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: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define REP(i,m,n) for(int i=(int)(m); i<(int)(n); i++)
#define rep(i,n) REP(i,0,n)
#define REPL(i,m,n) for(ll i=(ll)(m); i<(ll)(n); i++)
#define repl(i,n) REPL(i,0,n)
#define all(v) v.begin(), v.end()
const int inf = 1e9+7;
const ll longinf = 1LL<<60;
const ll mod = 1e9+7;

int main() {
  int N;
  cin >> N;
  vector<ll> A(N);
  rep(i, N) cin >> A[i];
  map<ll, int, greater<ll> > mp;
  rep(i, N) {
    if(!mp.count(A[i])) mp[A[i]] = 1;
    else mp[A[i]]++;
  }
  int ans = 0;
  for(auto a: mp) {
    ll tmp = a.first;
    ll pair = (ll)pow(2, ceil(log2(tmp))) - tmp;
    if(mp[tmp] > 0 && mp.count(pair) && mp[pair] > 0) {
      int cnt = min(mp[tmp], mp[pair]);
      mp[tmp] -= cnt;
      mp[pair] -= cnt;
      ans += cnt;
    }
  }
  cout << ans << endl;
  return 0;
}