#include <bits/stdc++.h>
#include "prize.h"
#define pii pair<int, int>
#define F first
#define S second
using namespace std;
unordered_map<int, pii> mp;
pii query(int p) {
if(mp.find(p) != mp.end()) return mp[p];
vector<int> v = ask(p);
return mp[p] = {v[0], v[1]};
}
vector<pii> ans;
void dfs(int l, int r, pii a, pii b, int mx) {
if(l == r) return ans.push_back({b.F + b.S, l});
if(a == b) return;
int m = l + r >> 1;
pii v = query(m);
if(v.F + v.S != mx) {
ans.push_back({v.F + v.S, m});
if(m != l) dfs(l, m - 1, a, query(m - 1), mx);
if(m != r) dfs(m + 1, r, query(m + 1), b, mx);
}
else {
if(v == a) return dfs(m + 1, r, v, b, mx);
if(v == b) return dfs( l, m, a, v, mx);
dfs( l, m, a, v, mx);
dfs(m + 1, r, v, b, mx);
}
}
int find_best(int n) {
srand(time(0));
int mx = query(0).F + query(0).S;
if(mx == 0) return 0;
dfs(0, n - 1, query(0), query(n - 1), mx);
for(auto it: ans) if(it.F == 0) return it.S;
}
