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 int mod = 998244353;
  const int gmod = 3;
  const int inf = 1039074182;
  const double eps = 1e-9;
  const double pi = 3.141592653589793238462643383279;
  const long long llinf = 2LL * inf * inf;
  template <typename T1, typename T2>
  inline void chmin(T1 &x, T2 b) {
    if (b < x) x = b;
  }
  template <typename T1, typename T2>
  inline void chmax(T1 &x, T2 b) {
    if (b > x) x = b;
  }
  inline void chadd(int &x, int b) {
    x += b - mod;
    x += (x >> 31 & mod);
  }
  template <typename T1, typename T2>
  inline void chadd(T1 &x, T2 b) {
    x += b;
    if (x >= mod) x -= mod;
  }
  template <typename T1, typename T2>
  inline void chmul(T1 &x, T2 b) {
    x = 1LL * x * b % mod;
  }
  template <typename T1, typename T2>
  inline void chmod(T1 &x, T2 b) {
    x %= b, x += b;
    if (x >= b) x -= b;
  }
  template <typename T>
  inline T mabs(T x) {
    return (x < 0 ? -x : x);
  }
  using namespace std;
  using namespace std;
  template <typename T>
  ostream &operator<<(ostream &cout, const vector<T> &vec) {
    cout << "{";
    for (int i = 0; i < (int)vec.size(); i++) {
      cout << vec[i];
      if (i != (int)vec.size() - 1) cout << ',';
    }
    cout << "}";
    return cout;
  }
  template <typename T1, typename T2>
  ostream &operator<<(ostream &cout, pair<T1, T2> p) {
    cout << "(" << p.first << ',' << p.second << ")";
    return cout;
  }
  template <typename T, typename T2>
  ostream &operator<<(ostream &cout, set<T, T2> s) {
    vector<T> t;
    for (auto x : s) t.push_back(x);
    cout << t;
    return cout;
  }
  template <typename T, typename T2>
  ostream &operator<<(ostream &cout, multiset<T, T2> s) {
    vector<T> t;
    for (auto x : s) t.push_back(x);
    cout << t;
    return cout;
  }
  template <typename T>
  ostream &operator<<(ostream &cout, queue<T> q) {
    vector<T> t;
    while (q.size()) {
      t.push_back(q.front());
      q.pop();
    }
    cout << t;
    return cout;
  }
  template <typename T1, typename T2, typename T3>
  ostream &operator<<(ostream &cout, map<T1, T2, T3> m) {
    for (auto &x : m) {
      cout << "Key: " << x.first << ' ' << "Value: " << x.second << endl;
    }
    return cout;
  }
  template <typename T1, typename T2>
  void operator+=(pair<T1, T2> &x, const pair<T1, T2> y) {
    x.first += y.first;
    x.second += y.second;
  }
  template <typename T1, typename T2>
  pair<T1, T2> operator+(const pair<T1, T2> &x, const pair<T1, T2> &y) {
    return make_pair(x.first + y.first, x.second + y.second);
  }
  template <typename T1, typename T2>
  pair<T1, T2> operator-(const pair<T1, T2> &x, const pair<T1, T2> &y) {
    return make_pair(x.first - y.first, x.second - y.second);
  }
  template <typename T1, typename T2>
  pair<T1, T2> operator-(pair<T1, T2> x) {
    return make_pair(-x.first, -x.second);
  }
  template <typename T>
  vector<vector<T>> operator~(vector<vector<T>> vec) {
    vector<vector<T>> v;
    int n = vec.size(), m = vec[0].size();
    v.resize(m);
    for (int i = 0; i < m; i++) {
      v[i].resize(n);
    }
    for (int i = 0; i < m; i++) {
      for (int j = 0; j < n; j++) {
        v[i][j] = vec[j][i];
      }
    }
    return v;
  }
  void print0x(int x) {
    std::vector<int> vec;
    while (x) {
      vec.push_back(x & 1);
      x >>= 1;
    }
    std::reverse(vec.begin(), vec.end());
    for (int i = 0; i < (int)vec.size(); i++) {
      std::cout << vec[i];
    }
    std::cout << ' ';
  }
  template <typename T>
  void print0x(T x, int len) {
