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;
int n, cnt, a[100001], b[100001];
long long res;
int process() {
  int i, tmp = 2, c, k, k1;
  while (tmp < 1e9) {
    b[++cnt] = tmp;
    tmp <<= 1;
  }
  b[++cnt] = tmp;
  cin >> n;
  for (int i = 0; i < n; i++) cin >> a[i];
  sort(a, a + n, greater<int>());
  for (int i = 0; i < n; i++) {
    k = upper_bound(b + 1, b + cnt + 1, a[i]) - b;
    if (k == cnt + 1) continue;
    c = b[k] - a[i];
    k = lower_bound(a + i + 1, a + n, c, greater<int>()) - a;
    k1 = upper_bound(a + i + 1, a + n, c, greater<int>()) - a;
    res += k1 - k;
  }
  cout << res;
  return 0;
}
int main() {
  process();
  return 0;
}
