description: You are given a rooted tree consisting of n vertices numbered from 1 to n. The root of the tree is the vertex 1.
  
  You have to color all vertices of the tree into n colors (also numbered from 1 to n) so that there is exactly one vertex for each color. Let c_i be the color of vertex i, and p_i be the parent of vertex i in the rooted tree. The coloring is considered beautiful if there is no vertex k (k > 1) such that c_k = c_{p_k} - 1, i. e. no vertex such that its color is less than the color of its parent by exactly 1.
  
  Calculate the number of beautiful colorings, and print it modulo 998244353.
  
  Input
  
  The first line contains one integer n (2 ≤ n ≤ 250000) — the number of vertices in the tree.
  
  Then n-1 lines follow, the i-th line contains two integers x_i and y_i (1 ≤ x_i, y_i ≤ n; x_i ≠ y_i) denoting an edge between the vertex x_i and the vertex y_i. These edges form a tree.
  
  Output
  
  Print one integer — the number of beautiful colorings, taken modulo 998244353.
  
  Examples
  
  Input
  
  
  5
  1 2
  3 2
  4 2
  2 5
  
  
  Output
  
  
  42
  
  
  Input
  
  
  5
  1 2
  2 3
  3 4
  4 5
  
  
  Output
  
  
  53
  
  
  Input
  
  
  20
  20 19
  20 4
  12 4
  5 8
  1 2
  20 7
  3 10
  7 18
  11 8
  9 10
  17 10
  1 15
  11 16
  14 11
  18 10
  10 1
  14 2
  13 17
  20 6
  