    std::vector<int> vec;
    while (x) {
      std::cout << (x & 1);
      x >>= 1;
      len--;
    }
    while (len--) cout << 0;
  }
  vector<string> vec_splitter(string s) {
    s += ',';
    vector<string> res;
    while (!s.empty()) {
      res.push_back(s.substr(0, s.find(',')));
      s = s.substr(s.find(',') + 1);
    }
    return res;
  }
  void debug_out(vector<string> __attribute__((unused)) args,
                 __attribute__((unused)) int idx,
                 __attribute__((unused)) int LINE_NUM) {
    cerr << endl;
  }
  template <typename Head, typename... Tail>
  void debug_out(vector<string> args, int idx, int LINE_NUM, Head H, Tail... T) {
    if (idx > 0)
      cerr << ", ";
    else
      cerr << "Line(" << LINE_NUM << ") ";
    stringstream ss;
    ss << H;
    cerr << args[idx] << " = " << ss.str();
    debug_out(args, idx + 1, LINE_NUM, T...);
  }
  template <int mod>
  struct ModInt {
    int x;
    ModInt() { x = 0; }
    ModInt(const int &_x) {
      x = _x % mod;
      if (x < 0) x += mod;
    }
    ModInt(const long long &_x) {
      x = _x % mod;
      if (x < 0) x += mod;
    }
    ModInt<mod> &operator++() {
      ++x;
      if (x == mod) x = 0;
      return *this;
    }
    ModInt<mod> operator++(int) {
      int t = x;
      x++;
      if (x == mod) x = 0;
      return t;
    }
    ModInt<mod> &operator--() {
      --x;
      if (x == -1) x += mod;
      return *this;
    }
    ModInt<mod> operator--(int) {
      int t = x;
      x--;
      if (x == -1) x += mod;
      return t;
    }
    ModInt<mod> operator-() const { return ModInt<mod>((x == 0 ? 0 : mod - x)); }
  };
  template <int mod>
  inline ModInt<mod> operator*(const ModInt<mod> &a, const int &c) {
    return 1LL * a.x * c % mod;
  }
  template <int mod>
  inline int mabs(const ModInt<mod> &a) {
    return a.x;
  }
  template <int mod>
  bool operator==(const ModInt<mod> &a, const ModInt<mod> &b) {
    return a.x == b.x;
  }
  template <int mod>
  bool operator!=(const ModInt<mod> &a, const ModInt<mod> &b) {
    return (a.x != b.x);
  }
  template <int mod>
  inline ModInt<mod> operator+(const ModInt<mod> &a, const ModInt<mod> &b) {
    int tmp = a.x + b.x;
    if (tmp >= mod) tmp -= mod;
    return tmp;
  }
  template <int mod>
  inline ModInt<mod> operator-(const ModInt<mod> &a, const ModInt<mod> &b) {
    int tmp = a.x - b.x;
    if (tmp < 0) tmp += mod;
    return tmp;
  }
  template <int mod>
  inline void operator-=(ModInt<mod> &a, const ModInt<mod> &b) {
    a.x -= b.x;
    a.x += (a.x >> 31 & mod);
  }
  template <int mod>
  inline ModInt<mod> operator*(const ModInt<mod> &a, const ModInt<mod> &b) {
    return 1LL * a.x * b.x % mod;
  }
  template <int mod>
  inline void operator*=(ModInt<mod> &a, const ModInt<mod> &b) {
    a.x = 1LL * a.x * b.x % mod;
  }
  template <int mod>
  inline void operator+=(ModInt<mod> &a, const ModInt<mod> &b) {
    a.x += b.x;
    if (a.x >= mod) a.x -= mod;
  }
  template <int mod>
  inline ModInt<mod> mod_inv(ModInt<mod> x) {
    int m = mod - 2;
    ModInt<mod> basic = x;
    x = 1;
    while (m) {
      if (m & 1) x *= basic;
      m >>= 1;
      basic *= basic;
    }
    return x;
  }
  template <int mod>
  ModInt<mod> operator/(const ModInt<mod> &a, const ModInt<mod> &b) {
    return a * mod_inv(b);
  }
  template <int mod>
  void operator/=(ModInt<mod> &a, const ModInt<mod> &b) {
    a = a / b;
  }
  template <int mod>
  inline ModInt<mod> operator^(const ModInt<mod> &basic, int x) {
    ModInt<mod> res = 1;
    while (x) {
      if (x & 1) res *= basic;
