Problem p02973 (C++)

Buggy submission (status: Time Limit Exceeded):
#include "bits/stdc++.h"

using namespace std;

typedef vector<int> VI;
typedef vector<VI> VVI;
typedef vector<string> VS;
typedef pair<int, int> PII;
typedef vector<PII> VPII;
typedef long long LL;
typedef vector<LL> VL;
typedef vector<VL> VVL;
typedef pair<LL, LL> PLL;
typedef vector<PLL> VPLL;
typedef priority_queue<int> PQ_DESC;
typedef priority_queue<int, vector<int>, greater<int>> PQ_ASC;
typedef priority_queue<PII> PQ_DESC_PII;
typedef priority_queue<PII, vector<PII>, greater<PII>> PQ_ASC_PII;
typedef priority_queue<VL> PQ_DESC_VL;
typedef priority_queue<VL, vector<VL>, greater<VL>> PQ_ASC_VL;
typedef priority_queue<PLL> PQ_DESC_PLL;
typedef priority_queue<PLL, vector<PLL>, greater<PLL>> PQ_ASC_PLL;

#define ALL(c) (c).begin(), (c).end()
#define PB push_back
#define MP make_pair
#define SORT_ASC(c) sort(ALL(c))
// #define SORT_DESC(c) sort(ALL(c), greater<typeof(*((c).begin()))>())
#define SORT_DESC(c) sort((c).rbegin(), (c).rend())
#define REV(c) reverse((c).begin(), (c).end())
#define SIZE(a) int((a).size())

#define FOR(i, a, b) for (int i = (a); i < (b); ++i)
#define ROF(i, a, b) for (int i = (b - 1); i >= (a); --i)
#define REP(i, n) FOR(i, 0, n)
#define PER(i, n) ROF(i, 0, n)

const double EPS = 1e-10;
const double PI = acos(-1.0);
const int LARGE_INT = 1e9 + 100;
const int INF = 2e9 + 100;
const LL INF_LL = (LL)INF * (LL)INF;
const int MOD = 1e9 + 7;

// debug
#define dump(x) cerr << #x << " = " << (x) << endl;
#define debug(x)                                                               \
  cerr << #x << " = " << (x) << " (L" << __LINE__ << ")"                       \
       << " " << __FILE__ << endl;

void Main() {
  int n;
  cin >> n;

  multiset<LL> s;

  REP(i, n) {
    LL a;
    cin >> a;
    auto itr = lower_bound(ALL(s), a);
    if (itr == s.begin()) {
      s.insert(a);
    } else {
      s.erase(--itr);
      s.insert(a);
    }
  }

  cout << s.size() << endl;

  return;
}

int main() {
  cin.tie(nullptr);
  ios_base::sync_with_stdio(false);
  cout << fixed << setprecision(15);
  Main();
  return 0;
}

Fixed submission:
#include "bits/stdc++.h"

using namespace std;

typedef vector<int> VI;
typedef vector<VI> VVI;
typedef vector<string> VS;
typedef pair<int, int> PII;
typedef vector<PII> VPII;
typedef long long LL;
typedef vector<LL> VL;
typedef vector<VL> VVL;
typedef pair<LL, LL> PLL;
typedef vector<PLL> VPLL;
typedef priority_queue<int> PQ_DESC;
typedef priority_queue<int, vector<int>, greater<int>> PQ_ASC;
typedef priority_queue<PII> PQ_DESC_PII;
typedef priority_queue<PII, vector<PII>, greater<PII>> PQ_ASC_PII;
typedef priority_queue<VL> PQ_DESC_VL;
typedef priority_queue<VL, vector<VL>, greater<VL>> PQ_ASC_VL;
typedef priority_queue<PLL> PQ_DESC_PLL;
typedef priority_queue<PLL, vector<PLL>, greater<PLL>> PQ_ASC_PLL;

#define ALL(c) (c).begin(), (c).end()
#define PB push_back
#define MP make_pair
#define SORT_ASC(c) sort(ALL(c))
// #define SORT_DESC(c) sort(ALL(c), greater<typeof(*((c).begin()))>())
#define SORT_DESC(c) sort((c).rbegin(), (c).rend())
#define REV(c) reverse((c).begin(), (c).end())
#define SIZE(a) int((a).size())

#define FOR(i, a, b) for (int i = (a); i < (b); ++i)
#define ROF(i, a, b) for (int i = (b - 1); i >= (a); --i)
#define REP(i, n) FOR(i, 0, n)
#define PER(i, n) ROF(i, 0, n)

const double EPS = 1e-10;
const double PI = acos(-1.0);
const int LARGE_INT = 1e9 + 100;
const int INF = 2e9 + 100;
const LL INF_LL = (LL)INF * (LL)INF;
const int MOD = 1e9 + 7;

// debug
#define dump(x) cerr << #x << " = " << (x) << endl;
#define debug(x)                                                               \
  cerr << #x << " = " << (x) << " (L" << __LINE__ << ")"                       \
       << " " << __FILE__ << endl;

void Main() {
  int n;
  cin >> n;

  multiset<LL> s;

  REP(i, n) {
    LL a;
    cin >> a;
    auto itr = s.lower_bound(a);
    if (itr == s.begin()) {
      s.insert(a);
    } else {
      s.erase(--itr);
      s.insert(a);
    }
  }

  cout << s.size() << endl;

  return;
}

int main() {
  cin.tie(nullptr);
  ios_base::sync_with_stdio(false);
  cout << fixed << setprecision(15);
  Main();
  return 0;
}