#include <bits/extc++.h>
using namespace std;
int use_machine(vector<int> x);
int small(int n) {
int b = 0;
for (int i = 1; i + 1 < n; i += 2) b += use_machine({i, 0, i + 1});
if ((n & 1) == 0) b += use_machine({0, n - 1});
return n - b;
}
// sqrt(20000) = 141.xx
vector<int> a[2] = {{0}, {}};
int idx = 1, k = 79;
// rule: https://oj.uz/submission/303279 model code 참고...
map<vector<int>, string> prec1 = {{{}, "A0B0C0DE"}, {{1}, "CED"}, {{2}, "DBE0A"}, {{3}, "CB0E0DA1"},
{{4}, "D0A0E0CB1"}, {{5}, "DBCE1"}, {{6}, "CED"}};
map<vector<int>, string> prec2 = {{{}, "ABCDE0"}, {{1}, "B0"}, {{1, 1}, "EADC"}, {{2}, "CB0D"},
{{2, 1}, "EADB"}, {{2, 2}, "DAE0CB"}, {{3}, "CB0D"}, {{3, 1}, "EDB0"},
{{3, 2}, "AED"}, {{3, 3}, "ED"}, {{4}, "B0"}, {{4, 1}, "0EACD"}};
// map<vector<int>, string> prec1 = {{{}, "A0B0C0D1E"}, {{1}, "0D"}, {{2}, "0A0D0E"}, {{3}, "0A1BC0E0D"},
// {{4}, "0A0E0BC1D"}, {{5}, "0A0BC1E0D"}, {{6}, "0A0D0E"}, {{7}, "0D"}};
// map<vector<int>, string> prec2 = {{{}, "0ABCDE"}, {{1}, "0ABCD"}, {{1, 1}, "AB0C"}, {{2}, "A0BCD"},
// {{2, 1}, "AB0CE"}, {{2, 2}, "ABDC"}, {{2, 3}, "0C"}, {{3}, "A0BCE"},
// {{3, 1}, "0B"}, {{3, 2}, "0BDC"}, {{3, 3}, "0D"}, {{3, 4}, "0D"},
// {{4}, "A0BCD"}, {{4, 2}, "0C"}, {{4, 3}, "0ABCD"}};
int chk(string s, int state) {
string t = s;
int ret = 0;
for (char& c: t) {
if ('A' <= c && c <= 'Z') c = (char) ('0' + ((state) >> (c - 'A') & 1));
}
for (int i = 1; i < t.size(); i++) ret += (t[i - 1] != t[i]);
return ret;
}
int count_mushrooms(int n) {
// if (n <= 450) return small(n);
int ret = 1;
while (idx < n) {
int t = a[0].size() < a[1].size();
if (n - idx < 5 || a[t].size() >= k) {
vector<int> query, &c = a[t];
int qcnt = 0;
// for (auto x: c) cout << x << ' ';
// cout << "gdgdg\n";
for (int i = 0; i < c.size() && idx < n; i++) query.push_back(c[i]), query.push_back(idx++), qcnt++;
// for (auto qq: query) cout << qq << ' ';
// cout << endl;
// cout << query.size() << endl;
int cnt = use_machine(query);
int p = (cnt + 1) / 2;
if (!t) p = qcnt - p;
ret += p;
if (cnt & 1) a[t ^ 1].push_back(idx - 1);
else a[t].push_back(idx - 1);
// cout << p << ' ' << ret << endl;
}
else { // 다 쳐넣음
map<vector<int>, string>& rule = (a[t].size() >= 3 && a[t ^ 1].size() >= 1) ? prec1 : prec2;
vector<int> record, valid(32, 1);
while (rule.count(record)) {
string tmp = rule[record];
// cout << "hi"<< rule[record] << endl;
vector<int> query, cnt(2, 0);
for (char c: tmp) {
if (c == '0' || c == '1') query.push_back(a[(c - '0') ^ t][cnt[(c - '0') ^ t]++]);
else query.push_back(idx + (c - 'A'));
}
// cout << tmp << endl;
// for (auto qq: query) cout << qq << ' ';
// cout << endl;
int q = use_machine(query);
// cout << q << ' ' << "chkquery\n";
record.push_back(q);
for (int state = 0; state < 32; state++) {
if (chk(tmp, state) != q) valid[state] = 0;
}
}
// cout<<"rsz: "<<record.size()<<endl;
// cout<<record[0]<<endl;
for (int state = 0; state < 32; state++) {
if (valid[state]) {
// cout<<"state = "<<state<<endl;
for (int i = 0; i < 5; i++) {
a[(state >> i & 1) ^ t].push_back(idx + i);
ret += (((state >> i & 1) ^ t) == 0);
}
// cout<<"a[0]: ";
// for (int x:a[0]) cout<<x<<' ';
// cout<<endl;
// cout<<"a[1]: ";
// for (int x:a[1]) cout<<x<<' ';
// cout<<endl;
idx += 5;
break;
}
}
}
}
return ret;
}