      basic *= basic;
      x >>= 1;
    }
    return res;
  }
  template <int mod>
  istream &operator>>(istream &cin, const ModInt<mod> &x) {
    cin >> x.x;
    x.x %= mod;
    if (x.x < 0) x.x += mod;
    return cin;
  }
  template <int mod>
  ostream &operator<<(ostream &cout, const ModInt<mod> x) {
    cout << x.x;
    return cout;
  }
  template <int mod, int root, int LogN>
  struct NTT {
    using Int = ModInt<mod>;
    static const int MaxN = (1 << LogN);
    int w[MaxN + 5];
    int fac[MaxN + 5], ifac[MaxN + 5], inum[MaxN + 5];
    int fastpow(int basic, int x) {
      int res = 1;
      while (x) {
        if (x & 1) res = 1LL * res * basic % mod;
        basic = 1LL * basic * basic % mod;
        x >>= 1;
      }
      return res;
    }
    int inv[MaxN + 5];
    int buf[MaxN + 5];
    int ww[MaxN + 5];
    inline void ntt(vector<int> &v, int rev, int lg) {
      int n = (1 << lg);
      memset(buf, 0, sizeof(int) * n);
      v.resize(n, 0);
      for (int i = 0; i < n; i++) {
        inv[i] = (inv[i >> 1] >> 1) | ((i & 1) << (lg - 1));
      }
      for (int i = 0; i < n; i++) {
        buf[i] = v[inv[i]];
      }
      int lvl = LogN;
      int *ba, *bb, *wa, *wb;
      int tmp;
      for (int b = 1; b < n; b *= 2) {
        lvl--;
        for (int i = 0; i < b * 2; i++)
          ww[i] = (rev ? w[MaxN - (i << lvl)] : w[i << lvl]);
        for (int i = 0; i < n; i += b * 2) {
          ba = buf + i;
          bb = buf + i + b;
          wa = ww;
          for (int j = 0; j < b; j++) {
            tmp = 1LL * *wa * *bb % mod;
            *bb = *ba - tmp;
            *ba += tmp - mod;
            *ba += ((*ba) >> 31 & mod);
            *bb += ((*bb) >> 31 & mod);
            ba++;
            bb++;
            wa++;
          }
        }
      }
      int t = fastpow(n, mod - 2);
      if (rev) {
        for (int i = 0; i < (1 << lg); i++) {
          buf[i] = 1LL * buf[i] * t % mod;
        }
      }
      for (int i = 0; i < (1 << lg); i++) v[i] = buf[i];
    }
    void add(const vector<int> &a, const vector<int> &b, vector<int> &c) {
      int n = a.size(), m = b.size();
      c.resize(max(n, m), 0);
      for (int i = 0; i < max(n, m); i++) {
        c[i] = (i >= n ? 0 : a[i]) + (i >= m ? 0 : b[i]) - mod;
        c[i] += (c[i] >> 31) & mod;
      }
    }
    void multiply(vector<int> a, vector<int> b, vector<int> &c) {
      int n = (int)a.size() + b.size() - 1;
      if (min(a.size(), b.size()) <= 30) {
        c.clear();
        c.resize(max(0, n), 0);
        for (int i = 0; i < (int)a.size(); i++) {
          for (int j = 0; j < (int)b.size(); j++) {
            c[i + j] = (1LL * a[i] * b[j] + c[i + j]) % mod;
          }
        }
        while (c.size() && c.back() == 0) c.pop_back();
        return;
      }
      int nn = 1, lg = 0;
      while (nn < n) {
        nn <<= 1;
        lg++;
      }
      c.resize(nn);
      a.resize(nn, 0);
      b.resize(nn, 0);
      ntt(a, 0, lg);
      ntt(b, 0, lg);
      for (int i = 0; i < nn; i++) {
        c[i] = 1LL * a[i] * b[i] % mod;
      }
      ntt(c, 1, lg);
      while (c.size() && c.back() == 0) c.pop_back();
    }
    inline void togf(vector<int> &v) {
      int n = v.size();
      for (int i = 0; i < n; i++) v[i] = 1LL * v[i] * fac[i] % mod;
    }
    inline void toegf(vector<int> &v) {
      int n = v.size();
      for (int i = 0; i < n; i++) v[i] = 1LL * v[i] * ifac[i] % mod;
    }
    void sqr(vector<int> &a) {
      int n = (int)a.size() + a.size() - 1;
      if (a.size() <= 20) {
        vector<int> res(n, 0);
