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;
const int Size = 1024;
const int mod2 = 998244353;
const int mod = 1e9 + 7;
const int INF = 0x3f3f3f3f;
const int maxn = 4e5 + 15;
const int base = 307;
long long a[maxn];
map<long long, long long> mp;
int main() {
  long long n;
  scanf("%lld", &n);
  long long ans = 0;
  for (long long i = 1; n >= i; i++) {
    scanf("%lld", &a[i]);
    ans += mp[a[i]];
    for (long long j = 0; 40 >= j; j++) {
      long long bit = (1ll << j);
      mp[bit - a[i]]++;
    }
  }
  printf("%lld\n", ans);
  return 0;
}
