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>
#pragma GCC optimize("O3")
using namespace std;
const int maxn = 3e5 + 5;
const double pi = acos(-1);
const double EPS = 1e-9;
const int mod = 1e9 + 7;
const long long oo = 1e18;
int const N = 1e6 + 5;
map<int, int> frq;
void myMain() {
  int n;
  cin >> n;
  int a[n + 5];
  for (int i = 0; i < n; i++) {
    cin >> a[i];
  }
  long long ans = 0;
  for (int i = 0; i < n; i++) {
    for (int j = 0; j <= 31; j++) {
      int p = 1 << j;
      ans += frq[p - a[i]];
    }
    frq[a[i]]++;
  }
  cout << ans << endl;
}
int32_t main() {
  ios_base::sync_with_stdio(0);
  int t = 1;
  while (t--) {
    myMain();
  }
}