        for (int i = 0; i < (int)a.size(); i++) {
          for (int j = 0; j < (int)a.size(); j++) {
            chadd(res[i + j], 1LL * a[i] * a[j] % mod);
          }
        }
        a = res;
        return;
      }
      int nn = 1, lg = 0;
      while (nn < n) {
        nn <<= 1;
        lg++;
      }
      a.resize(nn, 0);
      ntt(a, 0, lg);
      for (int i = 0; i < nn; i++) {
        a[i] = 1LL * a[i] * a[i] % mod;
      }
      ntt(a, 1, lg);
      while (a.size() && a.back() == 0) a.pop_back();
    }
    inline vector<int> derivative(const vector<int> &v) {
      int n = v.size();
      if (n == 0) return v;
      vector<int> rv(n - 1);
      for (int i = 0; i < n - 1; i++) {
        rv[i] = 1LL * v[i + 1] * (i + 1) % mod;
      }
      return rv;
    }
    inline void integral(vector<int> &v, int c = 0) {
      int n = v.size() + 1;
      v.emplace_back(0);
      for (int i = n - 1; i >= 1; i--) {
        v[i] = 1LL * inum[i] * v[i - 1] % mod;
      }
      v[0] = c;
    }
    inline void multiply(vector<int> &v, int c) {
      for (auto &x : v) {
        x = 1LL * x * c % mod;
      }
    }
    inline vector<int> add(const vector<int> &a, const vector<int> &b) {
      vector<int> v = a;
      if (v.size() < b.size()) v.resize(b.size(), 0);
      for (int i = 0; i < (int)b.size(); i++) {
        v[i] += b[i] - mod;
        v[i] += ((v[i] >> 31) & mod);
      }
      return v;
    }
    inline vector<int> sub(const vector<int> &a, const vector<int> &b) {
      vector<int> v = a;
      if (v.size() < b.size()) v.resize(b.size(), 0);
      for (int i = 0; i < (int)b.size(); i++) {
        v[i] -= b[i];
        v[i] += ((v[i] >> 31) & mod);
      }
      return v;
    }
    void inverse(vector<int> &v) {
      int n = v.size();
      if (n == 1) {
        v[0] = fastpow(v[0], mod - 2);
        return;
      }
      int tn = (n - 1) / 2 + 1;
      vector<int> f0(tn);
      for (int i = 0; i < tn; i++) f0[i] = v[i];
      inverse(f0);
      vector<int> rv = f0;
      multiply(rv, 2);
      sqr(f0);
      multiply(v, f0, f0);
      v = sub(rv, f0);
      v.resize(n);
    }
    void div(const vector<int> &F, const vector<int> &G, vector<int> &Q,
             vector<int> &R) {
      int n = F.size(), m = G.size();
      if (n < m) {
        Q.clear();
        R = F;
        return;
      }
      vector<int> f = F, g = G;
      reverse(f.begin(), f.end());
      reverse(g.begin(), g.end());
      g.resize(n - m + 1, 0);
      inverse(g);
      multiply(f, g, Q);
      Q.resize(n - m + 1, 0);
      reverse(Q.begin(), Q.end());
      multiply(G, Q, R);
      R.resize(m - 1, 0);
      for (int i = 0; i < m - 1; i++) {
        R[i] = (F[i] - R[i] + mod) % mod;
      }
    }
    void internal_multipoint_eval(const vector<int> &v, const vector<int> &u,
                                  int x, int l, int r, vector<int> &res,
                                  vector<int> *f) {
      if (l >= res.size()) return;
      if (r - l == 1) {
        res[l] = v[0];
        return;
      }
      vector<int> Q, R;
      div(v, f[x * 2], Q, R);
      internal_multipoint_eval(R, u, x * 2, l, l + r >> 1, res, f);
      div(v, f[x * 2 + 1], Q, R);
      internal_multipoint_eval(R, u, x * 2 + 1, l + r >> 1, r, res, f);
    }
    vector<int> multipoint_eval(vector<int> &v, const vector<int> &u) {
      if ((int)u.size() <= 32) {
        int n = u.size(), m = v.size();
        vector<int> res(n, 0);
        for (int i = 0; i < n; i++) {
          int ex = 1;
          for (int j = 0; j < m; j++) {
