#718782 (C++17) No.1776 Love Triangle 2 (Hard)

• 問題: No.1776 Love Triangle 2 (Hard)
• ユーザー: hitonanode
• 提出日時: 2021-11-21 10:03:21
• 言語: C++17 (gcc 12.3.0 + boost 1.83.0)
• 結果: WA (最新)
  AC
  (最初)
• 実行時間: -
• コード長: 17,015 bytes
• コンパイル時間: 2,889 ms
• コンパイル使用メモリ: 184,224 KB
• 実行使用メモリ: 11,472 KB
• 最終ジャッジ日時: 2024-07-02 12:15:44
• 合計ジャッジ時間: 118,397 ms
• ジャッジサーバーID （参考情報）: judge5 / judge4

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	5 ms; 11,472 KB
testcase_01	AC	4 ms; 5,376 KB
testcase_02	AC	7 ms; 5,376 KB
testcase_03	AC	5 ms; 5,376 KB
testcase_04	AC	447 ms; 5,376 KB
testcase_05	AC	435 ms; 5,376 KB
testcase_06	AC	451 ms; 5,376 KB
testcase_07	AC	356 ms; 5,376 KB
testcase_08	AC	576 ms; 5,376 KB
testcase_09	AC	53 ms; 5,376 KB
testcase_10	AC	58 ms; 5,376 KB
testcase_11	AC	95 ms; 5,376 KB
testcase_12	AC	78 ms; 5,376 KB
testcase_13	AC	110 ms; 5,376 KB
testcase_14	AC	276 ms; 5,376 KB
testcase_15	AC	577 ms; 5,376 KB
testcase_16	AC	677 ms; 5,376 KB
testcase_17	AC	1,812 ms; 5,376 KB
testcase_18	AC	3,637 ms; 5,376 KB
testcase_19	AC	81 ms; 5,376 KB
testcase_20	AC	92 ms; 5,376 KB
testcase_21	AC	88 ms; 5,376 KB
testcase_22	AC	129 ms; 5,376 KB
testcase_23	AC	119 ms; 5,376 KB
testcase_24	AC	89 ms; 5,376 KB
testcase_25	AC	130 ms; 5,376 KB
testcase_26	AC	125 ms; 5,376 KB
testcase_27	AC	95 ms; 5,376 KB
testcase_28	AC	225 ms; 5,376 KB
testcase_29	AC	3,901 ms; 5,376 KB
testcase_30	AC	3,640 ms; 5,376 KB
testcase_31	AC	1,586 ms; 5,376 KB
testcase_32	AC	3,494 ms; 5,376 KB
testcase_33	AC	3,314 ms; 5,376 KB
testcase_34	AC	1,721 ms; 5,376 KB
testcase_35	AC	1,287 ms; 5,376 KB
testcase_36	AC	629 ms; 5,376 KB
testcase_37	AC	232 ms; 5,376 KB
testcase_38	AC	112 ms; 5,376 KB
testcase_39	AC	7,944 ms; 5,376 KB
testcase_40	AC	3,970 ms; 5,376 KB
testcase_41	AC	1,651 ms; 5,376 KB
testcase_42	AC	2,719 ms; 5,376 KB
testcase_43	AC	1,554 ms; 5,376 KB
testcase_44	AC	1,247 ms; 5,376 KB
testcase_45	WA	-
testcase_46	AC	984 ms; 5,376 KB
testcase_47	AC	150 ms; 5,376 KB
testcase_48	AC	56 ms; 5,376 KB
testcase_49	AC	3,090 ms; 5,376 KB
testcase_50	AC	3,107 ms; 5,376 KB
testcase_51	AC	636 ms; 5,376 KB
testcase_52	AC	1,975 ms; 5,376 KB
testcase_53	AC	959 ms; 5,376 KB
testcase_54	AC	405 ms; 5,376 KB
testcase_55	AC	720 ms; 5,376 KB
testcase_56	AC	305 ms; 5,376 KB
testcase_57	AC	94 ms; 5,376 KB
testcase_58	AC	43 ms; 5,376 KB
testcase_59	AC	4,507 ms; 5,376 KB
testcase_60	AC	3,029 ms; 5,376 KB
testcase_61	AC	1,149 ms; 5,376 KB
testcase_62	AC	2,965 ms; 5,376 KB
