// #define MULTI_TESTCASE // #define AOJ_TESTCASE // #define FAST_IO // #define FAST_CIO // https://github.com/miscalculation53/library/tree/wip/template/template_all.hpp // https://github.com/miscalculation53/library/tree/wip/template/template_all_but_modint.hpp // https://github.com/miscalculation53/library/tree/wip/template/template_types.hpp #include namespace { using namespace std; using ll = long long; using uint = unsigned int; using ull = unsigned long long; using pll = pair; #define vc vector using i128 = __int128_t; using u128 = __uint128_t; #define cauto const auto // https://github.com/miscalculation53/library/tree/wip/template/template_rep.hpp #define overload4(_1,_2,_3,_4,name,...) name #define repi1(i,n) for (int i = 0, nnnnn = int(n); i < nnnnn; i++) #define repi(...) overload4(__VA_ARGS__, repi3, repi2, repi1)(__VA_ARGS__) #define fe(...) for (auto __VA_ARGS__) // https://github.com/miscalculation53/library/tree/wip/template/template_math.hpp // https://github.com/miscalculation53/library/tree/wip/utils/is_integral_ext.hpp template constexpr bool is_integral_ext = is_integral_v || is_same_v || is_same_v; template constexpr bool is_signed_ext = is_signed_v || is_same_v; template constexpr bool is_unsigned_ext = is_unsigned_v || is_same_v; // https://github.com/miscalculation53/library/tree/wip/utils/default_infty.hpp namespace default_infty_detail { template inline constexpr bool unsupported = false; } template && is_integral_ext>> inline constexpr T divfloor(U a, V b) { return T(a) / T(b) - (T(a) % T(b) && (T(a) ^ T(b)) < 0); } template && is_integral_ext>> inline constexpr T safemod(U a, V b) { return T(a) - T(b) * divfloor(a, b); } // https://github.com/miscalculation53/library/tree/wip/template/template_vector.hpp #define ALL(a) (a).begin(), (a).end() #define eb emplace_back // https://github.com/miscalculation53/library/tree/wip/template/template_algo.hpp // https://github.com/miscalculation53/library/tree/wip/utils/resolved_infty.hpp // https://github.com/miscalculation53/library/tree/wip/utils/resolved_value.hpp template struct has_e0 : false_type {}; template struct has_e0> : true_type {}; template inline constexpr bool has_e0_v = has_e0::value; namespace internal { } constexpr array DRULgrid = {{{1, 0}, {0, 1}, {-1, 0}, {0, -1}}}; constexpr array DRULplane = {{{0, -1}, {1, 0}, {0, 1}, {-1, 0}}}; // https://github.com/miscalculation53/library/tree/wip/template/template_binsearch.hpp template struct is_random_access_iterator { static constexpr bool value = is_same_v< typename iterator_traits::iterator_category, random_access_iterator_tag >; }; template constexpr bool is_random_access_iterator_v = is_random_access_iterator::value; namespace internal { }; // https://github.com/miscalculation53/library/tree/wip/template/template_bit.hpp template inline constexpr ull MASK(T k) { return (1ULL << k) - 1ULL; } inline constexpr ll bit_width(ll x) { return std::bit_width((ull)x); } inline constexpr ll bit_floor(ll x) { return std::bit_floor((ull)x); } inline constexpr ll bit_ceil(ll x) { return std::bit_ceil((ull)x); } inline constexpr ll countr_zero(ll x) { assert(x != 0); return std::countr_zero((ull)x); } inline constexpr ll popcount(ll x) { return std::popcount((ull)x); } inline constexpr bool has_single_bit(ll x) { return std::has_single_bit((ull)x); } // https://github.com/miscalculation53/library/tree/wip/template/template_inout.hpp // https://github.com/miscalculation53/library/tree/wip/template/template_dump.hpp // https://github.com/miscalculation53/library/tree/wip/template/template_dump_map.hpp #define dump(...) #define oj(...) __VA_ARGS__ template istream &operator>>(istream &is, pair &p) { is >> p.first >> p.second; return is; } template istream &operator>>(istream &is, vc &a) { const size_t n = a.size(); for (size_t i = 0; i < n; i++) is >> a[i]; return is; } namespace internal { template void CIN(Ts &...a) { (cin >> ... >> a); } template void READnodump(Ts &...a) { CIN(a...); } template void READVECnodump(int n, vc &...v) { (v.resize(n), ...); READnodump(v...); } }; #define READ(...) internal::READnodump(__VA_ARGS__); dump(__VA_ARGS__) #define IN(T,...) T __VA_ARGS__; READ(__VA_ARGS__) #define LL(...) IN(ll, __VA_ARGS__) #define STR(...) IN(string, __VA_ARGS__) #define READVEC(...) internal::READVECnodump(__VA_ARGS__); dump(__VA_ARGS__) #define VEC(T,n,...) vc __VA_ARGS__; READVEC(n, __VA_ARGS__) #define ENDL endl template ostream &operator<<(ostream &os, const pair &p) { os << p.first << ' ' << p.second; return os; } template ostream &operator<<(ostream &os, const tuple &t); template ostream &operator<<(ostream &os, const array &a); template ostream &operator<<(ostream &os, const vc &v) { const size_t n = v.size(); for (size_t i = 0; i < n; i++) { if (i) os << ' '; os << v[i]; } return os; } namespace internal { template void COUTP(const Ts &...a) { if constexpr (sizeof...(Ts)) { int i = 0; ((cout << (i++ ? " " : "") << a), ...); } cout << ENDL; } }; #define PRINT internal::COUTP template void PRINTV(const vc &v) { for (auto &vi : v) PRINT(vi); } template pair &operator+=(pair &a, const P &b) { a.first += b.first; a.second += b.second; return a; } namespace internal { }; template void offset(vc &v, const Add &add) { for (auto &vi : v) vi += add; } namespace internal { }; // https://github.com/miscalculation53/library/tree/wip/template/template_random.hpp mt19937_64 mt; namespace internal { }; // https://github.com/miscalculation53/library/tree/wip/math/modint/template_modint.hpp // https://github.com/miscalculation53/library/tree/wip/math/modint/modint.hpp // https://github.com/miscalculation53/library/tree/wip/math/modint/modint_internal_static.hpp // https://github.com/miscalculation53/library/tree/wip/utils/larger_int.hpp namespace larger_int_detail { } template struct larger_int { private: static constexpr bool check(); static_assert(check()); public: using type = T; }; #define LARGER_INT(T,U) template <> struct larger_int { using type = U; }; LARGER_INT(signed char, short) LARGER_INT(short, int) LARGER_INT(int, long long) LARGER_INT(long, __int128_t) LARGER_INT(long long, __int128_t) LARGER_INT(unsigned char, unsigned short) LARGER_INT(unsigned short, unsigned int) LARGER_INT(unsigned int, unsigned long long) LARGER_INT(unsigned long, __uint128_t) LARGER_INT(unsigned long long, __uint128_t) #undef LARGER_INT template struct Rational; template struct larger_int> { using type = Rational::type>; }; template using larger_int_t = typename larger_int::type; // https://github.com/miscalculation53/library/tree/wip/math/modint/modint_internal_isprime.hpp namespace internal { template constexpr ll powmod_constexpr(ll x, ll n, T m) { if (m == 1) return 0; using U = make_unsigned_t; using L = larger_int_t; U r = 1, y = safemod(x, m); while (n) { if (n & 1) r = L(r) * y % m; y = L(y) * y % m; n >>= 1; } return r; } template constexpr bool isprime = isprime_constexpr(n); }; namespace internal { template struct policy_static { using mod_type = decltype(M); using value_type = make_unsigned_t; using calc_type = larger_int_t; static constexpr bool is_prime = isprime_constexpr(M); static constexpr value_type init(value_type v) { return v; } static constexpr mod_type val(value_type v); }; }; // https://github.com/miscalculation53/library/tree/wip/math/modint/modint_internal_barrett32.hpp namespace internal { struct barrett32 { uint m; ull im; explicit barrett32(uint m) : m(m), im((ull)(-1) / m + 1) {} }; template struct policy_barrett32 { using value_type = uint; using calc_type = ull; using mod_type = int; static constexpr bool is_prime = false; static inline barrett32 reducer{998244353}; static value_type init(value_type v) { return v; } static mod_type val(value_type v); }; }; // https://github.com/miscalculation53/library/tree/wip/math/modint/modint_internal_montgomery64.hpp