This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include <bits/stdc++.h>
#include "trilib.h"
using namespace std;
// ordered set whith s.order_of_key(x) method, which returns rank of element x in set s
/*
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace __gnu_pbds;
typedef tree<int, null_type, less_equal<int>, rb_tree_tag, tree_order_statistics_node_update> ordered_set;
*/
// pair printing
template <class T, class U>
ostream& operator<<(ostream& out, const pair<T, U> &par) {out << "(" << par.first << "; " << par.second << ")"; return out;}
// set printing
template <class T>
ostream& operator<<(ostream& out, const set<T> &cont) { out << "{"; for(const auto &x:cont) out << x << ", "; out << "}"; return out; }
// map printing
template <class T, class U>
ostream& operator<<(ostream& out, const map<T, U> &cont) {out << "{"; for(const auto &x:cont) out << x << ", "; out << "}"; return out; }
// unordered_set printing
template <class T>
ostream& operator<<(ostream& out, const unordered_set<T> &cont) {out << "{";for(const auto &x:cont) out << x << ", ";out << "}";return out;}
// unordered_map printing
template <class T, class U>
ostream& operator<<(ostream& out, const unordered_map<T, U> &cont) {out << "{";for(const auto &x:cont) out << x << ", ";out << "}";return out;}
// vector printing
template<class T>
ostream& operator<<(ostream& out, const vector<T> &cont){ out << "["; for (const auto &x:cont) out << x << ", "; out << "]"; return out;}
#define print(x) cout << (x) << endl;
#define dmp(x) cerr << #x << " = " << x << endl
#define dmpn(x) cerr << #x << " = " << x << "; "
#define dmpl(x) cerr << "Line " << __LINE__ << ": " << #x << " = " << x << endl
using ll = long long;
using ld = long double;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
#define pb push_back
#define ff first
#define ss second
#define all(x) begin(x), end(x)
#define sz(x) (int)x.size()
#define contains(s,x) ((s).find(x) != (s).end())
const int MOD = 998244353;
int N, root = 3;
vector<int> sorted;
random_device dev;
mt19937 rng(dev());
void dac(vector<int> &a) {
if (a.empty()) return;
uniform_int_distribution<int> dist(0, sz(a) - 1);
int split = a[dist(rng)];
vector<int> left, right;
for (int x : a) if (x != split) {
if (is_clockwise(root, split, x)) right.pb(x);
else left.pb(x);
}
dac(left);
sorted.pb(split);
dac(right);
}
void solve() {
N = get_n();
vector<int> a;
for (int i = 1; i <= N; i++) if (i != root) a.pb(i);
sorted.pb(root);
dac(a);
vector<int> hull = { sorted[0], sorted[1] };
for (int i = 2; i < N; i++) {
while (!is_clockwise(hull[sz(hull) - 2], hull.back(), sorted[i])) hull.pop_back();
hull.pb(sorted[i]);
}
while (!is_clockwise(hull[sz(hull) - 2], hull.back(), hull[0])) hull.pop_back();
int j = 0;
while (!is_clockwise(hull.back(), hull[j], hull[j + 1])) j++;
vector<int> updated_hull;
for (int i = j; i < sz(hull); i++) updated_hull.pb(hull[i]);
swap(hull, updated_hull);
int ans = sz(hull);
for (int i = 0; i < sz(hull); i++) {
int prev = hull[(i - 1 + sz(hull)) % sz(hull)];
int nxt = hull[(i + 1) % sz(hull)];
if (!is_clockwise(prev, hull[i], nxt)) ans--;
}
give_answer(sz(hull));
}
int32_t main() {
ios::sync_with_stdio(false);
cin.tie(0);
cout.tie(0);
int t = 1;
// cin >> t;
while (t--) {
solve();
}
}
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