#include <bits/stdc++.h>
#include "mushrooms.h"
using namespace std;
const int magic = 100;
const int bound = 226;
mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count());
// generate random number between l, r : uniform_int_distribution<long long>(l, r)(rng)
// random shuffle : shuffle(.begin(), .end(), rng)
int count_mushrooms(int n) {
if (n <= bound + 1) {
int ret = 1;
for (int i = 1; i < n; i++) {
ret += use_machine({0, i}) ^ 1;
}
return ret;
}
vector<int> a(n, -1);
a[0] = 0;
vector<int> order(magic);
iota(order.begin(), order.end(), 1);
shuffle(order.begin(), order.end(), rng);
int cnt = magic + 1;
vector<int> ONE, ZERO;
ZERO.push_back(0);
for (int i = 0; i < 2; i++) {
a[cnt] = (use_machine({0, cnt}) & 1) ^ a[0];
cnt++;
if (a[cnt - 1] == 0) ZERO.push_back(cnt - 1);
else ONE.push_back(cnt - 1);
}
int p1, p2;
if (ZERO.size() >= 2) {
p1 = ZERO[0];
p2 = ZERO[1];
} else {
p1 = ONE[0];
p2 = ONE[1];
}
auto solve_one = [&](int p) {
int st = use_machine({p1, p, p2, cnt++});
a[cnt - 1] = a[p1] ^ (st & 1);
st -= a[cnt - 1] ^ a[p2];
a[p] = a[p1] ^ (st > 0);
};
int ite = 1;
while (a[ite] == -1) {
solve_one(ite);
ite++;
}
int ret = 0;
vector<int> zeros, ones;
for (int i = 0; i < cnt; i++) {
if (a[i] == 0) zeros.push_back(i);
else ones.push_back(i);
}
ret += zeros.size();
int it = 0;
while (cnt < n) {
it++;
int len = min(n - cnt, (int) max(zeros.size(), ones.size()));
vector<int> ids = zeros.size() >= ones.size() ? zeros : ones;
vector<int> que;
for (int i = 0; i < len; i++) {
que.push_back(ids[i]);
que.push_back(cnt++);
}
int st = use_machine(que);
if (ids == ones) {
a[cnt - 1] = 1 ^ (st & 1);
ret += a[cnt - 1] == 0;
st -= a[cnt - 1] == 0;
if (a[cnt - 1] == 0) zeros.push_back(cnt - 1);
else ones.push_back(cnt - 1);
assert(st % 2 == 0);
ret += st >> 1;
} else {
a[cnt - 1] = 0 ^ (st & 1);
ret += a[cnt - 1] == 0;
st -= a[cnt - 1] == 1;
if (a[cnt - 1] == 0) zeros.push_back(cnt - 1);
else ones.push_back(cnt - 1);
assert(st % 2 == 0);
ret += (len - 1) - (st >> 1);
}
}
return ret;
}
