/*************************************
* author: marvinthang *
* created: 25.08.2022 20:38:19 *
*************************************/
#include <bits/stdc++.h>
using namespace std;
#define fi first
#define se second
#define div ___div
#define left ___left
#define right ___right
#define TIME (1.0 * clock() / CLOCKS_PER_SEC)
#define MASK(i) (1LL << (i))
#define FULL(i) (MASK(i) - 1)
#define BIT(x, i) ((x) >> (i) & 1)
#define __builtin_popcount __builtin_popcountll
#define scan_op(...) istream & operator >> (istream &in, __VA_ARGS__ &u)
#define print_op(...) ostream & operator << (ostream &out, const __VA_ARGS__ &u)
#define file(name) if (fopen (name".inp", "r")) { freopen (name".inp", "r", stdin); freopen (name".out", "w", stdout); }
template <class T> scan_op(vector <T>) { for (size_t i = 0; i < u.size(); ++i) in >> u[i]; return in; }
template <class T> print_op(vector <T>) { out << '{'; for (size_t i = 0; i + 1 < u.size(); ++i) out << u[i] << ", "; if (!u.empty()) out << u.back(); return out << '}'; }
template <class U, class V> scan_op(pair <U, V>) { return in >> u.fi >> u.se; }
template <class U, class V> print_op(pair <U, V>) { return out << '(' << u.fi << ", " << u.se << ')'; }
const double PI = 3.1415926535897932384626433832795; // acos(-1.0); atan(-1.0);
const int dir[] = {1, 0, -1, 0, 1, 1, -1, -1, 1}; // {2, 1, -2, -1, -2, 1, 2, -1, 2};
const int NUM_BIT = 8;
const int NUM_STATE = 22;
const int p3[] = {1, 3, 9, 27, 81, 243, 729, 2187, 6561};
int get_bit(int n, int bit) { if (bit < 0) return 0; return (n % p3[bit + 1]) / p3[bit]; }
pair <int, int> decode(int code) {
--code;
if (code < 0) return make_pair(0, 0);
return make_pair(NUM_BIT - code / 3 - 1, code % 3);
}
int encode(int bit, int t) {
if (bit < 0) return 0;
return (NUM_BIT - bit - 1) * 3 + t + 1;
}
vector <vector <int>> devise_strategy(int n) {
vector <vector <int>> res(NUM_STATE, vector<int> (n + 1, 0));
// case 0
res[0][0] = 0;
for (int i = 1; i <= n; ++i)
res[0][i] = encode(NUM_BIT - 1, get_bit(i, NUM_BIT - 1));
// case 1 -> 18
for (int bit = 1; bit < NUM_BIT; ++bit) for (int t = 0; t < 3; ++t) {
int state = encode(bit, t);
int cur = bit & 1;
int pre = cur ^ 1;
res[state][0] = cur;
for (int i = 1; i <= n; ++i) {
int pre_bit = t;
int cur_bit = get_bit(i, bit);
if (pre_bit < cur_bit) res[state][i] = -1 - pre;
else if (pre_bit > cur_bit) res[state][i] = -1 - cur;
else {
if (bit > 2) res[state][i] = encode(bit - 1, get_bit(i, bit - 1));
else {
int r = i % 9;
if (r == 0) res[state][i] = -1 - cur;
else if (r == 8) res[state][i] = -1 - pre;
else if (r <= 4) res[state][i] = 19;
else res[state][i] = 20;
}
}
}
}
// case 19, 20
for (int state: {19, 20}) {
int cur = 1, pre = 0;
res[state][0] = cur;
for (int i = 1; i <= n; ++i) {
int r = i % 9;
if (state == 19) {
if (r <= 1) res[state][i] = -1 - cur;
else if (r >= 4) res[state][i] = -1 - pre;
else res[state][i] = 21;
} else {
if (r <= 5) res[state][i] = -1 - cur;
else if (r >= 7) res[state][i] = -1 - pre;
else res[state][i] = 21;
}
}
}
// case 21
int cur = 0, pre = 1;
res[21][0] = cur;
for (int i = 1; i <= n; ++i) {
int r = i % 9;
if (r <= 4) {
if (r <= 2) res[21][i] = -1 - cur;
else res[21][i] = -1 - pre;
} else {
if (r <= 6) res[21][i] = -1 - cur;
else res[21][i] = -1 - pre;
}
}
return res;
}
// vector <vector <int>> res;
// int n, a, b;
// void Try(int state) {
// if (state < 0) return void(cout << state << '\n');
// cout << decode(state) << '\n';
// Try(res[state][res[state][0] ? b : a]);
// }
// int main(void) {
// ios_base::sync_with_stdio(false); cin.tie(nullptr); // cout.tie(nullptr);
// file("ioi22_day1_prison");
// // cin >> n >> a >> b;
// // for (int i = NUM_BIT; i--; ) cout << get_bit(a, i);
// // cout << '\n';
// // for (int i = NUM_BIT; i--; ) cout << get_bit(b, i);
// // cout << '\n';
// // // // cout << bitset<13>(a) << '\n' << bitset<13>(b) << '\n';
// // res = devise_strategy(n);
// // // // for (int i = 0; i < NUM_STATE; ++i) {
// // // // cout << decode(i) << ": ";
// // // // cout << res[i][0] << ' ';
// // // // for (int j = 1; j <= n; ++j)
// // // // if (res[i][j] >= 0) cout << decode(res[i][j]) << ' '; else cout << res[i][j] << ' ';
// // // // cout << '\n';
// // // // }
// // Try(0);
// cerr << "Time elapsed: " << TIME << " s.\n";
// return (0^0);
// }
