Problem p03201 (C++)

Buggy submission (status: Time Limit Exceeded):
#include <bits/stdc++.h>
using namespace std;
#define pb push_back
#define eb emplace_back
#define mp make_pair
#define f first
#define s second
#define all(a) (a).begin(), (a).end()
#define For(i, a, b) for (auto i = (a); i < (b); i++)
#define FOR(i, b) For(i, 0, b)
#define Rev(i, a, b) for (auto i = (a); i > (b); i--)
#define REV(i, a) Rev(i, a, -1)
#define FORE(i, a) for (auto &&i : a)
#define sz(a) (int((a).size()))
using ll = long long;
using ld = long double;
using uint = unsigned int;
using ull = unsigned long long;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
using pill = pair<int, ll>;
using plli = pair<ll, int>;
using pdd = pair<double, double>;
using pld = pair<ld, ld>;
constexpr const char nl = '\n', sp = ' ';
constexpr const int INT_INF = 0x3f3f3f3f;
constexpr const ll LL_INF = 0x3f3f3f3f3f3f3f3f;
constexpr const double D_INF = numeric_limits<double>::infinity();
constexpr const ld LD_INF = numeric_limits<ld>::infinity();
template <class T> constexpr const T &_min(const T &x, const T &y) {
  return x < y ? x : y;
}
template <class T> constexpr const T &_max(const T &x, const T &y) {
  return x < y ? y : x;
}
template <class T, class... Ts>
constexpr const T &_min(const T &x, const Ts &...xs) {
  return _min(x, _min(xs...));
}
template <class T, class... Ts>
constexpr const T &_max(const T &x, const Ts &...xs) {
  return _max(x, _max(xs...));
}
template <class T, class... Ts> void MIN(T &x, const Ts &...xs) {
  x = _min(x, xs...);
}
template <class T, class... Ts> void MAX(T &x, const Ts &...xs) {
  x = _max(x, xs...);
}
template <class T>
constexpr const T &_clamp(const T &v, const T &lo, const T &hi) {
  return v < lo ? lo : hi < v ? hi : v;
}
template <class T> void CLAMP(T &v, const T &lo, const T &hi) {
  v = _clamp(v, lo, hi);
}
template <class T, class... Args> unique_ptr<T> _make_unique(Args &&...args) {
  return unique_ptr<T>(new T(forward<Args>(args)...));
}
template <class T, class... Args> shared_ptr<T> _make_shared(Args &&...args) {
  return shared_ptr<T>(new T(forward<Args>(args)...));
}
#define min(...) _min(__VA_ARGS__)
#define max(...) _max(__VA_ARGS__)
#define clamp(...) _clamp(__VA_ARGS__)
#define make_unique _make_unique
#define make_shared _make_shared
template <class... Ts> using uset = unordered_set<Ts...>;
template <class... Ts> using umap = unordered_map<Ts...>;
template <class... Ts> using pq = priority_queue<Ts...>;
template <class T> using minpq = pq<T, vector<T>, greater<T>>;
template <class T> using maxpq = pq<T, vector<T>, less<T>>;
template <class T1, class T2, class H1 = hash<T1>, class H2 = hash<T2>>
struct pair_hash {
  size_t operator()(const pair<T1, T2> &p) const {
    return 31 * H1{}(p.first) + H2{}(p.second);
  }
};
template <class T> struct is_iterator {
  template <class U, typename enable_if<!is_convertible<U, const char *>::value,
                                        int>::type = 0>
  constexpr static auto has_indirection(int)
      -> decltype(*declval<U>(), bool()) {
    return true;
  }
  template <class> constexpr static bool has_indirection(long) { return false; }
  constexpr static bool value = has_indirection<T>(0);
};
seed_seq seq{(uint64_t)chrono::duration_cast<chrono::nanoseconds>(
                 chrono::high_resolution_clock::now().time_since_epoch())
                 .count(),
             (uint64_t)__builtin_ia32_rdtsc(),
             (uint64_t)(uintptr_t)make_unique<char>().get()};
mt19937 rng(seq);
mt19937_64 rng64(seq);

constexpr const int _bufferSize = 4096, _maxNumLength = 128;
char _inputBuffer[_bufferSize + 1],
    *_inputPtr = _inputBuffer, _outputBuffer[_bufferSize], _c, _sign,
    *_tempInputBuf = nullptr, _numBuf[_maxNumLength],
    _tempOutputBuf[_maxNumLength], _fill = ' ';
FILE *_input = stdin, *_output = stdout, *_error = stderr;
const char *_delimiter = " ";
int _cur, _outputPtr = 0, _numPtr = 0, _precision = 6, _width = 0,
          _tempOutputPtr = 0, _cnt;
ull _precisionBase = 1000000;
#define _peekchar()                                                            \
  (*_inputPtr ? *_inputPtr                                                     \
              : (_inputBuffer[fread(_inputPtr = _inputBuffer, 1, _bufferSize,  \
                                    _input)] = '\0',                           \
                 *_inputPtr))
#define _getchar()                                                             \
  (*_inputPtr ? *_inputPtr++                                                   \
              : (_inputBuffer[fread(_inputPtr = _inputBuffer, 1, _bufferSize,  \
                                    _input)] = '\0',                           \
                 *_inputPtr++))
#define _hasNext() (*_inputPtr || !feof(_input))
#define _readSignAndNum(x)                                                     \
  do {                                                                         \
    (x) = _getchar();                                                          \
  } while ((x) <= ' ');                                                        \
  _sign = (x) == '-';                                                          \
  if (_sign)                                                                   \
    (x) = _getchar();                                                          \
  for ((x) -= '0'; (_c = _getchar()) >= '0'; (x) = (x)*10 + _c - '0')
#define _readFloatingPoint(x, T)                                               \
  for (T _div = 1.0; (_c = _getchar()) >= '0'; (x) += (_c - '0') / (_div *= 10))
#define rc(x)                                                                  \
  do {                                                                         \
    do {                                                                       \
      (x) = _getchar();                                                        \
    } while ((x) <= ' ');                                                      \
  } while (0)
#define ri(x)                                                                  \
  do {                                                                         \
    _readSignAndNum(x);                                                        \
    if (_sign)                                                                 \
      (x) = -(x);                                                              \
