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;
long long viv, i, n;
map<long long, long long> st, a;
map<long long, vector<long long> > mp;
vector<long long>::iterator it;
long long ans = 0;
int main() {
  viv = 1;
  for (i = 0; i <= 31; i++) {
    st[i] = viv;
    viv *= 2;
  }
  cin >> n;
  for (i = 0; i < n; i++) {
    cin >> a[i];
    mp[a[i]].push_back(i);
  }
  for (i = 0; i < n; i++) {
    long long x = 0;
    while (st[x] <= a[i]) x++;
    while (x <= 31) {
      if (mp[st[x] - a[i]].size() != 0) {
        long long ojha =
            upper_bound(mp[st[x] - a[i]].begin(), mp[st[x] - a[i]].end(), i) -
            mp[st[x] - a[i]].begin();
        if (ojha <= mp[st[x] - a[i]].size()) {
          ans += mp[st[x] - a[i]].size() - ojha;
        }
      }
      x++;
    }
  }
  cout << ans;
}
