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;
int n, a[100001], d[32];
long long res1, res2;
map<int, int> g;
int main() {
  cin >> n;
  for (int i = 0; i < n; i++) {
    cin >> a[i];
    g[a[i]]++;
    if ((a[i] & (a[i] - 1)) == 0) res1 += (d[(int)log2(a[i])]++);
  }
  for (int j = 1; j <= 30; j++)
    for (int i = 0; i < n; i++)
      if (a[i] != (1 << (j - 1))) res2 += g[(1 << j) - a[i]];
  cout << res1 + (res2 >> 1);
}