  } while (0)
#define rd(x)                                                                  \
  do {                                                                         \
    _readSignAndNum(x);                                                        \
    if (_c == '.')                                                             \
      _readFloatingPoint(x, double);                                           \
    if (_sign)                                                                 \
      (x) = -(x);                                                              \
  } while (0)
#define rld(x)                                                                 \
  do {                                                                         \
    _readSignAndNum(x);                                                        \
    if (_c == '.')                                                             \
      _readFloatingPoint(x, ld);                                               \
    if (_sign)                                                                 \
      (x) = -(x);                                                              \
  } while (0)
#define rcs(x)                                                                 \
  do {                                                                         \
    _cur = 0;                                                                  \
    do {                                                                       \
      _c = _getchar();                                                         \
    } while (_c <= ' ');                                                       \
    do {                                                                       \
      (x)[_cur++] = _c;                                                        \
    } while ((_c = _getchar()) > ' ');                                         \
    (x)[_cur] = '\0';                                                          \
  } while (0)
#define rs(x)                                                                  \
  do {                                                                         \
    if (!_tempInputBuf)                                                        \
      assert(0);                                                               \
    rcs(_tempInputBuf);                                                        \
    (x) = string(_tempInputBuf, _cur);                                         \
  } while (0)
#define rcln(x)                                                                \
  do {                                                                         \
    _cur = 0;                                                                  \
    do {                                                                       \
      _c = _getchar();                                                         \
    } while (_c <= ' ');                                                       \
    do {                                                                       \
      (x)[_cur++] = _c;                                                        \
    } while ((_c = _getchar()) >= ' ');                                        \
    (x)[_cur] = '\0';                                                          \
  } while (0)
#define rln(x)                                                                 \
  do {                                                                         \
    if (!_tempInputBuf)                                                        \
      assert(0);                                                               \
    rcln(_tempInputBuf);                                                       \
    (x) = string(_tempInputBuf, _cur);                                         \
  } while (0)
#define setLength(x)                                                           \
  do {                                                                         \
    if (_tempInputBuf)                                                         \
      delete[] (_tempInputBuf);                                                \
    _tempInputBuf = new char[(x) + 1];                                         \
  } while (0)
void read(int &x) { ri(x); }
void read(uint &x) { ri(x); }
void read(ll &x) { ri(x); }
void read(ull &x) { ri(x); }
void read(double &x) { rd(x); }
void read(ld &x) { rld(x); }
void read(char &x) { rc(x); }
void read(char *x) { rcs(x); }
void read(string &x) { rs(x); }
void readln(char *x) { rcln(x); }
void readln(string &x) { rln(x); }
template <class T1, class T2> void read(pair<T1, T2> &x) {
  read(x.first);
  read(x.second);
}
template <class T> void read(complex<T> &x) {
  T _re, _im;
  read(_re);
  read(_im);
  x.real(_re);
  x.imag(_im);
}
template <class T> void read(T &x);
template <class T, class... Ts> void read(T &x, Ts &&...xs);
template <class It>
typename enable_if<is_iterator<It>::value>::type read(It st, It en) {
  for (It _i = st; _i != en; _i++)
    read(*_i);
}
template <class It, class... Ts>
typename enable_if<is_iterator<It>::value>::type read(It st, It en,
                                                      Ts &&...xs) {
  read(st, en);
  read(forward<Ts>(xs)...);
}
template <class T> void read(T &x) {
  for (auto &&_i : x)
    read(_i);
}
template <class T, class... Ts> void read(T &x, Ts &&...xs) {
  read(x);
  read(forward<Ts>(xs)...);
}
bool hasNext() {
  while (_hasNext() && _peekchar() <= ' ')
    _getchar();
  return _hasNext();
}
void setInput(FILE *file) {
  *_inputPtr = '\0';
  _input = file;
}
void setInput(const char *s) {
  *_inputPtr = '\0';
  _input = fopen(s, "r");
}
void setInput(const string &s) {
  *_inputPtr = '\0';
  _input = fopen(s.c_str(), "r");
}
#define _flush()                                                               \
  do {                                                                         \
    _flushBuf();                                                               \
    fflush(_output);                                                           \
  } while (0)
#define _flushBuf()                                                            \
  (fwrite(_outputBuffer, 1, _outputPtr, _output), _outputPtr = 0)
#define _putchar(x)                                                            \
  (_outputBuffer[_outputPtr == _bufferSize ? _flushBuf() : _outputPtr] = (x),  \
