]]) % mod;
    else
      ans = (ans + t2[dp[20][i]]) % mod;
  }
  ans = (ans + mod) % mod;
  cout << ans << endl;
  return 0;
}