testcase_63	AC	993 ms; 5,376 KB
testcase_64	AC	1,015 ms; 5,376 KB
testcase_65	AC	552 ms; 5,376 KB
testcase_66	AC	164 ms; 5,376 KB
testcase_67	AC	84 ms; 5,376 KB
testcase_68	AC	61 ms; 5,376 KB
testcase_69	AC	1,308 ms; 6,112 KB
testcase_70	AC	1,321 ms; 6,148 KB
testcase_71	AC	1,348 ms; 5,984 KB
testcase_72	AC	369 ms; 5,376 KB
testcase_73	AC	1,326 ms; 6,228 KB
testcase_74	AC	121 ms; 5,376 KB
testcase_75	AC	108 ms; 5,376 KB
testcase_76	AC	147 ms; 5,376 KB
testcase_77	AC	171 ms; 5,376 KB
testcase_78	AC	368 ms; 5,376 KB
testcase_79	AC	603 ms; 5,376 KB
testcase_80	AC	791 ms; 5,376 KB
testcase_81	AC	2,381 ms; 5,376 KB
testcase_82	AC	3,089 ms; 5,376 KB
testcase_83	AC	7,402 ms; 5,936 KB
testcase_84	AC	117 ms; 5,376 KB
testcase_85	AC	152 ms; 5,376 KB
testcase_86	AC	135 ms; 5,376 KB
testcase_87	AC	165 ms; 5,376 KB
testcase_88	AC	559 ms; 5,376 KB
testcase_89	AC	165 ms; 5,376 KB
testcase_90	AC	294 ms; 5,376 KB
testcase_91	AC	376 ms; 5,376 KB
testcase_92	AC	174 ms; 5,376 KB
testcase_93	AC	500 ms; 5,376 KB
testcase_94	TLE	-
testcase_95	--	-
testcase_96	--	-
testcase_97	--	-
testcase_98	--	-
testcase_99	--	-
testcase_100	--	-
testcase_101	--	-
testcase_102	--	-
testcase_103	--	-
testcase_104	--	-
testcase_105	--	-
testcase_106	--	-
testcase_107	--	-
testcase_108	--	-
testcase_109	--	-
testcase_110	--	-
testcase_111	--	-
testcase_112	--	-
testcase_113	--	-
testcase_114	--	-
testcase_115	--	-
testcase_116	--	-
testcase_117	--	-
testcase_118	--	-
testcase_119	--	-
testcase_120	--	-
testcase_121	--	-
testcase_122	--	-
testcase_123	--	-
testcase_124	--	-
testcase_125	--	-
testcase_126	--	-
testcase_127	--	-
testcase_128	--	-
testcase_129	--	-
testcase_130	--	-
testcase_131	--	-
testcase_132	--	-
testcase_133	--	-
testcase_134	--	-
testcase_135	--	-
testcase_136	--	-
testcase_137	--	-
testcase_138	--	-
testcase_139	--	-
testcase_140	--	-
testcase_141	--	-
testcase_142	--	-
testcase_143	--	-
testcase_144	--	-
testcase_145	--	-
testcase_146	--	-
testcase_147	--	-
testcase_148	--	-
testcase_149	--	-
testcase_150	--	-
testcase_151	--	-
testcase_152	--	-
testcase_153	--	-
testcase_154	--	-
testcase_155	--	-
testcase_156	--	-
testcase_157	--	-
testcase_158	--	-
testcase_159	--	-
testcase_160	--	-
testcase_161	--	-
testcase_162	--	-
testcase_163	--	-
testcase_164	--	-
testcase_165	--	-
testcase_166	--	-
testcase_167	--	-
testcase_168	--	-
testcase_169	--	-
testcase_170	--	-
testcase_171	--	-
testcase_172	--	-
testcase_173	--	-
testcase_174	--	-
testcase_175	--	-