namespace internal { inline constexpr ull inv64(ull a) { ull x = a; while (a * x != 1) x *= 2 - a * x; return x; } struct montgomery64odd { ull m, im, sq; explicit montgomery64odd(ull m) : m(m), im(inv64(m)), sq(-u128(m) % m) {} ull reduce(u128 x) const { auto t = (x + u128(m) * (-im * ull(x))) >> 64; if (t >= m) t -= m; return (ull)t; } ull inv_reduce(i128 v) const { return reduce(u128(v % m + m) * sq); } }; struct montgomery64 { ull m, mx, imx, d, q; uint b; explicit montgomery64(ull m) : m(m) { b = countr_zero(m), mx = m >> b; imx = inv64(mx); d = powmod_constexpr((mx + 1) / 2, b, mx); u128 sq = -u128(mx) % mx; q = (1 + (((sq - 1) * d) << b)) % m; } ull reduce(u128 x) const { if (b == 0) { auto t = (x + u128(mx) * (-imx * ull(x))) >> 64; if (t >= m) t -= m; return (ull)t; } ull p = x & MASK(b); x = (x >> b) + p * d; ull y = p << (64 - b); auto t = (x + u128(mx) * (imx * (y - ull(x)))) >> (64 - b); if (t >= m) { t -= m; if (t >= m) t -= m; } return (ull)t; } ull inv_reduce(i128 v) const { return reduce(u128(v % m + m) * q); } }; template struct policy_montgomery64_odd { using value_type = ull; using calc_type = u128; using mod_type = ll; static constexpr bool is_prime = false; static inline montgomery64odd reducer{(1LL << 61) - 1}; static value_type init(value_type v) { return reducer.inv_reduce(v); } static mod_type val(value_type v); }; template struct policy_montgomery64 { using value_type = ull; using calc_type = u128; using mod_type = ll; static constexpr bool is_prime = false; static inline montgomery64 reducer{(1LL << 61) - 1}; static value_type init(value_type v) { return reducer.inv_reduce(v); } static mod_type val(value_type v); }; }; // https://github.com/miscalculation53/library/tree/wip/math/extgcd.hpp namespace internal { template struct modint_impl { using V = typename Policy::value_type; using M = typename Policy::mod_type; using mint = modint_impl; private: V _v; public: modint_impl(); template >> modint_impl(T v); M val() const; friend mint operator+(const mint &lhs, const mint &rhs) { return mint(lhs) += rhs; } friend mint operator-(const mint &lhs, const mint &rhs) { return mint(lhs) -= rhs; } friend mint operator*(const mint &lhs, const mint &rhs) { return mint(lhs) *= rhs; } friend mint operator/(const mint &lhs, const mint &rhs) { return mint(lhs) /= rhs; } friend bool operator==(const mint &lhs, const mint &rhs) { return lhs._v == rhs._v; } friend bool operator!=(const mint &lhs, const mint &rhs) { return lhs._v != rhs._v; } friend std::istream &operator>>(std::istream &is, mint &x) { long long a; is >> a; x = a; return is; } friend std::ostream &operator<<(std::ostream &os, const mint &x) { os << x.val(); return os; } }; }; template using static_modint32 = internal::modint_impl>; template using dynamic_modint32 = internal::modint_impl>; template using static_modint64 = internal::modint_impl>; template using dynamic_modint64_odd = internal::modint_impl>; template using dynamic_modint64 = internal::modint_impl>; using modint998244353 = static_modint32<998244353>; template struct is_modint : std::false_type { }; template struct is_modint> : std::true_type { }; template inline constexpr bool is_modint_v = is_modint::value; template struct is_static_modint : false_type {}; template struct is_static_modint> : true_type {}; template struct is_static_modint> : true_type {}; template inline constexpr bool is_static_modint_v = is_static_modint::value; template struct is_dynamic_modint : false_type {}; template struct is_dynamic_modint> : true_type {}; template struct is_dynamic_modint> : true_type {}; template struct is_dynamic_modint> : true_type {}; template inline constexpr bool is_dynamic_modint_v = is_dynamic_modint::value; // https://github.com/miscalculation53/library/tree/wip/math/modint/power_table.hpp // https://github.com/miscalculation53/library/tree/wip/math/modint/binomial.hpp