   _outputPtr++)
#define _writeTempBuf(x) (_tempOutputBuf[_tempOutputPtr++] = (x))
#define _writeOutput()                                                         \
  for (int _i = 0; _i < _tempOutputPtr; _putchar(_tempOutputBuf[_i++]))        \
    ;                                                                          \
  _tempOutputPtr = 0
#define _writeNum(x, T, digits)                                                \
  _cnt = 0;                                                                    \
  for (T _y = (x); _y; _y /= 10, _cnt++)                                       \
    _numBuf[_numPtr++] = '0' + _y % 10;                                        \
  for (; _cnt < digits; _cnt++)                                                \
    _numBuf[_numPtr++] = '0';                                                  \
  _flushNumBuf();
#define _writeFloatingPoint(x, T)                                              \
  ull _I = (ull)(x);                                                           \
  ull _F = ((x)-_I) * _precisionBase + (T)(0.5);                               \
  if (_F >= _precisionBase) {                                                  \
    _I++;                                                                      \
    _F = 0;                                                                    \
  }                                                                            \
  _writeNum(_I, ull, 1);                                                       \
  _writeTempBuf('.');                                                          \
  _writeNum(_F, ull, _precision)
#define _checkFinite(x)                                                        \
  if (std::isnan(x)) {                                                         \
    wcs("NaN");                                                                \
  } else if (std::isinf(x)) {                                                  \
    wcs("Inf");                                                                \
  }
#define _flushNumBuf() for (; _numPtr; _writeTempBuf(_numBuf[--_numPtr]))
#define _fillBuf(x)                                                            \
  for (int _i = 0; _i < (x); _i++)                                             \
  _putchar(_fill)
#define _flushTempBuf()                                                        \
  int _tempLen = _tempOutputPtr;                                               \
  _fillBuf(_width - _tempLen);                                                 \
  _writeOutput();                                                              \
  _fillBuf(-_width - _tempLen)
#define wb(x)                                                                  \
  do {                                                                         \
    if (x)                                                                     \
      _writeTempBuf('1');                                                      \
    else                                                                       \
      _writeTempBuf('0');                                                      \
    _flushTempBuf();                                                           \
  } while (0)
#define wc(x)                                                                  \
  do {                                                                         \
    _writeTempBuf(x);                                                          \
    _flushTempBuf();                                                           \
  } while (0)
#define wi(x)                                                                  \
  do {                                                                         \
    if ((x) < 0) {                                                             \
      _writeTempBuf('-');                                                      \
      _writeNum(-(x), uint, 1);                                                \
    } else {                                                                   \
      _writeNum(x, uint, 1);                                                   \
    }                                                                          \
    _flushTempBuf();                                                           \
  } while (0)
#define wll(x)                                                                 \
  do {                                                                         \
    if ((x) < 0) {                                                             \
      _writeTempBuf('-');                                                      \
      _writeNum(-(x), ull, 1);                                                 \
    } else {                                                                   \
      _writeNum(x, ull, 1);                                                    \
    }                                                                          \
    _flushTempBuf();                                                           \
  } while (0)
#define wd(x)                                                                  \
  do {                                                                         \
    _checkFinite(x) else if ((x) < 0) {                                        \
      _writeTempBuf('-');                                                      \
      _writeFloatingPoint(-(x), double);                                       \
    }                                                                          \
    else {                                                                     \
      _writeFloatingPoint(x, double);                                          \
    }                                                                          \
    _flushTempBuf();                                                           \
  } while (0)
#define wld(x)                                                                 \
  do {                                                                         \
    _checkFinite(x) else if ((x) < 0) {                                        \
      _writeTempBuf('-');                                                      \
      _writeFloatingPoint(-(x), ld);                                           \
    }                                                                          \
