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 INF = 1 << 29;
const long long LINF = 1LL << 60;
const double inf = 1e15;
long long mod = 1e9 + 7;
char READ_DATA;
int SIGNAL_INPUT;
template <typename Type>
inline Type ru(Type &v) {
  SIGNAL_INPUT = 1;
  while ((READ_DATA = getchar()) < '0' || READ_DATA > '9')
    if (READ_DATA == '-')
      SIGNAL_INPUT = -1;
    else if (READ_DATA == EOF)
      return EOF;
  v = READ_DATA - '0';
  while ((READ_DATA = getchar()) >= '0' && READ_DATA <= '9')
    v = v * 10 + READ_DATA - '0';
  v *= SIGNAL_INPUT;
  return v;
}
inline long long modru(long long &v) {
  long long p = 0;
  SIGNAL_INPUT = 1;
  while ((READ_DATA = getchar()) < '0' || READ_DATA > '9')
    if (READ_DATA == '-')
      SIGNAL_INPUT = -1;
    else if (READ_DATA == EOF)
      return EOF;
  p = v = READ_DATA - '0';
  while ((READ_DATA = getchar()) >= '0' && READ_DATA <= '9') {
    v = (v * 10 + READ_DATA - '0') % mod;
    p = (p * 10 + READ_DATA - '0') % (mod - 1);
  }
  v *= SIGNAL_INPUT;
  return p;
}
template <typename A, typename B>
inline char ru(A &x, B &y) {
  if (ru(x) == EOF) return EOF;
  ru(y);
  return 2;
}
template <typename A, typename B, typename C>
inline char ru(A &x, B &y, C &z) {
  if (ru(x) == EOF) return EOF;
  ru(y);
  ru(z);
  return 3;
}
template <typename A, typename B, typename C, typename D>
inline char ru(A &x, B &y, C &z, D &w) {
  if (ru(x) == EOF) return EOF;
  ru(y);
  ru(z);
  ru(w);
  return 4;
}
struct Edge {
  int u, v, next;
  long long w, cap, flow;
  Edge(int _u = 0, int _v = 0, int nxt = -1, long long _w = 1,
       long long _cap = 0) {
    u = _u;
    v = _v;
    w = _w;
    cap = _cap;
    flow = 0;
    next = nxt;
  }
  int operator<(const Edge &b) const { return w < b.w; }
};
const int maxn = 1e6 + 10, N = 2e6 + 1;
double eps = 1e-7, pi = acos(-1.0);
unsigned long long seed = 131, smod = (1LL << 32) - 267;
const int BIT = 1 << 20;
int bitcnt(int x) {
  int ans = 0;
  while (x) {
    ans += (x & 1);
    x >>= 1;
  }
  return ans;
}
long long qkpow(long long a, long long b) {
  long long ans = 1;
  while (b) {
    if (b & 1) (ans *= a) %= mod;
    (a *= a) %= mod;
    b >>= 1;
  }
  return ans;
}
long long f[20][BIT], n, x;
int main() {
  ru(n);
  while (n--) {
    ru(x);
    f[0][x]++;
    if (x & 1) f[0][x ^ 1]++;
  }
  for (register int i = 1; i < 20; ++i) {
    for (register int s = 0; s < BIT; ++s) {
      if ((s >> i) & 1) {
        f[i][s] = f[i - 1][s];
      } else
        f[i][s] = f[i - 1][s] + f[i - 1][s | (1 << i)];
    }
  }
  long long ans = 0;
  for (register int s = 0; s < BIT; ++s) {
    if (bitcnt(s) & 1) {
      (ans -= qkpow(2, f[19][s])) %= mod;
      if (ans < 0) ans += mod;
    } else
      (ans += qkpow(2, f[19][s])) %= mod;
  }
  cout << ans;
}