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 read();
const int N = 1 << 21, P = 1000000007;
int n, mx, h;
int a[N], g[N], bitcnt[N], pw[N];
void fwt(int *a) {
  for (int l = 2, mid = 1; l <= h; l <<= 1, mid <<= 1)
    for (int *p = a; p != a + h; p += l)
      for (int i = 0; i < mid; ++i) p[i] += p[i + mid];
}
int mo(int x) { return x >= P ? x - P : x; }
int main() {
  n = read();
  for (int i = 1, x; i <= n; ++i) ++g[x = read()], mx = max(mx, x);
  h = 1;
  while (h <= mx) h <<= 1;
  fwt(g);
  pw[0] = 1;
  for (int(i) = (1); (i) <= (n); ++(i)) pw[i] = mo(pw[i - 1] + pw[i - 1]);
  int ans = 0;
  for (int i = 0; i < h; ++i) {
    bitcnt[i] = bitcnt[i >> 1] + (i & 1);
    int res = mo(pw[g[i]] - 1 + P);
    if (bitcnt[i] & 1)
      ans = mo(ans - res + P);
    else
      ans = mo(ans + res);
  }
  printf("%d\n", ans);
  return 0;
}
int read() {
  int x = 0, f = 1;
  char c = getchar();
  while (c < '0' || c > '9') {
    if (c == '-') f = -1;
    c = getchar();
  }
  while (c >= '0' && c <= '9')
    x = (x << 3) + (x << 1) + (c ^ 48), c = getchar();
  return f * x;
}