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;

//#include <boost/multiprecision/cpp_int.hpp>
// using namespace boost::multiprecision;
// using cint = cpp_int;
//#pragma GCC optimize("", on)
//#pragma GCC optimization_level 3
//#define min(...) min({...})
//#define max(...) max({...})

// Define
using ll = long long;
using ull = unsigned long long;
using ld = long double;
const ll dx[4] = {1, 0, -1, 0};
const ll dy[4] = {0, 1, 0, -1};
const ll MOD = 1e9 + 7;
const ll inf = 1 << 30;
const ll INF = LONG_MAX;
const ull MAX = ULONG_MAX;
#define mp make_pair
#define pb push_back
#define eb emplace_back
#define x first
#define y second
#define endl '\n'
#define space ' '
#define def inline auto
#define func inline constexpr ll
#define run __attribute__((constructor)) def _
#define all(v) begin(v), end(v)
#define input(a) scanf("%lld", &(a))
#define print(a) printf("%lld\n", (a))
#define ok(a, b) (0 <= (a) && (a) < b)

// Debug
#define debug(...)                                                             \
    {                                                                          \
        cerr << __LINE__ << ": " << #__VA_ARGS__ << " = ";                     \
        for (auto &&X : {__VA_ARGS__}) cerr << "[" << X << "] ";               \
        cerr << endl;                                                          \
    }

#define dump(a, h, w)                                                          \
    {                                                                          \
        cerr << __LINE__ << ": " << #a << " = [" << endl;                      \
        rep(__i, h) {                                                          \
            rep(__j, w) cerr << a[__i][__j] << space;                          \
            cerr << endl;                                                      \
        }                                                                      \
        cerr << "]" << endl;                                                   \
    }

#define vdump(a, n)                                                            \
    {                                                                          \
        cerr << __LINE__ << ": " << #a << " = [";                              \
        rep(__i, n) if (__i) cerr << space << a[__i];                          \
        else cerr << a[__i];                                                   \
        cerr << "]" << endl;                                                   \
    }

// Loop
#define inc(i, a, n) for (ll i = (a), _##i = (n); i <= _##i; ++i)
#define dec(i, a, n) for (ll i = (a), _##i = (n); i >= _##i; --i)
#define rep(i, n) for (ll i = 0, _##i = (n); i < _##i; ++i)
#define each(i, a) for (auto &&i : a)
#define loop() for (;;)

// Stream
#define fout(n) cout << fixed << setprecision(n)
#define fasten cin.tie(0), ios::sync_with_stdio(0)

// Speed
run() { fasten, fout(10); }
#pragma GCC optimize("O3")
#pragma GCC target("avx")

// Math
func gcd(ll a, ll b) { return b ? gcd(b, a % b) : a; }
func lcm(ll a, ll b) { return a * b / gcd(a, b); }
func sign(ll a) { return a ? abs(a) / a : 0; }

def in() {
    ll A;
    cin >> A;
    return A;
}

ll N, A[200000], used[200000], used2[200000], res, res2, f = -1, s = -1;
signed main() {
    cin >> N;
    rep(i, N) cin >> A[i];
    sort(A, A + N);
    // vdump(A, N);
    rep(i, N) rep(j, 30) {
        ll sum = 1 << j, k = sum - A[i];
        if (k < 0 || used[i]) continue;
        ll iter = lower_bound(A, A + N, k) - A;
        ll iter2 = lower_bound(A, A + N, k + 1) - A;
        // debug(A[i], k, res);
        inc(p, iter, iter2 - 1) {
            if (i != p && !used[p]) {
                used[p] = used[i] = 1;
                if (f == -1) f = p;
                res++;
            }
        }
    }
    rep(i, N) rep(j, 30) {
        ll sum = 1 << j, k = sum - A[i];
        if (k < 0 || used2[i]) continue;
        ll iter = lower_bound(A, A + N, k) - A;
        ll iter2 = lower_bound(A, A + N, k + 1) - A;
        // debug(A[i], k, res2);
        inc(p, iter, iter2 - 1) {
            if (i != p && !used2[p] && (s != -1 || p != f)) {
                used2[p] = used2[i] = 1;
                s = 0;
                res2++;
            }
        }
    }
    cout << max(res, res2) << endl;
}

// for compilation: g++ -Ofast -march=native -o _ _.cpp -std=c++17