#include <algorithm>
#include <cstdio>
#include <set>

const int N = 200050;

int n;
std::multiset<int> S;

int main() {
  scanf("%d", &n);
  for (int i = 0, x; i < n; ++i) {
    scanf("%d", &x);
    S.insert(x);
  }
  int ans = 0;
  while (!S.empty()) {
    std::multiset<int>::iterator it = --S.end();
    int x = *it; S.erase(it);
    int k = 1;
    while (x >= k) k <<= 1;
    it = S.find(k - x);
    if (it != S.end()) ++ans, S.erase(it);
  }
  printf("%d\n", ans);
}
### Prompt

Please provide a Cpp coded solution to the problem described below:

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

### Response

```cpp
#include <algorithm>
#include <cstdio>
#include <set>

const int N = 200050;

int n;
std::multiset<int> S;

int main() {
  scanf("%d", &n);
  for (int i = 0, x; i < n; ++i) {
    scanf("%d", &x);
    S.insert(x);
  }
  int ans = 0;
  while (!S.empty()) {
    std::multiset<int>::iterator it = --S.end();
    int x = *it; S.erase(it);
    int k = 1;
    while (x >= k) k <<= 1;
    it = S.find(k - x);
    if (it != S.end()) ++ans, S.erase(it);
  }
  printf("%d\n", ans);
}
```