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;
map<int, int> x;
int arr[100000];
long long sum;
vector<long long> Powers;
int main() {
  long long Count = 1;
  for (int i = 1; i < 32; i++) Count *= 2, Powers.push_back(Count);
  int n;
  scanf("%d", &n);
  for (int i = 0; i < n; i++) scanf("%d", &arr[i]), x[arr[i]]++;
  for (int i = 0; i < n; i++) {
    x[arr[i]]--;
    for (int j = 0; j < Powers.size(); j++)
      if (x.count(Powers[j] - arr[i])) sum += x[Powers[j] - arr[i]];
  }
  cout << sum << endl;
}
