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;
using int64 = int_fast64_t;
using PAIR = pair<int64, int64>;
constexpr int64 INF = 1LL << 40 - 1;
constexpr int64 LINF = 1LL << 60 + 1;
constexpr int MOD = 1e9 + 7;
constexpr int MAX_N = 1e5 + 1;
 
// init/input
#define int int64
#define INIT ios::sync_with_stdio(false);cin.tie(0);
#define VAR(type, ...) type __VA_ARGS__;MACRO_VAR_Scan(__VA_ARGS__);
template<typename T> void MACRO_VAR_Scan(T &t) {cin>>t;}
template<typename First, typename...Rest> void MACRO_VAR_Scan(First &first, Rest&...rest) {cin>>first;MACRO_VAR_Scan(rest...);}
#define VEC(type, c, n) vector<type> c(n);for(auto &&i:c)cin>>i;
 
// out
#define OUT(dist) cout<<(dist);
#define FOUT(n, dist) cout<<fixed<<setprecision(n)<<(dist);
#define SP cout<<" ";
#define BR cout<<endl;
#define zero(n) cout<<setfill('0')<<right<<setw(n)
#define debug(x) cerr<<#x<<":"<< (x);BR;
 
// utility
#define ALL(a) (a).begin(), (a).end()
#define EACH(i, a) for(auto &&i:(a))
#define FOR(i, a, b) for(int i=(a);i<(b);++i)
#define RFOR(i, a, b) for(int i=(b)-1;i>=0;--i)
#define REP(i, n) for(int i=0;i<(n);++i)
#define RREP(i, n) for(int i=(n)-1;i>=0;--i)
 
 
signed main() {
  INIT;
	VAR(int, n);
	map< int, int > mp;
	vector< int > a;
	REP(i, n) {
		VAR(int, j);
		a.push_back(j);
	}
 
	sort(ALL(a));
	a.erase(unique(ALL(a)), a.end());
 
	int ans = 0;
	RREP(i, a.size()) {
		RREP(j, 31) {
            if (2 * a[i] > (1LL << j)) break;
            int target = (1 << j) - a[i];

			if (target == a[i]) {
				int tmp = mp[target] / 2;
				mp[target] -= tmp * 2;
				ans += tmp;
			} else {
				int tmp1 = mp[target];
				int tmp2 = mp[a[i]];
				mp[target] -= min(tmp1, tmp2);
				mp[a[i]] -= min(tmp1, tmp2);
				ans += min(tmp1, tmp2);
			}
		}
		mp[a[i]]++;
	}
 
	OUT(ans)BR;
  
  return 0;
}