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;
const int N = 1e5 + 5;
long long n, mod[40], m[N], tmp, ans;
map<long long, int> freq;
void start() {
  long long ans = 1;
  for (int i = 1; i <= 34; i++) {
    mod[i] = ans;
    ans *= 2;
  }
  return;
}
int main() {
  start();
  scanf("%I64d", &n);
  for (int i = 0; i < n; i++) {
    scanf("%I64d", &m[i]);
  }
  for (int i = 0; i < n; i++) {
    for (int j = 1; j <= 34; j++) {
      tmp = mod[j] - m[i];
      if (tmp > 0) {
        ans += (freq[tmp]);
      }
    }
    freq[m[i]]++;
  }
  printf("%I64d\n", ans);
}