    else {                                                                     \
      _writeFloatingPoint(x, ld);                                              \
    }                                                                          \
    _flushTempBuf();                                                           \
  } while (0)
#define wcs(x)                                                                 \
  do {                                                                         \
    int _slen = strlen(x);                                                     \
    _fillBuf(_width - _slen);                                                  \
    for (const char *_p = (x); *_p; _putchar(*_p++))                           \
      ;                                                                        \
    _fillBuf(-_width - _slen);                                                 \
  } while (0)
#define ws(x)                                                                  \
  do {                                                                         \
    _fillBuf(_width - int((x).length()));                                      \
    for (int _i = 0; _i < int((x).length()); _putchar(x[_i++]))                \
      ;                                                                        \
    _fillBuf(-_width - int((x).length()));                                     \
  } while (0)
#define setPrecision(x)                                                        \
  do {                                                                         \
    _precision = (x);                                                          \
    _precisionBase = 1;                                                        \
    for (int _i = 0; _i < (x); _i++, _precisionBase *= 10)                     \
      ;                                                                        \
  } while (0)
#define setDelimiter(x)                                                        \
  do {                                                                         \
    _delimiter = (x);                                                          \
  } while (0)
#define setWidth(x)                                                            \
  do {                                                                         \
    _width = (x);                                                              \
  } while (0)
#define setFill(x)                                                             \
  do {                                                                         \
    _fill = (x);                                                               \
  } while (0)
void writeDelimiter() {
  for (const char *_p = _delimiter; *_p; _putchar(*_p++))
    ;
}
void write(const bool &x) { wb(x); }
void write(const int &x) { wi(x); }
void write(const uint &x) { wi(x); }
void write(const ll &x) { wll(x); }
void write(const ull &x) { wll(x); }
void write(const double &x) { wd(x); }
void write(const ld &x) { wld(x); }
void write(const char &x) { wc(x); }
void write(const char *x) { wcs(x); }
void write(const string &x) { ws(x); }
template <class T1, class T2> void write(const pair<T1, T2> &x) {
  write(x.first);
  writeDelimiter();
  write(x.second);
}
template <class T> void write(const complex<T> &x) {
  write(x.real());
  writeDelimiter();
  write(x.imag());
}
template <class T> void write(const T &x);
template <class T, class... Ts> void write(const T &x, Ts &&...xs);
template <class It>
typename enable_if<is_iterator<It>::value>::type write(It st, It en) {
  bool _first = 1;
  for (It _i = st; _i != en; _i++) {
    if (_first)
      _first = 0;
    else
      writeDelimiter();
    write(*_i);
  }
}
template <class It, class... Ts>
typename enable_if<is_iterator<It>::value>::type write(It st, It en,
                                                       Ts &&...xs) {
  write(st, en);
  writeDelimiter();
  write(forward<Ts>(xs)...);
}
template <class T> void write(const T &x) {
  bool _first = 1;
  for (auto &&_i : x) {
    if (_first)
      _first = 0;
    else
      writeDelimiter();
    write(_i);
  }
}
template <class T, class... Ts> void write(const T &x, Ts &&...xs) {
  write(x);
  writeDelimiter();
  write(forward<Ts>(xs)...);
}
void writeln() { _putchar('\n'); }
template <class... Ts> void writeln(Ts &&...xs) {
  write(forward<Ts>(xs)...);
  _putchar('\n');
}
void flush() { _flush(); }
class IOManager {
public:
  ~IOManager() {
    flush();
    if (_tempInputBuf)
      delete[] (_tempInputBuf);
  }
};
unique_ptr<IOManager> iomanager = make_unique<IOManager>();
void setOutput(FILE *file) {
  flush();
  _output = file;
}
void setOutput(const char *s) {
  flush();
  _output = fopen(s, "w");
}
void setOutput(const string &s) {
  flush();
  _output = fopen(s.c_str(), "w");
}
template <class... Ts> void debug(const Ts &...xs) {
  FILE *_temp = _output;
  setOutput(_error);
  write(xs...);
  setOutput(_temp);
}
template <class... Ts> void debugln(const Ts &...xs) {
  FILE *_temp = _output;
  setOutput(_error);
  writeln(xs...);
  setOutput(_temp);
}
void setError(FILE *file) {
  flush();
  _error = file;
}
void setError(const char *s) {
  flush();
  _error = fopen(s, "w");
}
void setError(const string &s) {
  flush();
  _error = fopen(s.c_str(), "w");
}

const int MAXN = 2e5 + 5;

int N, A[MAXN], ord[MAXN], cnt[MAXN];
umap<int, int> freq;
umap<int, queue<int>> freq2;

int main() {
  // setInput("in.txt");
  // setOutput("out.txt");
  // setError("err.txt");
  read(N);
  read(A, A + N);
  fill(cnt, cnt + N, 0);
  FOR(i, N) freq[A[i]]++;
  FOR(i, N) {
    if (freq[A[i]]-- == 1)
      freq.erase(A[i]);
    FOR(j, 31) {
      int x = 1 << j;
      if (freq.count(x - A[i]))
        cnt[i] += freq[x - A[i]];
    }
    freq[A[i]]++;
  }
  iota(ord, ord + N, 0);
  sort(ord, ord + N,
       [&](const int &i, const int &j) { return cnt[i] < cnt[j]; });
  int ans = 0;
  FOR(i, N) freq2[A[i]] = queue<int>();
  FOR(i, N) {
    int minj = -1, mini = INT_INF;
    FOR(j, 31) {
      int x = 1 << j;
      if (!freq2[x - A[ord[i]]].empty() &&
          freq2[x - A[ord[i]]].front() < mini) {
        mini = freq2[x - A[ord[i]]].front();
        minj = j;
      }
    }
    if (minj == -1)
      freq2[A[ord[i]]].push(i);
    else {
      int x = 1 << minj;
      freq2[x - A[ord[i]]].pop();
      ans++;
    }
  }
  writeln(ans);
