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;
set<pair<int, int>> s;
int main() {
  int n;
  long long maxx = 0, x;
  scanf("%d", &n);
  map<int, int> m;
  for (int i = 0; i < n; i++) {
    scanf("%d", &x);
    m[x]++;
  }
  for (map<int, int>::iterator it = m.begin(); it != m.end(); it++) {
    for (long long j = 2; j <= 2e9; j *= 2) {
      if (j <= it->first || j - it->first < it->first) continue;
      map<int, int>::iterator it2 = m.find(j - it->first);
      if (it2 == it)
        maxx += (long long)it->second * (it->second - 1) / 2;
      else if (it2 != m.end())
        maxx += it2->second * it->second;
    }
  }
  printf("%lld", maxx);
}
