You are given n integers a1, a2, ..., an. Find the number of pairs of indexes i, j (i < j) that ai + aj is a power of 2 (i. e. some integer x exists so that ai + aj = 2x).

Input

The first line contains the single positive integer n (1 ≤ n ≤ 105) — the number of integers.

The second line contains n positive integers a1, a2, ..., an (1 ≤ ai ≤ 109).

Output

Print the number of pairs of indexes i, j (i < j) that ai + aj is a power of 2.

Examples

Input

4
7 3 2 1


Output

2


Input

3
1 1 1


Output

3

Note

In the first example the following pairs of indexes include in answer: (1, 4) and (2, 4).

In the second example all pairs of indexes (i, j) (where i < j) include in answer.
#include <bits/stdc++.h>
using namespace std;
unordered_map<unsigned, unsigned> mk;
unsigned i, j, n, a[100099], x;
unsigned long long k;
int main() {
  scanf("%u", &n);
  for (i = 0; i < n; i++) scanf("%u", a + i);
  mk[a[0]] = 1;
  k = 0;
  for (i = 1; i < n; i++) {
    x = log2(a[i]);
    for (j = x + 1; j <= 31; j++)
      if (mk.count((1 << j) - a[i])) k += mk[(1 << j) - a[i]];
    if (mk.count(a[i]))
      mk[a[i]]++;
    else
      mk[a[i]] = 1;
  }
  cout << k << '\n';
}
