#line 1 "library/Template/template.hpp" #include using namespace std; #define rep(i, a, b) for (int i = (int)(a); i < (int)(b); i++) #define rrep(i, a, b) for (int i = (int)(b)-1; i >= (int)(a); i--) #define ALL(v) (v).begin(), (v).end() #define UNIQUE(v) sort(ALL(v)), (v).erase(unique(ALL(v)), (v).end()) #define SZ(v) (int)v.size() #define MIN(v) *min_element(ALL(v)) #define MAX(v) *max_element(ALL(v)) #define LB(v, x) int(lower_bound(ALL(v), (x)) - (v).begin()) #define UB(v, x) int(upper_bound(ALL(v), (x)) - (v).begin()) using uint = unsigned int; using ll = long long int; using ull = unsigned long long; using i128 = __int128_t; using u128 = __uint128_t; const int inf = 0x3fffffff; const ll INF = 0x1fffffffffffffff; template inline bool chmax(T &a, T b) { if (a < b) { a = b; return 1; } return 0; } template inline bool chmin(T &a, T b) { if (a > b) { a = b; return 1; } return 0; } template T ceil(T x, U y) { assert(y != 0); if (y < 0) x = -x, y = -y; return (x > 0 ? (x + y - 1) / y : x / y); } template T floor(T x, U y) { assert(y != 0); if (y < 0) x = -x, y = -y; return (x > 0 ? x / y : (x - y + 1) / y); } template int popcnt(T x) { return __builtin_popcountll(x); } template int topbit(T x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); } template int lowbit(T x) { return (x == 0 ? -1 : __builtin_ctzll(x)); } template ostream &operator<<(ostream &os, const pair &p) { os << "P(" << p.first << ", " << p.second << ")"; return os; } template ostream &operator<<(ostream &os, const vector &vec) { os << "{"; for (int i = 0; i < vec.size(); i++) { os << vec[i] << (i + 1 == vec.size() ? "" : ", "); } os << "}"; return os; } template ostream &operator<<(ostream &os, const map &map_var) { os << "{"; for (auto itr = map_var.begin(); itr != map_var.end(); itr++) { os << "(" << itr->first << ", " << itr->second << ")"; itr++; if (itr != map_var.end()) os << ", "; itr--; } os << "}"; return os; } template ostream &operator<<(ostream &os, const set &set_var) { os << "{"; for (auto itr = set_var.begin(); itr != set_var.end(); itr++) { os << *itr; ++itr; if (itr != set_var.end()) os << ", "; itr--; } os << "}"; return os; } #ifdef LOCAL #define show(...) _show(0, #__VA_ARGS__, __VA_ARGS__) #else #define show(...) true #endif template void _show(int i, T name) { cerr << '\n'; } template void _show(int i, const T1 &a, const T2 &b, const T3 &...c) { for (; a[i] != ',' && a[i] != '\0'; i++) cerr << a[i]; cerr << ":" << b << " "; _show(i + 1, a, c...); } #line 2 "library/Utility/fastio.hpp" #include namespace fastio { static constexpr uint32_t SZ = 1 << 17; char ibuf[SZ]; char obuf[SZ]; char out[100]; // pointer of ibuf, obuf uint32_t pil = 0, pir = 0, por = 0; struct Pre { char num[10000][4]; constexpr Pre() : num() { for (int i = 0; i < 10000; i++) { int n = i; for (int j = 3; j >= 0; j--) { num[i][j] = n % 10 | '0'; n /= 10; } } } } constexpr pre; inline void load() { memmove(ibuf, ibuf + pil, pir - pil); pir = pir - pil + fread(ibuf + pir - pil, 1, SZ - pir + pil, stdin); pil = 0; if (pir < SZ) ibuf[pir++] = '\n'; } inline void flush() { fwrite(obuf, 1, por, stdout); por = 0; } void rd(char &c) { do { if (pil + 1 > pir) load(); c = ibuf[pil++]; } while (isspace(c)); } void rd(string &x) { x.clear(); char c; do { if (pil + 1 > pir) load(); c = ibuf[pil++]; } while (isspace(c)); do { x += c; if (pil == pir) load(); c = ibuf[pil++]; } while (!isspace(c)); } template void rd_real(T &x) { string s; rd(s); x = stod(s); } template void