  
  Output
  
  
  955085064
solution: #include <bits/stdc++.h>
  const double PI = 3.1415926535897932384626433;
  using namespace std;
  struct edge {
    long long to, cost;
    edge() {}
    edge(long long a, long long b) { to = a, cost = b; }
  };
  const int dx[] = {1, 0, -1, 0}, dy[] = {0, -1, 0, 1};
  const int mod = 998244353;
  struct mint {
    int x;
    mint(long long y = 0) {
      if (y < 0 || y >= mod) y = (y % mod + mod) % mod;
      x = y;
    }
    mint(const mint &ope) { x = ope.x; }
    mint operator-() { return mint(-x); }
    mint operator+(const mint &ope) { return mint(x) += ope; }
    mint operator-(const mint &ope) { return mint(x) -= ope; }
    mint operator*(const mint &ope) { return mint(x) *= ope; }
    mint operator/(const mint &ope) { return mint(x) /= ope; }
    mint &operator+=(const mint &ope) {
      x += ope.x;
      if (x >= mod) x -= mod;
      return *this;
    }
    mint &operator-=(const mint &ope) {
      x += mod - ope.x;
      if (x >= mod) x -= mod;
      return *this;
    }
    mint &operator*=(const mint &ope) {
      long long tmp = x;
      tmp *= ope.x, tmp %= mod;
      x = tmp;
      return *this;
    }
    mint &operator/=(const mint &ope) {
      long long n = mod - 2;
      mint mul = ope;
      while (n) {
        if (n & 1) *this *= mul;
        mul *= mul;
        n >>= 1;
      }
      return *this;
    }
    mint inverse() { return mint(1) / *this; }
    bool operator==(const mint &ope) { return x == ope.x; }
    bool operator!=(const mint &ope) { return x != ope.x; }
    bool operator<(const mint &ope) const { return x < ope.x; }
  };
  mint modpow(mint a, long long n) {
    if (n == 0) return mint(1);
    if (n % 2)
      return a * modpow(a, n - 1);
    else
      return modpow(a * a, n / 2);
  }
  istream &operator>>(istream &is, mint &ope) {
    long long t;
    is >> t, ope.x = t;
    return is;
  }
  ostream &operator<<(ostream &os, mint &ope) { return os << ope.x; }
  ostream &operator<<(ostream &os, const mint &ope) { return os << ope.x; }
  long long modpow(long long a, long long n, long long mod) {
    if (n == 0) return 1;
    if (n % 2)
      return ((a % mod) * (modpow(a, n - 1, mod) % mod)) % mod;
    else
      return modpow((a * a) % mod, n / 2, mod) % mod;
  }
  vector<mint> fact, fact_inv;
  void make_fact(int n) {
    fact.resize(n + 1), fact_inv.resize(n + 1);
    fact[0] = mint(1);
    for (long long i = (1); (i) <= (n); (i)++) fact[i] = fact[i - 1] * mint(i);
    fact_inv[n] = fact[n].inverse();
    for (long long i = (n - 1); (i) >= (0); (i)--)
      fact_inv[i] = fact_inv[i + 1] * mint(i + 1);
  }
  mint comb(int n, int k) {
    if (n < 0 || k < 0 || n < k) return mint(0);
    return fact[n] * fact_inv[k] * fact_inv[n - k];
  }
  mint perm(int n, int k) { return comb(n, k) * fact[k]; }
  vector<int> prime, pvec;
  void make_prime(int n) {
    prime.resize(n + 1);
    for (long long i = (2); (i) <= (n); (i)++) {
      if (prime[i] == 0) pvec.push_back(i), prime[i] = i;
      for (auto p : pvec) {
        if (i * p > n || p > prime[i]) break;
        prime[i * p] = p;
      }
    }
  }
  vector<int> qrime;
  void make_qrime(int n) {
    qrime.resize(n + 1);
    for (long long i = (2); (i) <= (n); (i)++) {
      int ni = i / prime[i];
      if (prime[i] == prime[ni])
        qrime[i] = qrime[ni] * prime[i];
      else
        qrime[i] = prime[i];
    }
  }
  bool exceed(long long x, long long y, long long m) { return x >= m / y + 1; }
  void mark() { cout << "*" << endl; }
  void yes() { cout << "YES" << endl; }
  void no() { cout << "NO" << endl; }
  long long floor(long long a, long long b) {
    if (b < 0) a *= -1, b *= -1;
    if (a >= 0)
      return a / b;
    else
      return -((-a + b - 1) / b);
  }
  long long ceil(long long a, long long b) {
    if (b < 0) a *= -1, b *= -1;
    if (a >= 0)
      return (a + b - 1) / b;
    else
      return -((-a) / b);
  }
  long long modulo(long long a, long long b) {
    b = abs(b);
    return a - floor(a, b) * b;
  }
  long long sgn(long long x) {
    if (x > 0) return 1;
    if (x < 0) return -1;
    return 0;
  }
  long long gcd(long long a, long long b) {
    if (b == 0) return a;
    return gcd(b, a % b);
  }
  long long lcm(long long a, long long b) { return a / gcd(a, b) * b; }
  long long arith(long long x) { return x * (x + 1) / 2; }
  long long arith(long long l, long long r) { return arith(r) - arith(l - 1); }
  long long digitnum(long long x, long long b = 10) {
    long long ret = 0;
    for (; x; x /= b) ret++;
    return ret;
  }
  long long digitsum(long long x, long long b = 10) {
    long long ret = 0;
    for (; x; x /= b) ret += x % b;
    return ret;
  }
  string lltos(long long x) {
    string ret;
    for (; x; x /= 10) ret += x % 10 + '0';
    reverse((ret).begin(), (ret).end());
    return ret;
  }
  long long stoll(string &s) {
    long long ret = 0;
    for (auto c : s) ret *= 10, ret += c - '0';
    return ret;
  }
  template <typename T>
  void uniq(T &vec) {
    sort((vec).begin(), (vec).end());
    vec.erase(unique((vec).begin(), (vec).end()), vec.end());
  }
  template <class S, class T>
  pair<S, T> &operator+=(pair<S, T> &s, const pair<S, T> &t) {
    s.first += t.first, s.second += t.second;
    return s;
  }
  template <class S, class T>
  pair<S, T> &operator-=(pair<S, T> &s, const pair<S, T> &t) {
    s.first -= t.first, s.second -= t.second;
    return s;
  }
  template <class S, class T>
  pair<S, T> operator+(const pair<S, T> &s, const pair<S, T> &t) {
