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 INFL = (int)1e9;
const long long int INFLL = (long long int)1e18;
const double INFD = numeric_limits<double>::infinity();
const double PI = 3.14159265358979323846;
bool nearlyeq(double x, double y) { return abs(x - y) < 1e6; }
long long int rndf(double x) {
  return (long long int)(x + (x >= 0 ? 0.5 : -0.5));
}
long long int floorsqrt(double x) {
  long long int m = (long long int)sqrt(x);
  return m + (m * m <= (long long int)(x) ? 0 : -1);
}
long long int ceilsqrt(double x) {
  long long int m = (long long int)sqrt(x);
  return m + ((long long int)x <= m * m ? 0 : 1);
}
long long int rnddiv(long long int a, long long int b) {
  return (a / b + (a % b * 2 >= b ? 1 : 0));
}
long long int ceildiv(long long int a, long long int b) {
  return (a / b + (a % b == 0 ? 0 : 1));
}
long long int gcd(long long int m, long long int n) {
  if (n == 0)
    return m;
  else
    return gcd(n, m % n);
}
namespace mod_op {
const long long int MOD = (long long int)1e9 + 7;
class modll {
 private:
  long long int val;
  inline long long int modify(long long int x) {
    long long int ret = x % MOD;
    if (ret < 0) ret += MOD;
    return ret;
  }
  inline long long int inv(long long int x) {
    if (x == 0)
      return 1 / x;
    else if (x == 1)
      return 1;
    else
      return modify(inv(MOD % x) * modify(-MOD / x));
  }

 public:
  modll(long long int init = 0) {
    val = modify(init);
    return;
  }
  modll(const modll &another) {
    val = another.val;
    return;
  }
  inline modll &operator=(const modll &another) {
    val = another.val;
    return *this;
  }
  inline modll operator+(const modll &x) { return modify(val + x.val); }
  inline modll operator-(const modll &x) { return modify(val - x.val); }
  inline modll operator*(const modll &x) { return modify(val * x.val); }
  inline modll operator/(const modll &x) { return modify(val * inv(x.val)); }
  inline modll &operator+=(const modll &x) {
    val = modify(val + x.val);
    return *this;
  }
  inline modll &operator-=(const modll &x) {
    val = modify(val - x.val);
    return *this;
  }
  inline modll &operator*=(const modll &x) {
    val = modify(val * x.val);
    return *this;
  }
  inline modll &operator/=(const modll &x) {
    val = modify(val * inv(x.val));
    return *this;
  }
  inline bool operator==(const modll &x) { return val == x.val; }
  inline bool operator!=(const modll &x) { return val != x.val; }
  friend inline istream &operator>>(istream &is, modll &x) {
    is >> x.val;
    return is;
  }
  friend inline ostream &operator<<(ostream &os, const modll &x) {
    os << x.val;
    return os;
  }
  long long int get_val() { return val; }
};
modll pow(modll n, long long int p) {
  modll ret;
  if (p == 0)
    ret = 1;
  else if (p == 1)
    ret = n;
  else {
    ret = pow(n, p / 2);
    ret *= ret;
    if (p % 2 == 1) ret *= n;
  }
  return ret;
}
vector<modll> facts;
inline void make_facts(int n) {
  if (facts.empty()) facts.push_back(modll(1));
  for (int i = (int)facts.size(); i <= n; ++i)
    facts.push_back(modll(facts.back() * (long long int)i));
  return;
}
vector<modll> ifacts;
vector<modll> invs;
inline void make_invs(int n) {
  if (invs.empty()) {
    invs.push_back(modll(0));
    invs.push_back(modll(1));
  }
  for (int i = (int)invs.size(); i <= n; ++i) {
    invs.push_back(invs[(int)MOD % i] * ((int)MOD - (int)MOD / i));
  }
  return;
}
inline void make_ifacts(int n) {
  make_invs(n);
  if (ifacts.empty()) ifacts.push_back(modll(1));
  for (int i = (int)ifacts.size(); i <= n; ++i)
    ifacts.push_back(modll(ifacts.back() * invs[i]));
  return;
}
modll combination(long long int n, long long int r) {
  if (n >= r && r >= 0) {
    modll ret;
    make_facts((int)n);
    make_ifacts((int)n);
    ret = facts[(unsigned)n] * ifacts[(unsigned)r] * ifacts[(unsigned)(n - r)];
    return ret;
  } else
    return 0;
}
modll get_fact(long long int n) {
  make_facts((int)n);
  return facts[(int)n];
}
modll get_ifact(long long int n) {
  make_ifacts((int)n);
  return ifacts[(int)n];
}
long long int disc_log(modll a, modll b) {
  long long int ret = -1;
  long long int m = ceilsqrt(MOD);
  unordered_map<long long int, long long int> mp;
  modll x = 1;
  for (int i = 0; i < (int)m; i++) {
    mp[x.get_val()] = i;
    x *= a;
  }
  x = modll(1) / pow(a, m);
  modll k = b;
  for (int i = 0; i < (int)m; i++) {
    if (mp.find(k.get_val()) == mp.end())
      k *= x;
    else {
      ret = i * m + mp[k.get_val()];
      break;
    }
  }
  return ret;
}
}  // namespace mod_op
using namespace mod_op;
namespace Zeta_and_Mobius_transform {
vector<modll> Zeta_trans_rev(vector<modll> f) {
  int n = f.size();
  int digit = int(rndf(log2(n)));
  vector<modll> ret = f;
  for (int i = 0; i < (int)digit; i++) {
    int x = 1 << i;
    for (int j = 0; j < (int)n; j++) {
      if (!(j & x)) ret[j] += ret[j | x];
    }
  }
  return ret;
}
int legal_size_of(int n) {
  int ret = 1 << (int)log2(n);
  if (ret < n) ret <<= 1;
  return ret;
}
}  // namespace Zeta_and_Mobius_transform
using namespace Zeta_and_Mobius_transform;
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  ;
  int n;
  cin >> n;
  vector<modll> x(legal_size_of(1000000));
  for (int i = 0; i < (int)n; i++) {
    int a;
    cin >> a;
    x[a] += 1;
  }
  vector<modll> y = Zeta_trans_rev(x);
  modll ans = 0;
  for (int i = 0; i < (int)y.size(); i++) {
    int cnt = 0;
    for (int j = 0; j < (int)21; j++) {
      cnt += (i & (1 << j) ? 1 : 0);
    }
    ans += pow(modll(-1), cnt) * pow(modll(2), y[i].get_val());
  }
  cout << ans << endl;
}