rd_integer(T &x) { if (pil + 100 > pir) load(); char c; do c = ibuf[pil++]; while (c < '-'); bool minus = 0; if constexpr (is_signed::value || is_same_v) { if (c == '-') { minus = 1, c = ibuf[pil++]; } } x = 0; while ('0' <= c) { x = x * 10 + (c & 15), c = ibuf[pil++]; } if constexpr (is_signed::value || is_same_v) { if (minus) x = -x; } } void rd(int &x) { rd_integer(x); } void rd(ll &x) { rd_integer(x); } void rd(i128 &x) { rd_integer(x); } void rd(uint &x) { rd_integer(x); } void rd(ull &x) { rd_integer(x); } void rd(u128 &x) { rd_integer(x); } void rd(double &x) { rd_real(x); } void rd(long double &x) { rd_real(x); } template void rd(pair &p) { return rd(p.first), rd(p.second); } template void rd_tuple(T &t) { if constexpr (N < std::tuple_size::value) { auto &x = std::get(t); rd(x); rd_tuple(t); } } template void rd(tuple &tpl) { rd_tuple(tpl); } template void rd(array &x) { for (auto &d : x) rd(d); } template void rd(vector &x) { for (auto &d : x) rd(d); } void read() {} template void read(H &h, T &...t) { rd(h), read(t...); } void wt(const char c) { if (por == SZ) flush(); obuf[por++] = c; } void wt(const string s) { for (char c : s) wt(c); } void wt(const char *s) { size_t len = strlen(s); for (size_t i = 0; i < len; i++) wt(s[i]); } template void wt_integer(T x) { if (por > SZ - 100) flush(); if (x < 0) { obuf[por++] = '-', x = -x; } int outi; for (outi = 96; x >= 10000; outi -= 4) { memcpy(out + outi, pre.num[x % 10000], 4); x /= 10000; } if (x >= 1000) { memcpy(obuf + por, pre.num[x], 4); por += 4; } else if (x >= 100) { memcpy(obuf + por, pre.num[x] + 1, 3); por += 3; } else if (x >= 10) { int q = (x * 103) >> 10; obuf[por] = q | '0'; obuf[por + 1] = (x - q * 10) | '0'; por += 2; } else obuf[por++] = x | '0'; memcpy(obuf + por, out + outi + 4, 96 - outi); por += 96 - outi; } template void wt_real(T x) { ostringstream oss; oss << fixed << setprecision(15) << double(x); string s = oss.str(); wt(s); } void wt(int x) { wt_integer(x); } void wt(ll x) { wt_integer(x); } void wt(i128 x) { wt_integer(x); } void wt(uint x) { wt_integer(x); } void wt(ull x) { wt_integer(x); } void wt(u128 x) { wt_integer(x); } void wt(double x) { wt_real(x); } void wt(long double x) { wt_real(x); } template void wt(const pair val) { wt(val.first); wt(' '); wt(val.second); } template void wt_tuple(const T t) { if constexpr (N < std::tuple_size::value) { if constexpr (N > 0) { wt(' '); } const auto x = std::get(t); wt(x); wt_tuple(t); } } template void wt(tuple tpl) { wt_tuple(tpl); } template void wt(const array val) { auto n = val.size(); for (size_t i = 0; i < n; i++) { if (i) wt(' '); wt(val[i]); } } template void wt(const vector val) { auto n = val.size(); for (size_t i = 0; i < n; i++) { if (i) wt(' '); wt(val[i]); } } void print() { wt('\n'); } template void print(Head &&head, Tail &&...tail) { wt(head); if (sizeof...(Tail)) wt(' '); print(forward(tail)...); } void __attribute__((destructor)) _d() { flush(); } } // namespace fastio using fastio::flush; using fastio::print; using fastio::read; inline void first(bool i = true) { print(i ? "first" : "second"); } inline void Alice(bool i = true) { print(i ? "Alice" : "Bob"); } inline void Takahashi(bool i = true) { print(i ? "Takahashi" : "Aoki"); } inline void yes(bool i = true) { print(i ? "yes" : "no"); } inline void Yes(bool i = true) { print(i ? "Yes" : "No"); } inline void No() { print("No"); } inline void YES(bool i = true) { print(i ? "YES" : "NO"); } inline void NO() { print("NO"); } inline