/* #region Head */ // #define _GLIBCXX_DEBUG #include using namespace std; using ll = long long; using ull = unsigned long long; using ld = long double; using pll = pair; template using vc = vector; template using vvc = vc>; using vll = vc; using vvll = vvc; using vld = vc; using vvld = vvc; using vs = vc; using vvs = vvc; template using um = unordered_map; template using pq = priority_queue; template using pqa = priority_queue, greater>; template using us = unordered_set; #define REP(i, m, n) for (ll i = (m), i##_len = (ll)(n); i < i##_len; ++(i)) #define REPM(i, m, n) for (ll i = (m), i##_max = (ll)(n); i <= i##_max; ++(i)) #define REPR(i, m, n) for (ll i = (m), i##_min = (ll)(n); i >= i##_min; --(i)) #define REPD(i, m, n, d) for (ll i = (m), i##_len = (ll)(n); i < i##_len; i += (d)) #define REPMD(i, m, n, d) for (ll i = (m), i##_max = (ll)(n); i <= i##_max; i += (d)) #define REPI(itr, ds) for (auto itr = ds.begin(); itr != ds.end(); itr++) #define ALL(x) begin(x), end(x) #define SIZE(x) ((ll)(x).size()) #define PERM(c) \ sort(ALL(c)); \ for (bool c##p = 1; c##p; c##p = next_permutation(ALL(c))) #define UNIQ(v) v.erase(unique(ALL(v)), v.end()); #define CEIL(a, b) (((a) + (b)-1) / (b)) #define endl '\n' #define sqrt sqrtl #define floor floorl #define log2 log2l constexpr ll INF = 1'010'000'000'000'000'017LL; constexpr int IINF = 1'000'000'007LL; constexpr ll MOD = 1'000'000'007LL; // 1e9 + 7 // constexpr ll MOD = 998244353; constexpr ld EPS = 1e-12; constexpr ld PI = 3.14159265358979323846; template istream &operator>>(istream &is, vc &vec) { // vector 入力 for (T &x : vec) is >> x; return is; } template ostream &operator<<(ostream &os, vc &vec) { // vector 出力 (for dump) os << "{"; REP(i, 0, SIZE(vec)) os << vec[i] << (i == i_len - 1 ? "" : ", "); os << "}"; return os; } template ostream &operator>>(ostream &os, vc &vec) { // vector 出力 (inline) REP(i, 0, SIZE(vec)) os << vec[i] << (i == i_len - 1 ? "\n" : " "); return os; } template istream &operator>>(istream &is, pair &pair_var) { // pair 入力 is >> pair_var.first >> pair_var.second; return is; } template ostream &operator<<(ostream &os, pair &pair_var) { // pair 出力 os << "(" << pair_var.first << ", " << pair_var.second << ")"; return os; } // map, um, set, us 出力 template ostream &out_iter(ostream &os, T &map_var) { os << "{"; REPI(itr, map_var) { os << *itr; auto itrcp = itr; if (++itrcp != map_var.end()) os << ", "; } return os << "}"; } template ostream &operator<<(ostream &os, map &map_var) { return out_iter(os, map_var); } template ostream &operator<<(ostream &os, um &map_var) { os << "{"; REPI(itr, map_var) { auto [key, value] = *itr; os << "(" << key << ", " << value << ")"; auto itrcp = itr; if (++itrcp != map_var.end()) os << ", "; } os << "}"; return os; } template ostream &operator<<(ostream &os, set &set_var) { return out_iter(os, set_var); } template ostream &operator<<(ostream &os, us &set_var) { return out_iter(os, set_var); } template ostream &operator<<(ostream &os, pq &pq_var) { pq pq_cp(pq_var); os << "{"; if (!pq_cp.empty()) { os << pq_cp.top(), pq_cp.pop(); while (!pq_cp.empty()) os << ", " << pq_cp.top(), pq_cp.pop(); } return os << "}"; } void pprint() { cout << endl; } template void pprint(Head &&head, Tail &&... tail) { cout << head; if (sizeof...(Tail) > 0) cout << ' '; pprint(move(tail)...); } // dump #define DUMPOUT cerr void dump_func() { DUMPOUT << endl; } template void dump_func(Head &&head, Tail &&... tail) { DUMPOUT << head; if (sizeof...