    return pair<S, T>(s.first + t.first, s.second + t.second);
  }
  template <class S, class T>
  pair<S, T> operator-(const pair<S, T> &s, const pair<S, T> &t) {
    return pair<S, T>(s.first - t.first, s.second - t.second);
  }
  template <class T>
  T dot(const pair<T, T> &s, const pair<T, T> &t) {
    return s.first * t.first + s.second * t.second;
  }
  template <class T>
  T cross(const pair<T, T> &s, const pair<T, T> &t) {
    return s.first * t.second - s.second * t.first;
  }
  template <typename T>
  ostream &operator<<(ostream &os, vector<T> &vec) {
    for (long long i = 0; (i) < (long long)(vec).size(); (i)++)
      os << vec[i] << " ";
    return os;
  }
  template <typename T>
  ostream &operator<<(ostream &os, const vector<T> &vec) {
    for (long long i = 0; (i) < (long long)(vec).size(); (i)++)
      os << vec[i] << " ";
    return os;
  }
  template <typename T>
  ostream &operator<<(ostream &os, deque<T> &deq) {
    for (long long i = 0; (i) < (long long)(deq).size(); (i)++)
      os << deq[i] << " ";
    return os;
  }
  template <typename T, typename U>
  ostream &operator<<(ostream &os, pair<T, U> &ope) {
    os << "(" << ope.first << ", " << ope.second << ")";
    return os;
  }
  template <typename T, typename U>
  ostream &operator<<(ostream &os, const pair<T, U> &ope) {
    os << "(" << ope.first << ", " << ope.second << ")";
    return os;
  }
  template <typename T, typename U>
  ostream &operator<<(ostream &os, map<T, U> &ope) {
    for (auto p : ope) os << "(" << p.first << ", " << p.second << "),";
    return os;
  }
  template <typename T>
  ostream &operator<<(ostream &os, set<T> &ope) {
    for (auto x : ope) os << x << " ";
    return os;
  }
  template <typename T>
  ostream &operator<<(ostream &os, multiset<T> &ope) {
    for (auto x : ope) os << x << " ";
    return os;
  }
  template <typename T>
  void outa(T a[], long long s, long long t) {
    for (long long i = (s); (i) <= (t); (i)++) {
      cout << a[i];
      if (i < t) cout << " ";
    }
    cout << endl;
  }
  void dump_func() { cout << endl; }
  template <class Head, class... Tail>
  void dump_func(Head &&head, Tail &&...tail) {
    cout << head;
    if (sizeof...(Tail) > 0) cout << " ";
    dump_func(std::move(tail)...);
  }
  struct NTT_Convolution {
    NTT_Convolution(){};
    static int rev(int x, int n) {
      int ret = 0;
      for (int i = 0; i < n; i++) ret <<= 1, ret |= (x >> i) & 1;
      return ret;
    }
    static void DFT(vector<mint> &f, vector<mint> &F, int n, mint root,
                    bool inv = false) {
      int N = 1 << n;
      F.resize(N);
      for (int i = 0; i < N; i++) F[rev(i, n)] = f[i];
      if (inv) root = root.inverse();
      mint a, b, x, z;
      for (int i = 0; i < n; i++) {
        int l = 1 << i;
        z = modpow(root, 1 << (n - (i + 1)));
        for (int j = 0; j < N; j += l * 2) {
          x = 1;
          for (int k = j; k < j + l; k++) {
            a = F[k], b = F[k + l] * x;
            F[k] = a + b, F[k + l] = a - b, x *= z;
          }
        }
      }
      if (inv) {
        mint Ninv = mint(N).inverse();
        for (int i = 0; i < N; i++) F[i] *= Ninv;
      }
    }
    static void conv(vector<mint> f, vector<mint> g, vector<mint> &dest) {
      long long logf = 0, logg = 0, len = f.size() + g.size();
      for (int i = f.size(); i; i /= 2) logf++;
      for (int i = g.size(); i; i /= 2) logg++;
      long long n = max(logf, logg) + 1, N = 1 << n;
      f.resize(N), g.resize(N);
      mint root = modpow(mint(3), 119 * (1 << 23 - n));
      vector<mint> F, G;
      DFT(f, F, n, root), DFT(g, G, n, root);
      for (int i = 0; i < N; i++) F[i] *= G[i];
      DFT(F, f, n, root, true);
      f.resize(len - 1);
      dest = f;
    }
  };
  struct ConvolutionMerge {
    int id;
    vector<vector<mint> > vec;
    priority_queue<pair<long long, long long>,
                   vector<pair<long long, long long> >,
                   greater<pair<long long, long long> > >
        Q;
    ConvolutionMerge() { init(); }
    void init() {
      id = 0;
      vec.clear();
      while (Q.size()) Q.pop();
      vector<mint> f;
      f.push_back(mint(1));
      add(f);
    }
    void add(vector<mint> &f) {
      Q.push(pair<long long, long long>(f.size(), id++));
      vec.push_back(f);
    }
    void calc(vector<mint> &dest) {
      while (Q.size() >= 2) {
        long long u = Q.top().second;
        Q.pop();
        long long v = Q.top().second;
        Q.pop();
        NTT_Convolution::conv(vec[u], vec[v], vec[u]);
        Q.push(pair<long long, long long>(vec[u].size(), u));
      }
      dest = vec[Q.top().second];
    }
  };
  long long n;
  vector<long long> G[250005];
  ConvolutionMerge cm;
  int main(void) {
    ios::sync_with_stdio(0);
    cin.tie(0);
    make_fact(300000);
    cin >> n;
    long long u, v;
    for (long long i = (1); (i) <= (n - 1); (i)++) {
      cin >> u >> v;
      G[u].push_back(v);
      G[v].push_back(u);
    }
    for (long long i = (1); (i) <= (n); (i)++) {
      long long deg = ((long long)(G[i]).size());
      if (i != 1) deg--;
      if (deg > 0) {
        vector<mint> f;
        f.push_back(mint(1));
        f.push_back(mint(deg));
        cm.add(f);
      }
    }
    vector<mint> res;
    cm.calc(res);
    mint ans = 0;
    for (long long i = 0; (i) < (long long)(res).size(); (i)++) {
      mint tmp = fact[n - i] * res[i];
      if (i % 2)
        ans -= tmp;
      else
        ans += tmp;
    }
    dump_func(ans);
    return 0;
  }
  