#include "prize.h"
#include <bits/stdc++.h>
using namespace std;
#define ll int
#define endl "\n"
#define sz(x) (ll)x.size()
#define F first
#define S second
#define pb push_back
typedef vector <ll> vi;
typedef pair <ll,ll> ii;
typedef vector <ii> vii;
#define dbg(x) cout<<#x<<": "<<x<<endl;
#define dbg2(x,y) cout<<#x<<": "<<x<<" "<<#y<<": "<<y<<endl;
#define dbg3(x,y,z) cout<<#x<<": "<<x<<" "<<#y<<": "<<y<<" "<<#z<<": "<<z<<endl;
void printVct(vi &v){
for (ll i =0; i<sz(v); i++){
cout<<v[i]<<" ";
}
cout<<endl;
}
ll common_val = 0;
ll ans = -1;
void query(ll q, vi &v, ll &s){
v = ask(q);
s = v[0] + v[1];
if (s == 0){
ans = q;
}
}
void bs(ll l, ll r, ll x, ll belowL, ll aboveR){
if (x == 0) return;
if (l > r) return;
if (ans != -1) return;
ll mid = (l+r)/2;
vi v; ll s;
query(mid, v, s);
if (s != common_val){
ll l_mid = mid-1;
ll c = 1;
while (l_mid >= l && s != common_val){
query(l_mid, v, s);
if (s == common_val) break;
l_mid--;
c++;
}
if (l_mid < l){
ll val_r = x - c;
bs(mid+1,r,val_r,c,aboveR);
}
else{
ll val_l = v[0] - belowL;
ll val_r = v[1] - aboveR - c;
bs(l,mid-1,val_l,belowL,v[1]);
bs(mid+1,r,val_r,v[0]+c,aboveR);
}
}
ll val_l = v[0] - belowL;
ll val_r = v[1] - aboveR;
//hit on a common val:
bs(l,mid-1,val_l,belowL,v[1]);
bs(mid+1,r,val_r,v[0],aboveR);
}
int find_best(int n) {
//n < 5000: BF - linear search
if (n <= 5000){
for (ll i =0; i<n; i++){
vi v = ask(i);
ll s = v[0] + v[1];
if (s == 0){
return i;
}
}
}
//step 1: Find common value
for (ll i =0; i<500; i++){
vi v = ask(i);
ll s = v[0] + v[1];
common_val = max(common_val, s);
}
// common_val = 4;
//identify all uncommon one by one
//start from pos = 0, and move like binary lifting
bs(0, n-1, common_val, 0, 0);
return ans;
}
/*
6
1 2 2 2 2 2
*/
