#include "mushrooms.h"
#include <bits/stdc++.h>
using namespace std;
using pii = pair<int, int>;
template<typename T>
using Prior = priority_queue<T>;
template<typename T>
using prior = priority_queue<T, vector<T>, greater<T>>;
#define X first
#define Y second
#define ALL(x) (x).begin(), (x).end()
#define eb emplace_back
#define pb push_back
int count_mushrooms(int n) {
const int B = (int)floor(sqrt(2 * n + 0.5));
vector<int> m{0};
// cout << "Block size = " << B << "\n";
for (int i = 1; i <= min(n-1, B); ++i) {
m.eb(m.back() ^ use_machine({i-1, i}));
}
vector<int> tA, tB;
for (int i = 0; i <= min(n-1, B); ++i) {
if (m[i] == 0) tA.eb(i);
if (m[i] == 1) tB.eb(i);
}
// cout << "tA : "; for (auto x : tA) cout << x << " "; cout << "\n";
// cout << "tB : "; for (auto x : tB) cout << x << " "; cout << "\n";
int ans = tA.size();
if (tA.size() >= tB.size()) {
/// 0 x 0 x 0 x 0 ... 0 x 0 x ///
int sz = tA.size(), tok = B + 1;
while (tok < n) {
vector<int> tmp;
for (int i = 0; i < sz and tok < n; ++i) {
tmp.eb(tA[i]), tmp.eb(tok++);
}
ans += tmp.size() / 2 - (use_machine(tmp) + 1) / 2;
}
}
else if (tB.size() > tA.size()) {
/// 1 x 1 x 1 x 1 ... 1 x 1 x ///
int sz = tB.size(), tok = B + 1;
while (tok < n) {
vector<int> tmp;
for (int i = 0; i < sz and tok < n; ++i) {
tmp.eb(tB[i]), tmp.eb(tok++);
}
ans += (use_machine(tmp) + 1) / 2;
}
}
return ans;
}