  return 0;
}


Fixed submission:
#include <bits/stdc++.h>
using namespace std;
#define pb push_back
#define eb emplace_back
#define mp make_pair
#define f first
#define s second
#define all(a) (a).begin(), (a).end()
#define For(i, a, b) for (auto i = (a); i < (b); i++)
#define FOR(i, b) For(i, 0, b)
#define Rev(i, a, b) for (auto i = (a); i > (b); i--)
#define REV(i, a) Rev(i, a, -1)
#define FORE(i, a) for (auto &&i : a)
#define sz(a) (int((a).size()))
using ll = long long;
using ld = long double;
using uint = unsigned int;
using ull = unsigned long long;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
using pill = pair<int, ll>;
using plli = pair<ll, int>;
using pdd = pair<double, double>;
using pld = pair<ld, ld>;
constexpr const char nl = '\n', sp = ' ';
constexpr const int INT_INF = 0x3f3f3f3f;
constexpr const ll LL_INF = 0x3f3f3f3f3f3f3f3f;
constexpr const double D_INF = numeric_limits<double>::infinity();
constexpr const ld LD_INF = numeric_limits<ld>::infinity();
template <class T> constexpr const T &_min(const T &x, const T &y) {
  return x < y ? x : y;
}
template <class T> constexpr const T &_max(const T &x, const T &y) {
  return x < y ? y : x;
}
template <class T, class... Ts>
constexpr const T &_min(const T &x, const Ts &...xs) {
  return _min(x, _min(xs...));
}
template <class T, class... Ts>
constexpr const T &_max(const T &x, const Ts &...xs) {
  return _max(x, _max(xs...));
}
template <class T, class... Ts> void MIN(T &x, const Ts &...xs) {
  x = _min(x, xs...);
}
template <class T, class... Ts> void MAX(T &x, const Ts &...xs) {
  x = _max(x, xs...);
}
template <class T>
constexpr const T &_clamp(const T &v, const T &lo, const T &hi) {
  return v < lo ? lo : hi < v ? hi : v;
}
template <class T> void CLAMP(T &v, const T &lo, const T &hi) {
  v = _clamp(v, lo, hi);
}
template <class T, class... Args> unique_ptr<T> _make_unique(Args &&...args) {
  return unique_ptr<T>(new T(forward<Args>(args)...));
}
template <class T, class... Args> shared_ptr<T> _make_shared(Args &&...args) {
  return shared_ptr<T>(new T(forward<Args>(args)...));
}
#define min(...) _min(__VA_ARGS__)
#define max(...) _max(__VA_ARGS__)
#define clamp(...) _clamp(__VA_ARGS__)
#define make_unique _make_unique
#define make_shared _make_shared
template <class... Ts> using uset = unordered_set<Ts...>;
template <class... Ts> using umap = unordered_map<Ts...>;
template <class... Ts> using pq = priority_queue<Ts...>;
template <class T> using minpq = pq<T, vector<T>, greater<T>>;
template <class T> using maxpq = pq<T, vector<T>, less<T>>;
template <class T1, class T2, class H1 = hash<T1>, class H2 = hash<T2>>
struct pair_hash {
  size_t operator()(const pair<T1, T2> &p) const {
    return 31 * H1{}(p.first) + H2{}(p.second);
  }
};
template <class T> struct is_iterator {
  template <class U, typename enable_if<!is_convertible<U, const char *>::value,
                                        int>::type = 0>
  constexpr static auto has_indirection(int)
      -> decltype(*declval<U>(), bool()) {
    return true;
  }
  template <class> constexpr static bool has_indirection(long) { return false; }
  constexpr static bool value = has_indirection<T>(0);
};
seed_seq seq{(uint64_t)chrono::duration_cast<chrono::nanoseconds>(
                 chrono::high_resolution_clock::now().time_since_epoch())
                 .count(),
             (uint64_t)__builtin_ia32_rdtsc(),
             (uint64_t)(uintptr_t)make_unique<char>().get()};
mt19937 rng(seq);
mt19937_64 rng64(seq);

constexpr const int _bufferSize = 4096, _maxNumLength = 128;
char _inputBuffer[_bufferSize + 1],
    *_inputPtr = _inputBuffer, _outputBuffer[_bufferSize], _c, _sign,
    *_tempInputBuf = nullptr, _numBuf[_maxNumLength],
    _tempOutputBuf[_maxNumLength], _fill = ' ';
FILE *_input = stdin, *_output = stdout, *_error = stderr;
const char *_delimiter = " ";
int _cur, _outputPtr = 0, _numPtr = 0, _precision = 6, _width = 0,
          _tempOutputPtr = 0, _cnt;
ull _precisionBase = 1000000;
#define _peekchar()                                                            \
  (*_inputPtr ? *_inputPtr                                                     \
              : (_inputBuffer[fread(_inputPtr = _inputBuffer, 1, _bufferSize,  \
                                    _input)] = '\0',                           \
                 *_inputPtr))
#define _getchar()                                                             \
  (*_inputPtr ? *_inputPtr++                                                   \
              : (_inputBuffer[fread(_inputPtr = _inputBuffer, 1, _bufferSize,  \
                                    _input)] = '\0',                           \
                 *_inputPtr++))
#define _hasNext() (*_inputPtr || !feof(_input))
#define _readSignAndNum(x)                                                     \
  do {                                                                         \
    (x) = _getchar();                                                          \
  } while ((x) <= ' ');                                                        \
  _sign = (x) == '-';                                                          \
  if (_sign)                                                                   \
    (x) = _getchar();                                                          \
  for ((x) -= '0'; (_c = _getchar()) >= '0'; (x) = (x)*10 + _c - '0')
#define _readFloatingPoint(x, T)                                               \
  for (T _div = 1.0; (_c = _getchar()) >= '0'; (x) += (_c - '0') / (_div *= 10))
#define rc(x)                                                                  \
  do {                                                                         \
    do {                                                                       \
      (x) = _getchar();                                                        \
    } while ((x) <= ' ');                                                      \
  } while (0)
#define ri(x)                                                                  \
  do {                                                                         \
    _readSignAndNum(x);                                                        \
    if (_sign)                                                                 \
      (x) = -(x);                                                              \
  } while (0)