ソースコード

// 嘘ヒューリスティック
// x-y, y-z, z-x のうち一つを固定して残り二つの長さの和を MCF で最小化するのを反復する山登り
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <chrono>
#include <cmath>
#include <complex>
#include <deque>
#include <forward_list>
#include <fstream>
#include <functional>
#include <iomanip>
#include <ios>
#include <iostream>
#include <limits>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <tuple>
#include <type_traits>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
using namespace std;
using lint = long long;
using pint = pair<int, int>;
using plint = pair<lint, lint>;
struct fast_ios { fast_ios(){ cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(20); }; } fast_ios_;
#define ALL(x) (x).begin(), (x).end()
#define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i<i##_end_;i++)
#define IFOR(i, begin, end) for(int i=(end)-1,i##_begin_=(begin);i>=i##_begin_;i--)
#define REP(i, n) FOR(i,0,n)
#define IREP(i, n) IFOR(i,0,n)
template <typename T, typename V>
void ndarray(vector<T>& vec, const V& val, int len) { vec.assign(len, val); }
template <typename T, typename V, typename... Args> void ndarray(vector<T>& vec, const V& val, int len, Args... args) { vec.resize(len), for_each(begin(vec), end(vec), [&](T& v) { ndarray(v, val, args...); }); }
template <typename T> bool chmax(T &m, const T q) { return m < q ? (m = q, true) : false; }
template <typename T> bool chmin(T &m, const T q) { return m > q ? (m = q, true) : false; }
int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); }
template <typename T1, typename T2> pair<T1, T2> operator+(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first + r.first, l.second + r.second); }
template <typename T1, typename T2> pair<T1, T2> operator-(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first - r.first, l.second - r.second); }
template <typename T> vector<T> sort_unique(vector<T> vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; }
template <typename T> int arglb(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::lower_bound(v.begin(), v.end(), x)); }
template <typename T> int argub(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::upper_bound(v.begin(), v.end(), x)); }
template <typename T> istream &operator>>(istream &is, vector<T> &vec) { for (auto &v : vec) is >> v; return is; }
template <typename T> ostream &operator<<(ostream &os, const vector<T> &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <typename T, size_t sz> ostream &operator<<(ostream &os, const array<T, sz> &arr) { os << '['; for (auto v : arr) os << v << ','; os << ']'; return os; }
#if __cplusplus >= 201703L
template <typename... T> istream &operator>>(istream &is, tuple<T...> &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; }
template <typename... T> ostream &operator<<(ostream &os, const tuple<T...> &tpl) { os << '('; std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os << ')'; }
#endif
template <typename T> ostream &operator<<(ostream &os, const deque<T> &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <typename T> ostream &operator<<(ostream &os, const set<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T, typename TH> ostream &operator<<(ostream &os, const unordered_set<T, TH> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T> ostream &operator<<(ostream &os, const multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T> ostream &operator<<(ostream &os, const unordered_multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T1, typename T2> ostream &operator<<(ostream &os, const pair<T1, T2> &pa) { os << '(' << pa.first << ',' << pa.second << ')'; return os; }
template <typename TK, typename TV> ostream &operator<<(ostream &os, const map<TK, TV> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
template <typename TK, typename TV, typename TH> ostream &operator<<(ostream &os, const unordered_map<TK, TV, TH> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
#ifdef HITONANODE_LOCAL
const string COLOR_RESET = "\033[0m", BRIGHT_GREEN = "\033[1;32m", BRIGHT_RED = "\033[1;31m", BRIGHT_CYAN = "\033[1;36m", NORMAL_CROSSED = "\033[0;9;37m", RED_BACKGROUND = "\033[1;41m", NORMAL_FAINT = "\033[0;2m";
#define dbg(x) cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << endl
#define dbgif(cond, x) ((cond) ? cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << endl : cerr)
#else
#define dbg(x) (x)
#define dbgif(cond, x) 0
#endif

template <typename T, T INF = std::numeric_limits<T>::max() / 2, int INVALID = -1> struct ShortestPath {
    int V, E;
    bool single_positive_weight;
    T wmin, wmax;
    std::vector<std::vector<std::pair<int, T>>> to;

