#include <bits/stdc++.h>
#include "mushrooms.h"
using namespace std;
int magic = 50;
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(2 * magic);
iota(order.begin(), order.end(), 1);
int cnt = 2 * magic + 1;
vector<int> zeros, ones;
zeros.push_back(0);
while (zeros.size() < 3 && ones.size() < 3) {
int st = use_machine({0, cnt++});
a[cnt - 1] = a[0] ^ (st & 1);
if (a[cnt - 1] == 0) zeros.push_back(cnt - 1);
else ones.push_back(cnt - 1);
}
int p1, p2, p3, bit;
if (zeros.size() >= 3) {
p1 = zeros[0], p2 = zeros[1], p3 = zeros[2], bit = 0;
} else {
p1 = ones[0], p2 = ones[1], p3 = ones[2], bit = 1;
}
zeros.clear();
ones.clear();
auto calc = [&](vector<int> d) {
vector<int> que = {p1, d[0], p2};
if (d.size() > 1) {
que.push_back(d[1]);
que.push_back(p3);
}
que.push_back(cnt++);
int st = use_machine(que);
a[cnt - 1] = bit ^ (st & 1);
st -= st & 1;
st >>= 1;
if (bit == 1) st = d.size() - st;
return st;
};
function<void(vector<int>)> solve = [&](vector<int> pos) {
if (pos.empty()) return;
if (pos.size() == 1) {
int p = pos[0];
a[p] = calc({p});
return;
}
shuffle(pos.begin(), pos.end(), rng);
vector<int> L, R;
for (int i = 0; i + 1 < (int) pos.size(); i += 2) {
int sum = calc({pos[i], pos[i + 1]});
if (sum == 1) {
L.push_back(pos[i]);
R.push_back(pos[i + 1]);
} else {
a[pos[i]] = a[pos[i + 1]] = sum >> 1;
}
}
if (pos.size() & 1) {
int p = pos.back();
a[p] = calc({p});
}
solve(L);
for (int i = 0; i < (int) L.size(); i++) {
int l = L[i], r = R[i];
assert(a[l] != -1);
a[r] = a[l] ^ 1;
}
};
solve(order);
int ret = 0;
for (int i = 0; i < n; i++) {
ret += a[i] == 0;
if (a[i] == 0) zeros.push_back(i);
if (a[i] == 1) ones.push_back(i);
}
while (cnt < n) {
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;
}