#define rd(x)                                                                  \
  do {                                                                         \
    _readSignAndNum(x);                                                        \
    if (_c == '.')                                                             \
      _readFloatingPoint(x, double);                                           \
    if (_sign)                                                                 \
      (x) = -(x);                                                              \
  } while (0)
#define rld(x)                                                                 \
  do {                                                                         \
    _readSignAndNum(x);                                                        \
    if (_c == '.')                                                             \
      _readFloatingPoint(x, ld);                                               \
    if (_sign)                                                                 \
      (x) = -(x);                                                              \
  } while (0)
#define rcs(x)                                                                 \
  do {                                                                         \
    _cur = 0;                                                                  \
    do {                                                                       \
      _c = _getchar();                                                         \
    } while (_c <= ' ');                                                       \
    do {                                                                       \
      (x)[_cur++] = _c;                                                        \
    } while ((_c = _getchar()) > ' ');                                         \
    (x)[_cur] = '\0';                                                          \
  } while (0)
#define rs(x)                                                                  \
  do {                                                                         \
    if (!_tempInputBuf)                                                        \
      assert(0);                                                               \
    rcs(_tempInputBuf);                                                        \
    (x) = string(_tempInputBuf, _cur);                                         \
  } while (0)
#define rcln(x)                                                                \
  do {                                                                         \
    _cur = 0;                                                                  \
    do {                                                                       \
      _c = _getchar();                                                         \
    } while (_c <= ' ');                                                       \
    do {                                                                       \
      (x)[_cur++] = _c;                                                        \
    } while ((_c = _getchar()) >= ' ');                                        \
    (x)[_cur] = '\0';                                                          \
  } while (0)
#define rln(x)                                                                 \
  do {                                                                         \
    if (!_tempInputBuf)                                                        \
      assert(0);                                                               \
    rcln(_tempInputBuf);                                                       \
    (x) = string(_tempInputBuf, _cur);                                         \
  } while (0)
#define setLength(x)                                                           \
  do {                                                                         \
    if (_tempInputBuf)                                                         \
      delete[] (_tempInputBuf);                                                \
    _tempInputBuf = new char[(x) + 1];                                         \
  } while (0)
void read(int &x) { ri(x); }
void read(uint &x) { ri(x); }
void read(ll &x) { ri(x); }
void read(ull &x) { ri(x); }
void read(double &x) { rd(x); }
void read(ld &x) { rld(x); }
void read(char &x) { rc(x); }
void read(char *x) { rcs(x); }
void read(string &x) { rs(x); }
void readln(char *x) { rcln(x); }
void readln(string &x) { rln(x); }
template <class T1, class T2> void read(pair<T1, T2> &x) {
  read(x.first);
  read(x.second);
}
template <class T> void read(complex<T> &x) {
  T _re, _im;
  read(_re);
  read(_im);
  x.real(_re);
  x.imag(_im);
}
template <class T> void read(T &x);
template <class T, class... Ts> void read(T &x, Ts &&...xs);
template <class It>
typename enable_if<is_iterator<It>::value>::type read(It st, It en) {
  for (It _i = st; _i != en; _i++)
    read(*_i);
}
template <class It, class... Ts>
typename enable_if<is_iterator<It>::value>::type read(It st, It en,
                                                      Ts &&...xs) {
  read(st, en);
  read(forward<Ts>(xs)...);
}
template <class T> void read(T &x) {
  for (auto &&_i : x)
    read(_i);
}
template <class T, class... Ts> void read(T &x, Ts &&...xs) {
  read(x);
  read(forward<Ts>(xs)...);
}
bool hasNext() {
  while (_hasNext() && _peekchar() <= ' ')
    _getchar();
  return _hasNext();
}
void setInput(FILE *file) {
  *_inputPtr = '\0';
  _input = file;
}
void setInput(const char *s) {
  *_inputPtr = '\0';
  _input = fopen(s, "r");
}
void setInput(const string &s) {
  *_inputPtr = '\0';
  _input = fopen(s.c_str(), "r");
}
#define _flush()                                                               \
  do {                                                                         \
    _flushBuf();                                                               \
    fflush(_output);                                                           \
  } while (0)
#define _flushBuf()                                                            \
  (fwrite(_outputBuffer, 1, _outputPtr, _output), _outputPtr = 0)
#define _putchar(x)                                                            \
  (_outputBuffer[_outputPtr == _bufferSize ? _flushBuf() : _outputPtr] = (x),  \