(Tail) > 0) DUMPOUT << ", "; dump_func(move(tail)...); } // chmax (更新「される」かもしれない値が前) template > bool chmax(T &xmax, const U &x, Comp comp = {}) { if (comp(xmax, x)) { xmax = x; return true; } return false; } // chmin (更新「される」かもしれない値が前) template > bool chmin(T &xmin, const U &x, Comp comp = {}) { if (comp(x, xmin)) { xmin = x; return true; } return false; } // ローカル用 #define DEBUG_ #ifdef DEBUG_ #define DEB #define dump(...) \ DUMPOUT << " " << string(#__VA_ARGS__) << ": " \ << "[" << to_string(__LINE__) << ":" << __FUNCTION__ << "]" << endl \ << " ", \ dump_func(__VA_ARGS__) #else #define DEB if (false) #define dump(...) #endif #define VAR(type, ...) \ type __VA_ARGS__; \ cin >> __VA_ARGS__; template istream &operator,(istream &is, T &rhs) { return is >> rhs; } template ostream &operator,(ostream &os, const T &rhs) { return os << ' ' << rhs; } struct AtCoderInitialize { static constexpr int IOS_PREC = 15; static constexpr bool AUTOFLUSH = true; AtCoderInitialize() { ios_base::sync_with_stdio(false), cin.tie(nullptr), cout.tie(nullptr); cout << fixed << setprecision(IOS_PREC); if (AUTOFLUSH) cout << unitbuf; } } ATCODER_INITIALIZE; void Yn(bool p) { cout << (p ? "Yes" : "No") << endl; } void YN(bool p) { cout << (p ? "YES" : "NO") << endl; } /* #endregion */ // #include // using namespace atcoder; // Problem void solve() { VAR(ll, n); // vll grundy(n + 1); grundy[0] = 0; REPM(i, 1, n) { set st; // 1 マス塗って i-1 マスにする st.insert(grundy[i - 1]); // 2 マス塗って i-2 マスにする if (i >= 2) st.insert(grundy[i - 2]); // 間を 1 マス塗って x マス + (i-1-x) マス にする (1<=x<=i-2) -> i>=3 if (i >= 3) REPM(x, 1, i - 2) st.insert(grundy[x] ^ grundy[i - 1 - x]); // 間を 2 マス塗って x マス + (i-2-x) マス にする (1<=x<=i-3) -> i>=4 if (i >= 4) REPM(x, 1, i - 3) st.insert(grundy[x] ^ grundy[i - 2 - x]); // mex ll mex = 0; while (st.count(mex)) mex++; grundy[i] = mex; } // dump(grundy); // exit(0); // 勝てる(相手に grundy 数が 0 で手番を渡せる)手が見つかったらそれを選ぶ ll g = grundy[n]; set ranges; ranges.emplace(1, n + 1); // 半開区間 auto search = [&]() -> pll { bool ok = false; int ans_offset = -1, ans_cnt = -1; REPI(itr, ranges) { ll d = itr->second - itr->first; // マス数 // この区間の端 1 マスを塗れば勝てる if ((g ^ grundy[d] ^ grundy[d - 1]) == 0) { ans_offset = itr->first, ans_cnt = 1; if (d == 1) { ranges.erase(itr); } else { pll key = {itr->first + 1, itr->second}; ranges.erase(itr); ranges.emplace(key); } ok = true; break; } // この区間の端 2 マスを塗れば勝てる if (d >= 2 && (g ^ grundy[d] ^ grundy[d - 2]) == 0) { ans_offset = itr->first, ans_cnt = 2; if (d == 2) { ranges.erase(itr); } else { pll key = {itr->first + 2, itr->second}; ranges.erase(itr); ranges.emplace(key); } ok = true; break; } // 区間内の中間 1 マスを塗れば勝てる if (d >= 3) { REPM(x, 1, d - 2) if ((g ^ grundy[d] ^ grundy[x] ^ grundy[d - 1 - x]) == 0) { ans_offset = itr->first + x, ans_cnt = 1; pll key0 = {itr->first, itr->first + x}; pll key1 = {itr->first + x + 1, itr->second}; ranges.erase(itr); ranges.emplace(key0); ranges.emplace(key1); ok = true; break; } if (ok) break; } // 区間内の中間 2 マスを塗れば勝てる if (d >= 4) { REPM(x, 1, d - 3) if ((g ^ grundy[d] ^ grundy[x] ^ grundy[d - 2 - x]) == 0) { ans_offset = itr->first + x, ans_cnt = 2; pll key0 = {itr->first, itr->first + x}; pll key1 = {itr->first + x + 2, itr->second}; ranges.erase(itr); ranges.emplace(key0); ranges.emplace(key1); ok = true; break; } if (ok) break; } } assert(ok); // dump(ans_offset, ans_cnt); // for (auto v : ranges) pprint(v); return {ans_offset, ans_cnt}; }; pll result = search(); pprint(result.second, result.first); for (;;) { VAR(ll, t); if (t == 0 || t == 1) break; VAR(ll, k, x); // k マス分を,位置 x から塗る if (t == 2) break; assert(t == 3); // x から k マス塗る auto it = ranges.lower_bound(pll(x, 0)); if (it == ranges.end()) it--; if (it->first > x) it--; // dump((pll)(*it)); assert(it->first <= x && x + k <= it->second); // 区間セットの更新と grundy 数の更新 ll d = it->second - it->first; g ^= grundy[d]; if (it->first == x) { //最初のマスが消える if (d == k) { // 区間がすべて消える ranges.erase(it); } else { pll key = {it->first + k, it->second}; ranges.erase(it); ranges.emplace(key); g ^= grundy[d - k]; } } else if (x == it->second - k) { // 最後のマスが消える pll key = {it->first, it->second - k}; ranges.erase(it); ranges.emplace(key); g ^= grundy[d - k]; } else { // 区間が2つに分断される pll key0 = {it->first, x}; pll key1 = {x + k, it->second}; // dump(key0, key1); ranges.erase(it); ranges.emplace(key0); ranges.emplace(key1); g ^= grundy[key0.second - key0.first]; g ^= grundy[key1.second - key1.first]; } result = search(); pprint(result.second, result.first); } } // entry point int main() { solve(); return 0; }