#include "prize.h"
#include <bits/stdc++.h>
#define P pair<int,int>
using namespace std;
const int maxn = 200100;
bool visited[maxn];
int q[maxn][2];
int max_sum, ind;
P query(int i) {
if(visited[i]) return {q[i][0], q[i][1]};
visited[i] = true;
vector<int>curr = ask(i);
q[i][0] = curr[0];
q[i][1] = curr[1];
return {q[i][0], q[i][1]};
}
int sum(int i) {
query(i);
return q[i][0] + q[i][1];
}
void solve(int l, int r) {
//cout<<l<<" "<<r<<"\n";
if(l > r || ind != -1) return;
P ql = query(l);
P qr = query(r);
int suml = ql.first + ql.second;
int sumr = qr.first + qr.second;
if(suml == 0) {
ind = l;
return;
}
if(sumr == 0) {
ind = r;
return;
}
if(ql.second == 0 || qr.first == 0) return;
if(l == r) return;
if(suml != max_sum) {
solve(l+1, r);
return;
}
if(sumr != max_sum) {
solve(l, r-1);
return;
}
int between = qr.first - ql.first;
if(between == 0) return;
int mid = (l + r) / 2;
solve(l, mid);
solve(mid+1, r);
}
int find_best(int n) {
ind = -1;
int b = sqrt(n) + 1;
b = min(n, b);
mt19937 g(chrono::high_resolution_clock::now().time_since_epoch().count());
uniform_int_distribution<int> uid(0, n - 1);
for(int i=0;i-b<n;i+=b) {
int x = min(i, n-1);
if(sum(x) == 0) return x;
max_sum = max(max_sum, sum(x));
} //max_sum = 1;
for(int i=0;i<100;i++) {
int pos = uid(g);
if(sum(pos) == 0) return pos;
max_sum = max(max_sum, sum(pos));
}
int l = 0, r = b;
while(l < n) {
solve(l, r);
l += b; r += b;
if(r >= n) r = n - 1;
}
return ind;
}