   _outputPtr++)
#define _writeTempBuf(x) (_tempOutputBuf[_tempOutputPtr++] = (x))
#define _writeOutput()                                                         \
  for (int _i = 0; _i < _tempOutputPtr; _putchar(_tempOutputBuf[_i++]))        \
    ;                                                                          \
  _tempOutputPtr = 0
#define _writeNum(x, T, digits)                                                \
  _cnt = 0;                                                                    \
  for (T _y = (x); _y; _y /= 10, _cnt++)                                       \
    _numBuf[_numPtr++] = '0' + _y % 10;                                        \
  for (; _cnt < digits; _cnt++)                                                \
    _numBuf[_numPtr++] = '0';                                                  \
  _flushNumBuf();
#define _writeFloatingPoint(x, T)                                              \
  ull _I = (ull)(x);                                                           \
  ull _F = ((x)-_I) * _precisionBase + (T)(0.5);                               \
  if (_F >= _precisionBase) {                                                  \
    _I++;                                                                      \
    _F = 0;                                                                    \
  }                                                                            \
  _writeNum(_I, ull, 1);                                                       \
  _writeTempBuf('.');                                                          \
  _writeNum(_F, ull, _precision)
#define _checkFinite(x)                                                        \
  if (std::isnan(x)) {                                                         \
    wcs("NaN");                                                                \
  } else if (std::isinf(x)) {                                                  \
    wcs("Inf");                                                                \
  }
#define _flushNumBuf() for (; _numPtr; _writeTempBuf(_numBuf[--_numPtr]))
#define _fillBuf(x)                                                            \
  for (int _i = 0; _i < (x); _i++)                                             \
  _putchar(_fill)
#define _flushTempBuf()                                                        \
  int _tempLen = _tempOutputPtr;                                               \
  _fillBuf(_width - _tempLen);                                                 \
  _writeOutput();                                                              \
  _fillBuf(-_width - _tempLen)
#define wb(x)                                                                  \
  do {                                                                         \
    if (x)                                                                     \
      _writeTempBuf('1');                                                      \
    else                                                                       \
      _writeTempBuf('0');                                                      \
    _flushTempBuf();                                                           \
  } while (0)
#define wc(x)                                                                  \
  do {                                                                         \
    _writeTempBuf(x);                                                          \
    _flushTempBuf();                                                           \
  } while (0)
#define wi(x)                                                                  \
  do {                                                                         \
    if ((x) < 0) {                                                             \
      _writeTempBuf('-');                                                      \
      _writeNum(-(x), uint, 1);                                                \
    } else {                                                                   \
      _writeNum(x, uint, 1);                                                   \
    }                                                                          \
    _flushTempBuf();                                                           \
  } while (0)
#define wll(x)                                                                 \
  do {                                                                         \
    if ((x) < 0) {                                                             \
      _writeTempBuf('-');                                                      \
      _writeNum(-(x), ull, 1);                                                 \
    } else {                                                                   \
      _writeNum(x, ull, 1);                                                    \
    }                                                                          \
    _flushTempBuf();                                                           \
  } while (0)
#define wd(x)                                                                  \
  do {                                                                         \
    _checkFinite(x) else if ((x) < 0) {                                        \
      _writeTempBuf('-');                                                      \
      _writeFloatingPoint(-(x), double);                                       \
    }                                                                          \
    else {                                                                     \
      _writeFloatingPoint(x, double);                                          \
    }                                                                          \
    _flushTempBuf();                                                           \
  } while (0)
#define wld(x)                                                                 \
  do {                                                                         \
    _checkFinite(x) else if ((x) < 0) {                                        \
      _writeTempBuf('-');                                                      \
      _writeFloatingPoint(-(x), ld);                                           \
    }                                                                          \
    else {                                                                     \