    ShortestPath(int V = 0) : V(V), E(0), single_positive_weight(true), wmin(0), wmax(0), to(V) {}
    void add_edge(int s, int t, T w) {
        assert(0 <= s and s < V);
        assert(0 <= t and t < V);
        to[s].emplace_back(t, w);
        E++;
        if (w > 0 and wmax > 0 and wmax != w) single_positive_weight = false;
        wmin = std::min(wmin, w);
        wmax = std::max(wmax, w);
    }

    std::vector<T> dist;
    std::vector<int> prev;

    void ZeroOneBFS(int s) {
        assert(0 <= s and s < V);
        dist.assign(V, INF), prev.assign(V, INVALID);
        dist[s] = 0;
        std::deque<int> que;
        que.push_back(s);
        while (!que.empty()) {
            int v = que.front();
            que.pop_front();
            for (auto nx : to[v]) {
                T dnx = dist[v] + nx.second;
                if (dist[nx.first] > dnx) {
                    dist[nx.first] = dnx, prev[nx.first] = v;
                    if (nx.second) {
                        que.push_back(nx.first);
                    } else {
                        que.push_front(nx.first);
                    }
                }
            }
        }
    }
};


#include <atcoder/mincostflow>

uint32_t rand_int() // XorShift random integer generator
{
    static uint32_t x = 123456789, y = 362436069, z = 521288629, w = 88675123;
    uint32_t t = x ^ (x << 11);
    x = y;
    y = z;
    z = w;
    return w = (w ^ (w >> 19)) ^ (t ^ (t >> 8));
}


struct State {
    // x -> y -> z -> x のウォーク
    int x, y, z;
    vector<int> xy;  // [x, ..., y] or (empty)
    vector<int> yz;  // [y, ..., z] or (empty)
    vector<int> zx;  // [z, ..., x] or (empty)

    int nb_good_e() const { return (!xy.empty()) + (!yz.empty()) + (!zx.empty()); }
    bool feasible() const { return xy.size() and yz.size() and zx.size(); }

    int length() const {
        if (!feasible()) return -1;
        return xy.size() + yz.size() + zx.size() - 3;
    }

    vector<int> render() const {
        // 以下のいずれかを出力
        // - 現状態が表す解 [x, ..., y, ..., z, ..., x] (feasible)
        // - [] (infeasible)
        if (!feasible()) return {};
        vector<int> ret = xy;
        ret.pop_back();
        ret.insert(ret.end(), yz.begin(), yz.end());
        ret.pop_back();
        ret.insert(ret.end(), zx.begin(), zx.end());
        return ret;
    }

    // 状態に順序を導入
    // - (feasible soluton) < (infeasible solution)
    // - (shorter feasible solution) < (longer feasible solution)
    // - (lexicographically smaller feasible solution) < (lexicographically greater feasible solution)
    bool operator<(const State &x) const {
        if (!this->feasible()) return false;
        if (!x.feasible()) return true;
        int len = this->length(), xlen = x.length();
        if (len != xlen) return len < xlen;
        return this->render() < x.render();
    }

    void clear() {
        xy.clear();
        yz.clear();
        zx.clear();
    }

    vector<int> enum_inner_vs() const {
        // 現在の状態でパス上にある，端点 (x, y, z) 以外の頂点を列挙
        vector<int> ret;
        for (int i = 1; i + 1 < int(xy.size()); ++i) ret.push_back(xy[i]);
        for (int i = 1; i + 1 < int(yz.size()); ++i) ret.push_back(yz[i]);
        for (int i = 1; i + 1 < int(zx.size()); ++i) ret.push_back(zx[i]);
        return ret;
    }

    void init(int x_, int y_, int z_) {
        clear();
        x = x_, y = y_, z = z_;
    }

    void rev() {
        // パスの順序を逆転させる
        swap(y, z);
        swap(xy, zx);
        reverse(xy.begin(), xy.end());
        reverse(yz.begin(), yz.end());
        reverse(zx.begin(), zx.end());
    }
};

int N;
vector<vector<int>> to;

