#include "bits/stdc++.h"
#include "prize.h"
//#define int long long
#define all(v) v.begin() , v.end()
#define sz(a) (int)a.size()
using namespace std;
int suf = -1;
vector<int> Cache={-1,-1};
map<int,vector<int>> dp;
vector<int> Ask(int i){
if(dp.count(i)) return dp[i];
return dp[i]=ask(i);
}
int ask_all(int l,int r){
for(int i=l;i<=r;i++){
vector<int> x = Ask(i);
if(x[0] + x[1] == 0) return i;
if(x[1] == suf) Cache=x;
else suf--;
}
return -23;
}
int Learn(int l,int r){
if(l>r) return -1;
if(l==r){
auto u = Ask(l);
if(u[0] + u[1] == 0) return l;
if(u[1] == suf) Cache=u;
else suf--;
return -1;
}
auto X = Ask(r);
if(X[0] + X[1] == 0) return r;
if(X[1] == suf) return -1;
int mid = (l + r) / 2;
auto u = Ask(mid);
if(u[0] + u[1] == 0) return mid;
if(u[1] == suf) return Learn(mid + 1,r - 1);
int lf = Learn(l,mid - 1);
if(lf != -1) return lf;
if(u[1]==suf) Cache=u;
else suf--;
if(X[1] == suf - (Cache[0]+Cache[1] > X[0] + X[1]) ) return -1;
int hm = Learn(mid+1,r-1);
if(hm !=- 1) return hm;
if(X[1] == suf) Cache = X;
else suf--;
return -1;
}
int find_best(int n){
if(n<=1000) return ask_all(0,n-1);
int art=0;
for(int i=0;i<=500;i++){
if(art==5) return Learn(i,n-1);
vector<int> x = Ask(i);
if(x[0]+x[1]==0) return i;
if(x[0]+x[1]>Cache[0]+Cache[1]) art++;
if(x[0]+x[1]>=Cache[0]+Cache[1]){
Cache=x;
suf=Cache[1];
}
else suf--;
}
return Learn(501,n-1);
}
