Problem:
Score : 600 points

Problem Statement

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.

Sample Input 1

3
1 2 3

Sample Output 1

1

We can form one pair whose sum of the written numbers is 4 by pairing the first and third balls.
Note that we cannot pair the second ball with itself.

Sample Input 2

5
3 11 14 5 13

Sample Output 2

2

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
using namespace std;
#define FOR(i,a,b) for(int i=(a);i<(b);++i)
#define rep(i, n) for(int i = 0; i < (int)(n); i++)
#define all(x) (x).begin(),(x).end()
inline int toInt(string s) {int v; istringstream sin(s);sin>>v;return v;}
typedef long long ll;


int main(){
  int N;
  cin >> N;
  vector<int> A(N);
  rep(i,N){
    cin >> A[i];
  }
  sort(all(A),greater<int>());
  map<int,int> m;
  int ans = 0;
  for(int a:A){
    if(m.count(a) && m[a]>0) m[a]--,ans++;
    else m[(1<<(32-__builtin_clz(a))) - a]++;
    //最上位ビットの次に立っているビットの数 - a
  }
  cout << ans << endl;
  return 0;
}