#include "prize.h"
#include <vector>
#include <utility>
#include <algorithm>
#include <queue>
#include <set>
template <class T>
using Vec = std::vector<T>;
int find_best(int N) {
std::set<int> lower;
Vec<Vec<int>> memo(N);
const auto query = [&](const int i) -> const Vec<int>& {
if (memo[i].empty()) {
memo[i] = ask(i);
}
return memo[i];
};
int L = 0;
while (L < N) {
lower.insert(query(L)[0] + query(L)[1]);
L += 1;
if (lower.size() == 5) {
break;
}
const auto x = *lower.rbegin();
if (x + x * x + 1 > N - L) {
break;
}
}
const auto max = *lower.rbegin();
std::set<int> pos;
for (int i = 0; i < L; ++i) {
if (query(i)[0] + query(i)[1] < max) {
pos.insert(i);
}
}
std::queue<std::pair<int, int>> que;
que.emplace(L, N - 1);
Vec<int> left_count(N + 1, -1);
left_count[N] = max;
left_count[L - 1] = (int) pos.size();
const auto count = [&](const int l, const int r) {
return (left_count[r + 1] == -1 ? query(r + 1)[0] : left_count[r + 1]) - (left_count[l - 1] == -1 ? query(l - 1)[0] : left_count[l - 1]);
};
while (!que.empty() && (int) pos.size() < max) {
const auto [l, r] = que.front();
que.pop();
if (l > r) {
continue;
}
if (count(l, r) == 0) {
continue;
}
const auto mid = (l + r) / 2;
auto nr = mid - 1;
auto nl = mid;
while (nl <= r) {
if (query(nl)[0] + query(nl)[1] == max) {
break;
}
else {
pos.insert(nl);
nl += 1;
}
}
if (nl == r + 1) {
while (nr >= l) {
if (query(nr)[0] + query(nr)[1] == max) {
break;
}
else {
pos.insert(nr);
nr -= 1;
}
}
que.emplace(l, nr - 1);
}
else {
left_count[mid] = query(nl)[0] - (nl - mid);
que.emplace(l, mid - 1);
que.emplace(nl + 1, r);
}
}
for (const auto x: pos) {
if (query(x)[0] + query(x)[1] == 0) {
return x;
}
}
return -1;
}
