Problem: You are given an array s of n non-negative integers.

A 5-tuple of integers (a, b, c, d, e) is said to be valid if it satisfies the following conditions: 

  * 1 ≤ a, b, c, d, e ≤ n
  * (sa | sb) & sc & (sd ^ se) = 2i for some integer i
  * sa & sb = 0



Here, '|' is the bitwise OR, '&' is the bitwise AND and '^' is the bitwise XOR operation.

Find the sum of f(sa|sb) * f(sc) * f(sd^se) over all valid 5-tuples (a, b, c, d, e), where f(i) is the i-th Fibonnaci number (f(0) = 0, f(1) = 1, f(i) = f(i - 1) + f(i - 2)).

Since answer can be is huge output it modulo 109 + 7.

Input

The first line of input contains an integer n (1 ≤ n ≤ 106).

The second line of input contains n integers si (0 ≤ si < 217).

Output

Output the sum as described above, modulo 109 + 7

Examples

Input

2
1 2


Output

32


Input

3
7 4 1


Output

3520


Input

10
1 3 0 7 3 7 6 5 7 5


Output

1235424


Input

10
50 9 11 44 39 40 5 39 23 7


Output

113860062

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using std::cerr;
using std::cin;
using std::max;
using std::min;
int n, len, inv, cnt[270000], size[270000], fib[270000], A[18][270000],
    B[18][270000], C[270000], D[270000], E[270000], ans;
int cal(int x) {
  x -= x < 1000000007 ? 0 : 1000000007;
  return x;
}
class FWT {
 public:
  void dft(int *x, int f, int op) {
    for (int i = 1, a, b; i < len; i <<= 1)
      for (int j = 0; j < len; j += i << 1)
        for (int k = 0; k < i; k++) {
          a = x[j + k], b = x[i + j + k];
          if (op == 1)
            f > 0 ? x[i + j + k] = cal(b + a)
                  : x[i + j + k] = cal(b - a + 1000000007);
          if (op == 2)
            f > 0 ? x[j + k] = cal(a + b) : x[j + k] = cal(a - b + 1000000007);
          if (op == 3) {
            x[j + k] = cal(a + b), x[i + j + k] = cal(a - b + 1000000007);
            if (f < 0)
              x[j + k] = (long long)x[j + k] * inv % 1000000007,
                    x[i + j + k] = (long long)x[i + j + k] * inv % 1000000007;
          }
        }
  }
} fwt;
int main() {
  scanf("%d", &n), len = 1 << 18, inv = 1000000007 + 1 >> 1,
                   fib[1] = size[1] = 1;
  for (int i = 1, a; i <= n; i++) scanf("%d", &a), cnt[a]++;
  for (int i = 2; i < len; i++)
    fib[i] = cal(fib[i - 1] + fib[i - 2]), size[i] = size[i >> 1] + (i & 1);
  for (int i = 0; i < len; i++)
    A[size[i]][i] = E[i] = cnt[i],
    D[i] = (long long)cnt[i] * fib[i] % 1000000007;
  for (int i = 0; i < 18; i++) fwt.dft(A[i], 1, 1);
  for (int i = 0; i < 18; i++)
    for (int j = 0; i + j < 18; j++)
      for (int k = 0; k < len; k++)
        B[i + j][k] =
            cal(B[i + j][k] + (long long)A[i][k] * A[j][k] % 1000000007);
  for (int i = 0; i < 18; i++) fwt.dft(B[i], -1, 1);
  for (int i = 0; i < len; i++)
    C[i] = (long long)B[size[i]][i] * fib[i] % 1000000007;
  fwt.dft(E, 1, 3);
  for (int i = 0; i < len; i++) E[i] = (long long)E[i] * E[i] % 1000000007;
  fwt.dft(E, -1, 3);
  for (int i = 0; i < len; i++) E[i] = (long long)E[i] * fib[i] % 1000000007;
  fwt.dft(C, 1, 2), fwt.dft(D, 1, 2), fwt.dft(E, 1, 2);
  for (int i = 0; i < len; i++)
    C[i] = (long long)C[i] * D[i] % 1000000007 * E[i] % 1000000007;
  fwt.dft(C, -1, 2);
  for (int i = 0; i < 18; i++) ans = cal(ans + C[1 << i]);
  printf("%d\n", ans);
  return 0;
}