void Yay(bool i = true) { print(i ? "Yay!" : ":("); } inline void Possible(bool i = true) { print(i ? "Possible" : "Impossible"); } inline void POSSIBLE(bool i = true) { print(i ? "POSSIBLE" : "IMPOSSIBLE"); } /** * @brief Fast IO */ #line 3 "sol.cpp" #line 2 "library/Math/modint.hpp" template struct fp { unsigned v; static constexpr int get_mod() { return mod; } constexpr unsigned inv() const { assert(v != 0); int x = v, y = mod, p = 1, q = 0, t = 0, tmp = 0; while (y > 0) { t = x / y; x -= t * y, p -= t * q; tmp = x, x = y, y = tmp; tmp = p, p = q, q = tmp; } if (p < 0) p += mod; return p; } constexpr fp(ll x = 0) : v(x >= 0 ? x % mod : (mod - (-x) % mod) % mod) {} fp operator-() const { return fp() - *this; } fp pow(ull t) { fp res = 1, b = *this; while (t) { if (t & 1) res *= b; b *= b; t >>= 1; } return res; } fp &operator+=(const fp &x) { if ((v += x.v) >= mod) v -= mod; return *this; } fp &operator-=(const fp &x) { if ((v += mod - x.v) >= mod) v -= mod; return *this; } fp &operator*=(const fp &x) { v = ull(v) * x.v % mod; return *this; } fp &operator/=(const fp &x) { v = ull(v) * x.inv() % mod; return *this; } fp operator+(const fp &x) const { return fp(*this) += x; } fp operator-(const fp &x) const { return fp(*this) -= x; } fp operator*(const fp &x) const { return fp(*this) *= x; } fp operator/(const fp &x) const { return fp(*this) /= x; } bool operator==(const fp &x) const { return v == x.v; } bool operator!=(const fp &x) const { return v != x.v; } friend istream &operator>>(istream &is, fp &x) { return is >> x.v; } friend ostream &operator<<(ostream &os, const fp &x) { return os << x.v; } }; template void rd(fp &x) { fastio::rd(x.v); } template void wt(fp x) { fastio::wt(x.v); } /** * @brief Modint */ #line 2 "library/Math/comb.hpp" template T Inv(ll n) { static int md; static vector buf({0, 1}); if (md != T::get_mod()) { md = T::get_mod(); buf = vector({0, 1}); } assert(n > 0); n %= md; while (SZ(buf) <= n) { int k = SZ(buf), q = (md + k - 1) / k; buf.push_back(buf[k * q - md] * q); } return buf[n]; } template T Fact(ll n, bool inv = 0) { static int md; static vector buf({1, 1}), ibuf({1, 1}); if (md != T::get_mod()) { md = T::get_mod(); buf = ibuf = vector({1, 1}); } assert(n >= 0 and n < md); while (SZ(buf) <= n) { buf.push_back(buf.back() * SZ(buf)); ibuf.push_back(ibuf.back() * Inv(SZ(ibuf))); } return inv ? ibuf[n] : buf[n]; } template T nPr(int n, int r, bool inv = 0) { if (n < 0 || n < r || r < 0) return 0; return Fact(n, inv) * Fact(n - r, inv ^ 1); } template T nCr(int n, int r, bool inv = 0) { if (n < 0 || n < r || r < 0) return 0; return Fact(n, inv) * Fact(r, inv ^ 1) * Fact(n - r, inv ^ 1); } // sum = n, r tuples template T nHr(int n, int r, bool inv = 0) { return nCr(n + r - 1, r - 1, inv); } // sum = n, a nonzero tuples and b tuples template T choose(int n, int a, int b) { if (n == 0) return !a; return nCr(n + b - 1, a + b - 1); } /** * @brief Combination */ #line 6 "sol.cpp" using Fp = fp<998244353>; int main() { int n; read(n); vector g(n, vector()); rep(_, 0, n - 1) { int u, v; read(u, v); u--, v--; g[u].push_back(v); g[v].push_back(u); } vector sz(n); vector dp(n); int base = n; auto dfs = [&](auto &dfs, int v, int p) -> void { dp[v] = 1; int leaf = 0; sz[v] = 1; for (auto &to : g[v]) if (to != p) { dfs(dfs, to, v); sz[v] += sz[to]; leaf++; dp[v] *= dp[to]; } show(base, leaf); if (v != 0) dp[v] *= Fp(base) * nCr(base, leaf + 1, 1); base -= leaf; }; dfs(dfs, 0, -1); print(dp[0]); return 0; }