// used_vs に含まれる頂点は使わずに，from -> to1 と from->to2 の点素なパスを構成する．
// 両方のパスが構築できなければ empty vector の組を返す．
// already_feasible が true ならば最短パスを構築し，
// false ならばもう少しランダムに解を構築する．
pair<vector<int>, vector<int>> twopaths(const vector<int> &used_vs, bool already_feasible, int from, int to1, int to2) {
    const int gt = N * 2;
    atcoder::mcf_graph<int, int> graph(gt + 1);

    vector<int> valid_v(N, 1);
    for (auto i : used_vs) valid_v[i] = 0;

    if (!already_feasible) {
        REP(i, N) {
            if (rand_int() % 100 == 0) valid_v[i] = 0;
        }
    }

    valid_v[to1] = valid_v[to2] = 1;

    for (int i = 0; i < N; ++i) {
        graph.add_edge(i, i + N, valid_v[i], 0);
    }

    for (int i = 0; i < N; ++i) {
        for (auto j : to[i]) {
            int cost = 1;
            if (!already_feasible) cost = rand_int() % 5 + 1;
            graph.add_edge(i + N, j, 1, cost);
        }
    }
    graph.add_edge(to1 + N, gt, 1, 0);
    graph.add_edge(to2 + N, gt, 1, 0);
    auto f = graph.flow(from + N, gt, 2);
    if (f.first < 2) return {{}, {}};

    vector<int> conn(N);
    for (auto e : graph.edges()) {
        if (e.flow) {
            if (e.to == gt) continue;
            int s = e.from % N, t = e.to % N;
            conn[s] ^= t;
            conn[t] ^= s;  // ループがないので生えている辺の xor だけ持っておけば後で解が復元できる
        }
    }

    vector<int> ret1, ret2;
    while (to1 != from) {
        ret1.push_back(to1);
        to1 = conn[to1];
        conn[to1] ^= ret1.back();
    }
    while (to2 != from) {
        ret2.push_back(to2);
        to2 = conn[to2];
        conn[to2] ^= ret2.back();
    }
    ret1.push_back(from);
    ret2.push_back(from);
    reverse(ret1.begin(), ret1.end());
    reverse(ret2.begin(), ret2.end());
    return {ret1, ret2};
}

// a から b を経由し c に辿り着く点素なパスで，banned にあるものを使わないもののうち
// 最短で辞書順最小のものを求め，{[a, ..., b], [b, ..., c]} という pair of vector を返す．
pair<vector<int>, vector<int>> refine_path(int a, int b, int c, vector<int> banned) {
    vector<int> is_banned(N);
    for (auto i : banned) is_banned[i] = 1;
    auto [v1, v2] = twopaths(banned, true, b, a, c);
    const int len = v1.size() + v2.size();
    vector<int> ab{a};
    banned.push_back(a);
    is_banned[a] = 1;
    while (ab.back() != b) {
        int cur = ab.back();
        for (auto j : to[cur]) {
            if (j == b) {
                ab.push_back(b);
                break;
            }
            if (is_banned[j]) continue;
            if (j == c) continue;
            auto [p1, p2] = twopaths(banned, true, b, j, c);
            if (p1.empty()) continue;
            if (int(p1.size() + p2.size() + ab.size()) != len) continue;

            ab.push_back(j);
            banned.push_back(j);
            is_banned[j] = 1;
            break;
        }
    }

    ShortestPath<int, 1 << 20> sssp(N);
    for (int i = 0; i < N; ++i) {
        if (is_banned[i]) continue;
        for (auto j : to[i]) {
            if (is_banned[j]) continue;
            sssp.add_edge(i, j, 1);
        }
    }
    sssp.ZeroOneBFS(b);
    const auto Db = sssp.dist;
    sssp.ZeroOneBFS(c);
    const auto Dc = sssp.dist;

    vector<int> bc{b};
    int cur = b;
    while (cur != c) {
        for (auto nxt : to[cur]) {
            if (Db[nxt] == Db[cur] + 1 and Dc[nxt] == Dc[cur] - 1) {
                cur = nxt;
                bc.push_back(cur);
                break;
            }
        }
    }
    return {ab, bc};
}

