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 maxv = 1e5 + 30;
const long long mod = 1000000007;
int N;
int a[1 << 20];
int dp[22][1 << 20];
int fpow(int x, long long p) {
  long long ans = 1;
  while (p > 0) {
    if (p & 1) ans = (x * ans) % mod;
    x = (x * x) % mod;
    p >>= 1;
  }
  return (int)ans;
}
int q_pow(int x, int n, long long mod) {
  long long ans = 1, xx = x;
  for (; n > 0; n >>= 1) {
    if (n & 1) ans = ans * xx % mod;
    xx = xx * xx % mod;
  }
  return (int)ans;
}
void add(int &a, int b) {
  a += b;
  if (a < 0) a += mod;
  if (a >= mod) a -= mod;
}
int main() {
  cin >> N;
  for (int i = 0; i < N; i++) scanf("%d", &a[i]);
  sort(a, a + N);
  for (int i = 0; i < N; i++) {
    if (a[i] & 1)
      dp[0][a[i]]++, dp[0][a[i] - 1]++;
    else
      dp[0][a[i]]++;
  }
  for (int i = 0; i < 19; i++) {
    for (int j = 0; j < (1 << 20); j++) {
      int t = 1 << (1 + i);
      if (j & t)
        dp[i + 1][j] += dp[i][j], dp[i + 1][j - t] += dp[i][j];
      else
        dp[i + 1][j] += dp[i][j];
    }
  }
  int ans = 0;
  for (int j = 0; j < (1 << 20); j++) {
    int t = 1;
    for (int i = 0; i < 20; i++)
      if ((1 << i) & j) t = -t;
    int tt = q_pow(2, dp[19][j], mod);
    tt--;
    if (tt < 0) tt += mod;
    ans += t * tt;
    if (ans >= mod) ans -= mod;
    if (ans < 0) ans += mod;
  }
  cout << ans << endl;
  return 0;
}