#include "majority.h"

#include <cassert>
#include <cmath>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <algorithm>
#include <bitset>
#include <complex>
#include <deque>
#include <functional>
#include <iostream>
#include <limits>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

using namespace std;

namespace {
using Int = long long;

template <class T1, class T2> ostream &operator<<(ostream &os, const pair<T1, T2> &a) { return os << "(" << a.first << ", " << a.second << ")"; };
template <class T> ostream &operator<<(ostream &os, const vector<T> &as) { const int sz = as.size(); os << "["; for (int i = 0; i < sz; ++i) { if (i >= 256) { os << ", ..."; break; } if (i > 0) { os << ", "; } os << as[i]; } return os << "]"; }
template <class T> void pv(T a, T b) { for (T i = a; i != b; ++i) cerr << *i << " "; cerr << endl; }
template <class T> bool chmin(T &t, const T &f) { if (t > f) { t = f; return true; } return false; }
template <class T> bool chmax(T &t, const T &f) { if (t < f) { t = f; return true; } return false; }
#define COLOR(s) ("\x1b[" s "m")

int Q = 0;
vector<D_t> X{D_t(-1)};

// (id, [same as path[i - 2]])
vector<pair<int, int>> path;
// same as path[$ - 1]
set<int> rems;

bool answer() {
  if (path.size() >= 1) {
    int i = (int)path.size() - 1;
    for (; path[i].second; i -= 2) {}
    if (i == 0 || (i == 1 && rems.size())) {
      submit(X[path.back().first]);
      return true;
    }
    return false;
  } else {
    return false;
  }
}
}  // namespace

bool insert(const D_t &x) {
  ++Q;
  X.push_back(x);
  if (path.size() >= 1) {
    if (X[path.back().first] == X[Q]) {
      int i = (int)path.size() - 1;
      for (; path[i].second; i -= 2) {}
      if (i == 0) {
        rems.insert(Q);
      } else {
        path.emplace(path.begin() + (i - 1), Q, (i >= 3 && X[path[i - 3].first] == X[Q]) ? 1 : 0);
        path[i].second = 0;
        path[i + 1].second = 1;
      }
    } else {
      path.emplace_back(Q, (path.size() >= 2 && X[path[path.size() - 2].first] == X[Q]) ? 1 : 0);
      if (rems.size()) {
        path.emplace_back(*rems.begin(), 1);
        rems.erase(rems.begin());
      }
    }
  } else {
    path.emplace_back(Q, 0);
  }
  return answer();
}

bool erase(int id) {
  // TODO
  auto it = rems.find(id);
  if (it != rems.end()) {
    rems.erase(it);
  } else {
    int j;
    for (j = 0; j < (int)path.size(); ++j) if (path[j].first == id) break;
    assert(j < (int)path.size());
    path.erase(path.begin() + j);
    if (j < (int)path.size() && path[j].second) {
      const int t = path[j].first;
      path.erase(path.begin() + j);
      if (j < (int)path.size()) {
        path[j].second = (j - 2 >= 0 && X[path[j - 2].first] == X[path[j].first]) ? 1 : 0;
      }
      int i = j - 1;
      for (; path[i].second; i -= 2) {}
      if (i == 0) {
        i = j - 1;
        for (; i + 2 < (int)path.size() && path[i + 2].second; i += 2) {}
        if (i == (int)path.size() - 1) {
          rems.insert(t);
        } else {
          path.emplace(path.begin() + (i + 2), t, 1);
          if (i + 3 < (int)path.size()) {
            path[i + 3].second = 0;
          }
          if (i + 4 < (int)path.size()) {
            path[i + 4].second = (X[t] == X[path[i + 4].first]) ? 1 : 0;
          }
        }
      } else {
        path.emplace(path.begin() + (i - 1), t, (i >= 3 && X[path[i - 3].first] == X[t]) ? 1 : 0);
        path[i].second = 0;
        path[i + 1].second = 1;
      }
    } else {
      if (j < (int)path.size()) {
        path[j].second = (j - 2 >= 0 && X[path[j - 2].first] == X[path[j].first]) ? 1 : 0;
      }
      if (j + 1 < (int)path.size()) {
        path[j + 1].second = (j - 1 >= 0 && X[path[j - 1].first] == X[path[j + 1].first]) ? 1 : 0;
      }
    }
  }
  return answer();
}