// x->y->z->x の feasible な解について， z->x には手を加えず残りを辞書順最小にする
void refine_xyz(State &state) {
    if (!state.feasible()) return;  // infeasible なら何もしない
    const int x = state.xy[0], y = state.yz[0], z = state.zx[0];
    auto [xy, yz] = refine_path(x, y, z, vector<int>(state.zx.begin() + 1, state.zx.end() - 1));
    state.xy = move(xy);
    state.yz = move(yz);
}

// x->y->z->x の feasible な解について，x->y には手を加えず残りを辞書順最小にする
void refine_yzx(State &state) {
    if (!state.feasible()) return; // infeasible なら何もしない
    const int x = state.xy[0], y = state.yz[0], z = state.zx[0];
    auto [yz, zx] = refine_path(y, z, x, vector<int>(state.xy.begin() + 1, state.xy.end() - 1));
    state.yz = move(yz);
    state.zx = move(zx);
}

void refine(State &state) {
    if (!state.feasible()) return;
    refine_xyz(state);
    refine_yzx(state);
    auto v = state.render();
    auto vrev = v;
    reverse(vrev.begin(), vrev.end());
    if (vrev < v) {
        state.rev();
        refine_xyz(state);
        refine_yzx(state);
    }
}

void step(State &state, int x, int y, int z) {
    while (state.nb_good_e() >= 2) {
        int i = rand_int() % 3;
        if (i == 0) state.xy.clear();
        if (i == 1) state.yz.clear();
        if (i == 2) state.zx.clear();
    }

    for (int t = 0; t < 10; ++t) {
        if (rand_int() % 5 == 0 and state.xy.empty() and state.zx.empty()) {
            auto [xy, xz] = twopaths(state.enum_inner_vs(), state.feasible(), x, y, z);
            reverse(xz.begin(), xz.end());
            state.xy = xy;
            state.zx = xz;
        }
        if (rand_int() % 5 == 0 and state.xy.empty() and state.yz.empty()) {
            auto [yx, yz] = twopaths(state.enum_inner_vs(), state.feasible(), y, x, z);
            reverse(yx.begin(), yx.end());
            state.xy = yx;
            state.yz = yz;
        }
        if (rand_int() % 5 == 0 and state.yz.empty() and state.zx.empty()) {
            auto [zx, zy] = twopaths(state.enum_inner_vs(), state.feasible(), z, x, y);
            reverse(zy.begin(), zy.end());
            state.zx = zx;
            state.yz = zy;
        }
    }
}

int main() {
    int M;
    int x, y, z;
    cin >> N >> M;
    cin >> x >> y >> z;

    --x, --y, --z;
    vector conn(N, vector<int>(N, 1));
    REP(i, N) conn[i][i] = 0;
    while (M--) {
        int a, b;
        cin >> a >> b;
        --a, --b;
        conn[a][b] = conn[b][a] = 0;
    }
    to.assign(N, {});
    int E = 0;
    REP(i, N) REP(j, N) if (conn[i][j]) to[i].push_back(j), ++E;
    dbg(E);

    int n_iter = 10;
    if (E > 5000) n_iter = 5;

    State best_all;
    REP(iter, n_iter) {
        for (int dir = 0; dir < 2; ++dir) {
            State best, state;
            state.init(x, y, z);
            FOR(t, 1, 31) {
                step(state, x, y, z);
                if (state < best) best = state;
                if (t % 10 == 0) {
                    refine_xyz(state);
                    refine_yzx(state);
                    if (state < best) best = state;
                }
            }
            refine(best);
            if (best < best_all) best_all = best;
            swap(y, z);
        }
    }

    cout << best_all.length() << '\n';
    auto path = best_all.render();
    if (path.size()) {
        for (auto x : path) cout << x + 1 << ' ';
        cout << '\n';
    }
}