Takahashi has N balls with positive integers written on them. The integer written on the i-th ball is A_i. He would like to form some number of pairs such that the sum of the integers written on each pair of balls is a power of 2. Note that a ball cannot belong to multiple pairs. Find the maximum possible number of pairs that can be formed.

Here, a positive integer is said to be a power of 2 when it can be written as 2^t using some non-negative integer t.

Constraints

* 1 \leq N \leq 2\times 10^5
* 1 \leq A_i \leq 10^9
* A_i is an integer.

Input

Input is given from Standard Input in the following format:


N
A_1 A_2 ... A_N


Output

Print the maximum possible number of pairs such that the sum of the integers written on each pair of balls is a power of 2.

Examples

Input

3
1 2 3


Output

1


Input

5
3 11 14 5 13


Output

2
#include <cstdio>
#include <map>
#include <algorithm>

using namespace std;

int main() {
  int n;
  scanf("%d", &n);
  map<int, int> cnt;
  for (int i = 0; i < n; ++i) {
    int x;
    scanf("%d", &x);
    ++cnt[x];
  }
  int ans = 0;
  for (int i = 30; i >= 1; --i) {
    ans += cnt[1 << (i - 1)] / 2;
    for (auto &e : cnt) {
      if (e.first < (1 << (i - 1)) && cnt.count((1 << i) - e.first) != 0) {
        int by = min(e.second, cnt[(1 << i) - e.first]);
        ans += by;
        e.second -= by;
      }
    }
  }
  printf("%d\n", ans);
}
