#include <bits/stdc++.h>
#include "mushrooms.h"
using namespace std;
const int magic = 84;
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;
int iter = 5;
map<int, vector<int>> best_choice;
while (iter--) {
order.insert(order.begin(), 0);
order.push_back(cnt++);
int st = use_machine(order);
a[cnt - 1] = a[0] ^ (st & 1);
best_choice[st] = order;
int sz = order.size() / (st + 1);
vector<int> Lorder, Rorder;
for (int i = 1; i < (int) order.size() - 1; i++) {
int md = i % (2 * sz);
if (md >= sz) Rorder.push_back(order[i]);
else Lorder.push_back(order[i]);
}
shuffle(Lorder.begin(), Lorder.end(), rng);
shuffle(Rorder.begin(), Rorder.end(), rng);
order = Lorder;
order.insert(order.end(), Rorder.begin(), Rorder.end());
}
int st = best_choice.begin()->first;
order = best_choice.begin()->second;
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);
}
function<void(int, int, int, vector<int>)> dfs = [&](int vL, int vR, int tot, vector<int> p) {
assert(vL != -1 && vR != -1 && vL == a[p[0]] && vR == a[p.back()]);
assert(0 <= tot && tot <= (int) p.size() - 1);
if (p.size() <= 2) return;
if (tot == 0) {
for (int i = 1; i < (int) p.size() - 1; i++) a[p[i]] = a[p[i - 1]];
return;
}
if (tot == (int) p.size() - 1) {
for (int i = 1; i < (int) p.size() - 1; i++) a[p[i]] = a[p[i - 1]] ^ 1;
return;
}
int sz = p.size();
int mid = (sz + 1) / 2;
assert(mid > 1);
if (mid > 2) {
vector<int> que(p.begin(), p.begin() + mid);
que.push_back(cnt++);
int st = use_machine(que);
a[cnt - 1] = vL ^ (st & 1);
dfs(vL, a[cnt - 1], st, que);
for (int i = 1; i < mid; i++) {
int u = que[i], v = que[i - 1];
tot -= a[u] ^ a[v];
}
} else {
vector<int> pii = ONE.size() >= 2 ? ONE : ZERO;
int st = use_machine({pii[0], p[mid - 1], pii[1], cnt++});
a[cnt - 1] = a[pii[0]] ^ (st & 1);
st -= a[pii[1]] ^ a[cnt - 1];
if (st > 0) a[p[mid - 1]] = a[pii[0]] ^ 1;
else a[p[mid - 1]] = a[pii[0]];
tot -= a[p[mid - 1]] ^ a[p[0]];
}
vector<int> que = vector<int>(p.begin() + mid - 1, p.end());
dfs(a[p[mid - 1]], vR, tot, que);
};
dfs(a[0], a[order.back()], st, order);
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();
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;
}