template struct Binomial { private: inline static decltype(T::mod()) mod; public: inline static vc fac_, finv_, inv_; }; // https://github.com/miscalculation53/library/tree/wip/math/modint/stom.hpp // https://github.com/miscalculation53/library/tree/wip/math/modint/to_rational.hpp // https://github.com/miscalculation53/library/tree/wip/math/svp2d.hpp namespace cpp_dump { template struct rat_value { T p, q; friend ostream &operator<<(ostream &os, const rat_value &x) { os << x.p; if (x.q != 1) os << '/' << x.q; return os; } }; template inline constexpr bool rat_is_map = false; template inline constexpr bool rat_is_map> = true; template inline constexpr bool rat_is_map> = true; template inline constexpr bool rat_is_map> = true; template inline constexpr bool rat_is_map> = true; } using mint = modint998244353; // using mint = modint1000000007; // using mint = static_modint<1000000000>; // using mint = modint; void init() { oj(mt.seed(random_device()())); } // https://github.com/miscalculation53/library/tree/wip/graph/tree/rooted_tree.hpp struct RootedTree { protected: static const int MSK = 1 << 30; int n; vc p_head, dep, pre, post, preinv; public: RootedTree() {} class ChildIterator; class ChildRange; class ChildIterator { private: const RootedTree* t; int cur; friend class RootedTree; friend class ChildRange; ChildIterator(const RootedTree* t, int cur) : t(t), cur(cur) {} public: using iterator_category = std::input_iterator_tag; using value_type = int; using difference_type = std::ptrdiff_t; using pointer = int*; using reference = int; int operator*() const { return t->preinv[cur]; } void operator++() { cur = t->post[t->preinv[cur]]; } bool operator!=(const ChildIterator& r) const { return cur != r.cur; } bool operator==(const ChildIterator& r) const { return cur == r.cur; } }; class ChildRange { private: const RootedTree* t; int cur, end_pos; friend class RootedTree; ChildRange(const RootedTree* t, int cur, int end_pos) : t(t), cur(cur), end_pos(end_pos) {} public: ChildIterator begin() const { return ChildIterator(t, cur); } ChildIterator end() const { return ChildIterator(t, end_pos); } }; }; // https://cp-algorithms.com/graph/pruefer_code.html vector> adj; vector parent; void dfs(int v) { for (int u : adj[v]) { if (u != parent[v]) { parent[u] = v; dfs(u); } } } vector pruefer_code() { int n = adj.size(); parent.resize(n); parent[n-1] = -1; dfs(n-1); int ptr = -1; vector degree(n); for (int i = 0; i < n; i++) { degree[i] = adj[i].size(); if (degree[i] == 1 && ptr == -1) ptr = i; } vector code(n - 2); int leaf = ptr; for (int i = 0; i < n - 2; i++) { int next = parent[leaf]; code[i] = next; if (--degree[next] == 1 && next < ptr) { leaf = next; } else { ptr++; while (degree[ptr] != 1) ptr++; leaf = ptr; } } return code; } vector> pruefer_decode(vector const& code) { int n = code.size() + 2; vector degree(n, 1); for (int i : code) degree[i]++; int ptr = 0; while (degree[ptr] != 1) ptr++; int leaf = ptr; vector> edges; for (int v : code) { edges.emplace_back(leaf, v); if (--degree[v] == 1 && v < ptr) { leaf = v; } else { ptr++; while (degree[ptr] != 1) ptr++; leaf = ptr; } } edges.emplace_back(leaf, n-1); return edges; } void main2() { STR(player); if (player == "Alice") { LL(N); PRINT(N - 2); VEC(pll, N - 1, UV); offset(UV, pll{-1, -1}); adj.resize(N); fe([ u, v ] : UV) adj[u].eb(v), adj[v].eb(u); auto ans = pruefer_code(); offset(ans, 1); PRINT(ans); } else { LL(N); PRINT(N - 2); VEC(int, N - 2, A); offset(A, -1); auto UV = pruefer_decode(A); offset(UV, pll{1, 1}); PRINTV(UV); } } void test() { } // https://github.com/miscalculation53/library/tree/wip/template/template_main.hpp template struct Main { Main() { cauto CERR = [](string val, string color) { string s = "\033[" + color + "m" + val + "\033[m"; }; cout << fixed << setprecision(20); init(); CERR("\n[SINGLE_TESTCASE]\n\n", "36"); main2(); } }; Main main_dummy; } int main() {}