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;
void READ(string INPUT = "NO", string OUTPUT = "NO") {
  if (INPUT != "NO") freopen(INPUT.c_str(), "r", stdin);
  if (OUTPUT != "NO") freopen(OUTPUT.c_str(), "w", stdout);
}
map<int, int> frq;
int n;
int a[100000];
long long ans;
int main() {
  scanf("%d", &n);
  for (int i = 0; i < n; i++) {
    scanf("%d", a + i);
    frq[a[i]]++;
  }
  for (int i = 0; i < n; i++) {
    for (int p = 1; p <= 30; p++) {
      int P = pow(2, p);
      P -= a[i];
      if ((frq[P] > 0 && P != a[i])) {
        ans += frq[P];
      } else if (frq[P] > 1) {
        ans += frq[P] - 1;
      }
    }
    frq[a[i]]--;
  }
  cout << ans << "\n";
  return 0;
}
