Problem 10

#pragma gcc optimze("Ofast")
#pragma loop_opt(on)
//#include <ext/pb_ds/assoc_container.hpp>
//#include <ext/pb_ds/tree_policy.hpp>
#include <bits/stdc++.h>
#define debug(x) 1&&(cout<<#x<<':'<<x<<'\n')
#define mkp make_pair
#define pb emplace_back
#define pf emplace_front
#define ff first
#define ss second
#define siz(v) (ll(v.size()))
#define all(v) begin(v),end(v)
#define rall(v) rbegin(v),rend(v)
#define REP(i,l,r) for(int i=(l);i<(r);i++)
#define mid (l+(r-l>>1))

using namespace std;
//using namespace __gnu_pbds;
typedef long long ll;
typedef long double ld;
typedef pair<ll,ll> pll;
//typedef tree<ll,null_type,less<ll>,rb_tree_tag,tree_order_statistics_node_update> rank_tree;
//const long double PI = acos(-1),eps = 1e-8;
constexpr ll N = 100000, INF = 1e18, MOD = 1000000007;

ll n,p=0,x,y;
map<ll,ll> mp;
pll stk[N+1] = {};
ll cross(pll u,pll v){return u.ff*v.ss-u.ss*v.ff;}
ll isConv(pll a,pll b,pll c){return cross(pll(b.ff-a.ff,b.ss-a.ss),pll(c.ff-b.ff,c.ss-b.ss))<0;}
signed main(){
    cin >> n;
    REP(i,0,n){
        cin >> x >> y, y-=x*x;
        if(mp.count(x))mp[x] = max(mp[x],y);
        else mp[x] = y;
    }
    for(auto dot:mp){
        while(p>1 && !isConv(stk[p-2],stk[p-1],dot))--p;
        stk[p++] = dot;
    }
    cout << p-1;
}