      _writeFloatingPoint(x, ld);                                              \
    }                                                                          \
    _flushTempBuf();                                                           \
  } while (0)
#define wcs(x)                                                                 \
  do {                                                                         \
    int _slen = strlen(x);                                                     \
    _fillBuf(_width - _slen);                                                  \
    for (const char *_p = (x); *_p; _putchar(*_p++))                           \
      ;                                                                        \
    _fillBuf(-_width - _slen);                                                 \
  } while (0)
#define ws(x)                                                                  \
  do {                                                                         \
    _fillBuf(_width - int((x).length()));                                      \
    for (int _i = 0; _i < int((x).length()); _putchar(x[_i++]))                \
      ;                                                                        \
    _fillBuf(-_width - int((x).length()));                                     \
  } while (0)
#define setPrecision(x)                                                        \
  do {                                                                         \
    _precision = (x);                                                          \
    _precisionBase = 1;                                                        \
    for (int _i = 0; _i < (x); _i++, _precisionBase *= 10)                     \
      ;                                                                        \
  } while (0)
#define setDelimiter(x)                                                        \
  do {                                                                         \
    _delimiter = (x);                                                          \
  } while (0)
#define setWidth(x)                                                            \
  do {                                                                         \
    _width = (x);                                                              \
  } while (0)
#define setFill(x)                                                             \
  do {                                                                         \
    _fill = (x);                                                               \
  } while (0)
void writeDelimiter() {
  for (const char *_p = _delimiter; *_p; _putchar(*_p++))
    ;
}
void write(const bool &x) { wb(x); }
void write(const int &x) { wi(x); }
void write(const uint &x) { wi(x); }
void write(const ll &x) { wll(x); }
void write(const ull &x) { wll(x); }
void write(const double &x) { wd(x); }
void write(const ld &x) { wld(x); }
void write(const char &x) { wc(x); }
void write(const char *x) { wcs(x); }
void write(const string &x) { ws(x); }
template <class T1, class T2> void write(const pair<T1, T2> &x) {
  write(x.first);
  writeDelimiter();
  write(x.second);
}
template <class T> void write(const complex<T> &x) {
  write(x.real());
  writeDelimiter();
  write(x.imag());
}
template <class T> void write(const T &x);
template <class T, class... Ts> void write(const T &x, Ts &&...xs);
template <class It>
typename enable_if<is_iterator<It>::value>::type write(It st, It en) {
  bool _first = 1;
  for (It _i = st; _i != en; _i++) {
    if (_first)
      _first = 0;
    else
      writeDelimiter();
    write(*_i);
  }
}
template <class It, class... Ts>
typename enable_if<is_iterator<It>::value>::type write(It st, It en,
                                                       Ts &&...xs) {
  write(st, en);
  writeDelimiter();
  write(forward<Ts>(xs)...);
}
template <class T> void write(const T &x) {
  bool _first = 1;
  for (auto &&_i : x) {
    if (_first)
      _first = 0;
    else
      writeDelimiter();
    write(_i);
  }
}
template <class T, class... Ts> void write(const T &x, Ts &&...xs) {
  write(x);
  writeDelimiter();
  write(forward<Ts>(xs)...);
}
void writeln() { _putchar('\n'); }
template <class... Ts> void writeln(Ts &&...xs) {
  write(forward<Ts>(xs)...);
  _putchar('\n');
}
void flush() { _flush(); }
class IOManager {
public:
  ~IOManager() {
    flush();
    if (_tempInputBuf)
      delete[] (_tempInputBuf);
  }
};
unique_ptr<IOManager> iomanager = make_unique<IOManager>();
void setOutput(FILE *file) {
  flush();
  _output = file;
}
void setOutput(const char *s) {
  flush();
  _output = fopen(s, "w");
}
void setOutput(const string &s) {
  flush();
  _output = fopen(s.c_str(), "w");
}
template <class... Ts> void debug(const Ts &...xs) {
  FILE *_temp = _output;
  setOutput(_error);
  write(xs...);
  setOutput(_temp);
}
template <class... Ts> void debugln(const Ts &...xs) {
  FILE *_temp = _output;
  setOutput(_error);
  writeln(xs...);
  setOutput(_temp);
}
void setError(FILE *file) {
  flush();
  _error = file;
}
void setError(const char *s) {
  flush();
  _error = fopen(s, "w");
}
void setError(const string &s) {
  flush();
  _error = fopen(s.c_str(), "w");
}

const int MAXN = 2e5 + 5;

int N, A[MAXN], ord[MAXN], cnt[MAXN];
umap<int, int> freq;
umap<int, queue<int>> freq2;

int main() {
  // setInput("in.txt");
  // setOutput("out.txt");
  // setError("err.txt");
  read(N);
  read(A, A + N);
  fill(cnt, cnt + N, 0);
  FOR(i, N) freq[A[i]]++;
  FOR(i, N) {
    if (freq[A[i]]-- == 1)
      freq.erase(A[i]);
    FOR(j, 31) {
      int x = 1 << j;
      if (freq.count(x - A[i]))
        cnt[i] += freq[x - A[i]];
    }
    freq[A[i]]++;
  }
  iota(ord, ord + N, 0);
  sort(ord, ord + N,
       [&](const int &i, const int &j) { return cnt[i] < cnt[j]; });
  int ans = 0;
  FOR(i, N) freq2[A[i]] = queue<int>();
  FOR(i, N) {
    int minj = -1, mini = INT_INF;
    FOR(j, 31) {
      int x = 1 << j;
      if (freq2.count(x - A[ord[i]]) && !freq2[x - A[ord[i]]].empty() &&
          freq2[x - A[ord[i]]].front() < mini) {
        mini = freq2[x - A[ord[i]]].front();
        minj = j;
      }
    }
    if (minj == -1)
      freq2[A[ord[i]]].push(i);
    else {
      int x = 1 << minj;
      freq2[x - A[ord[i]]].pop();
      ans++;
    }
  }
  writeln(ans);
  return 0;
}