#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using lint = long long; using pint = pair; using plint = pair; 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##_begin_;i--) #define REP(i, n) FOR(i,0,n) #define IREP(i, n) IFOR(i,0,n) template void ndarray(vector& vec, const V& val, int len) { vec.assign(len, val); } template void ndarray(vector& vec, const V& val, int len, Args... args) { vec.resize(len), for_each(begin(vec), end(vec), [&](T& v) { ndarray(v, val, args...); }); } template bool chmax(T &m, const T q) { return m < q ? (m = q, true) : false; } template 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 pair operator+(const pair &l, const pair &r) { return make_pair(l.first + r.first, l.second + r.second); } template pair operator-(const pair &l, const pair &r) { return make_pair(l.first - r.first, l.second - r.second); } template vector sort_unique(vector vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; } template int arglb(const std::vector &v, const T &x) { return std::distance(v.begin(), std::lower_bound(v.begin(), v.end(), x)); } template int argub(const std::vector &v, const T &x) { return std::distance(v.begin(), std::upper_bound(v.begin(), v.end(), x)); } template istream &operator>>(istream &is, vector &vec) { for (auto &v : vec) is >> v; return is; } template ostream &operator<<(ostream &os, const vector &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; } template ostream &operator<<(ostream &os, const array &arr) { os << '['; for (auto v : arr) os << v << ','; os << ']'; return os; } #if __cplusplus >= 201703L template istream &operator>>(istream &is, tuple &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; } template ostream &operator<<(ostream &os, const tuple &tpl) { os << '('; std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os << ')'; } #endif template ostream &operator<<(ostream &os, const deque &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; } template ostream &operator<<(ostream &os, const set &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const unordered_set &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const multiset &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const unordered_multiset &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const pair &pa) { os << '(' << pa.first << ',' << pa.second << ')'; return os; } template ostream &operator<<(ostream &os, const map &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const unordered_map &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) 0 #define dbgif(cond, x) 0 #endif vector bruteforce(int N) { vector state(N * 3, -1); vector ret; int retcost = 1e9; int cost = 0; auto rec = [&](auto &&self, int nxt) -> void { // if (ret.size()) return; if (nxt == int(N)) { if (chmin(retcost, cost)) ret = state; return; } if (cost >= retcost) return; REP(i, state.size()) { if (state[i] != -1) continue; state[i] = nxt; FOR(j, i + 1, state.size()) { if (state[j] != -1) continue; state[j] = nxt; int k = -i + j * 2 + nxt; int addcost = 0; if (j < k and k < N * 3 and state[k] == -1) { // addcost = !(i < N and j >= N and j < N * 2 and k >= N * 2); addcost = (i + N != j); state[k] = nxt, cost += addcost; self(self, nxt + 1); state[k] = -1, cost -= addcost; } k = -i + j * 2 - nxt; if (j < k and k < N * 3 and state[k] == -1) { // addcost = !(i < N and j >= N and j < N * 2 and k >= N * 2); addcost = (i + N != j); state[k] = nxt, cost += addcost; self(self, nxt + 1); state[k] = -1, cost -= addcost; } state[j] = -1; } state[i] = -1; } }; rec(rec, 0); return ret; } vector solve(int n) { if (n == 1) return {0, 0, 0}; if (n == 2) return {-1}; if (n == 3) return {2, 0, 2, 1, 0, 1, 2, 0, 1}; vector> deq(3); int nmd4 = n % 4; if (nmd4 == 0) { REP(d, 3) { deq[d].push_back(1); deq[d].push_back(0); } } else if (nmd4 == 1) { for (int x : {2, 1, 0}) deq[0].push_back(x); for (int x : {1, 2, 0}) deq[1].push_back(x); for (int x : {1, 2, 0}) deq[2].push_back(x); } else if (nmd4 == 2) { for (int x : {2, 3, 2, 2}) deq[0].push_back(x); for (int x : {0, 0, 0, 3}) deq[1].push_back(x); for (int x : {1, 1, 3, 1}) deq[2].push_back(x); } else if (nmd4 == 3) { for (int x : {3, 4, 0, 3, 3}) deq[0].push_back(x); for (int x : {4, 1, 0, 1, 1}) deq[1].push_back(x); for (int x : {2, 2, 0, 4, 2}) deq[2].push_back(x); } else { exit(1); } for (int y = nmd4 + 2; y + 3 < n; y += 4) { // y, y + 1, y + 2, y + 3 int a = deq[0].front(); deq[0].pop_front(); deq[0].push_front(y); deq[0].push_front(a); deq[0].push_back(y + 1); deq[0].push_front(y + 2); deq[0].push_back(y + 3); deq[1].push_back(y); deq[1].push_front(y + 1); deq[1].push_front(y + 2); deq[1].push_back(y + 3); deq[2].push_back(y); deq[2].push_front(y + 1); deq[2].push_back(y + 2); deq[2].push_front(y + 3); } int a = deq[0].front(); deq[0].pop_front(); deq[0].push_front(n - 2); deq[0].push_front(a); deq[1].push_back(n - 2); deq[2].push_back(n - 2); deq[0].push_back(n - 1); deq[1].push_front(n - 1); deq[2].push_front(n - 1); vector ret; for (auto &d : deq) { while (d.size()) { ret.push_back(d.front()); d.pop_front(); } } return ret; } bool check(int N, const vector &V) { if (int(V.size()) != N * 3) return false; vector> poss(N); REP(i, V.size()) { int a = V[i]; if (a < 0 or a >= N) return false; poss[a].push_back(i); } REP(n, N) { const auto &pos = poss.at(n); if (pos.size() != 3) return false; int diff = abs(pos[1] - pos[0] - (pos[2] - pos[1])); if (diff != n) { dbg(make_tuple(N, n, pos, diff)); return false; } } return true; } int main() { // FOR(n, 3, 200) { // auto sol = solve(n); // if (!check(n, sol)) { // dbg(n); // dbg(sol); // exit(1); // } // } // FOR(n, 1, 21) { // dbg(bruteforce(n)); // } int N; cin >> N; for (auto x : solve(N)) cout << x << ' '; cout << endl; }