            chadd(res[i], 1LL * ex * v[j] % mod);
            ex = 1LL * ex * u[i] % mod;
          }
        }
        return res;
      }
      vector<int> *f;
      int n = u.size(), nn = 1;
      while (nn < n) nn <<= 1;
      f = new vector<int>[nn + nn];
      for (int i = 0; i < n; i++) f[nn + i] = {mod - u[i], 1};
      for (int i = n; i < nn; i++) f[nn + i] = {1};
      for (int i = nn - 1; i >= 2; i--) {
        multiply(f[i * 2], f[i * 2 + 1], f[i]);
      }
      vector<int> res(n);
      internal_multipoint_eval(v, u, 1, 0, nn, res, f);
      delete[] f;
      return res;
    }
    vector<int> interpolation(const vector<int> &x, vector<int> y) {
      int n = x.size();
      vector<int> *f = new vector<int>[n];
      vector<int> *f2 = new vector<int>[n];
      for (int i = 0; i < n; i++) {
        f[i] = {mod - x[i], 1};
      }
      for (int b = 1; b < n; b *= 2) {
        for (int i = 0; i < n; i += b * 2) {
          if (i + b < n) multiply(f[i], f[i + b], f[i]);
        }
      }
      vector<int> M = f[0], dM = derivative(M);
      vector<int> tmp = multipoint_eval(dM, x);
      for (int i = 0; i < n; i++) {
        y[i] = 1LL * y[i] * fastpow(tmp[i], mod - 2) % mod;
      }
      for (int i = 0; i < n; i++) {
        f[i] = {mod - x[i], 1};
        f2[i] = {y[i]};
      }
      for (int b = 1; b < n; b <<= 1) {
        for (int i = 0; i < n; i += b * 2) {
          if (i + b < n) {
            vector<int> tmp;
            multiply(f2[i], f[i + b], tmp);
            multiply(f[i], f2[i + b], f2[i]);
            f2[i] = add(f2[i], tmp);
            multiply(f[i], f[i + b], f[i]);
          }
        }
      }
      vector<int> res = f2[0];
      delete[] f2;
      delete[] f;
      return res;
    }
    vector<int> log(const vector<int> &v) {
      int n = v.size();
      vector<int> dv = derivative(v), iv = v;
      inverse(iv);
      multiply(dv, iv, dv);
      integral(dv);
      dv.resize(n);
      return dv;
    }
    vector<int> exp(const vector<int> &v) {
      int n = v.size(), tn = (n - 1) / 2 + 1;
      vector<int> rv;
      if (n == 1) {
        rv.push_back(1);
        return rv;
      }
      vector<int> f0(tn);
      for (int i = 0; i < tn; i++) f0[i] = v[i];
      f0 = exp(f0);
      f0.resize(n, 0);
      vector<int> rhs(1, 1);
      rhs = sub(rhs, log(f0));
      rhs = add(rhs, v);
      multiply(f0, rhs, f0);
      f0.resize(n);
      return f0;
    }
    inline void multiply(const vector<Int> &a, const vector<Int> &b,
                         vector<Int> &c) {
      vector<int> ta(a.size()), tb(b.size());
      for (int i = 0; i < (int)a.size(); i++) ta[i] = a[i].x;
      for (int i = 0; i < (int)b.size(); i++) tb[i] = b[i].x;
      vector<int> tc;
      multiply(ta, tb, tc);
      c.clear();
      c.resize(tc.size());
      for (int i = 0; i < (int)c.size(); i++) c[i].x = tc[i];
    }
    vector<Int> multiply(const vector<Int> &a, const vector<Int> &b) {
      vector<int> ta(a.size()), tb(b.size());
      for (int i = 0; i < (int)a.size(); i++) ta[i] = a[i].x;
      for (int i = 0; i < (int)b.size(); i++) tb[i] = b[i].x;
      vector<int> tc;
      multiply(ta, tb, tc);
      vector<Int> c(tc.size());
      for (int i = 0; i < (int)c.size(); i++) c[i].x = tc[i];
      return c;
    }
    vector<int> pow(vector<int> bas, int n, int n2) {
      int c0 = 0;
      for (int i = 0; i < (int)bas.size(); i++) {
        if (bas[i]) break;
        c0 = i + 1;
      }
      for (int i = 0; i < (int)bas.size() - c0; i++) bas[i] = bas[i + c0];
      for (int i = 0; i < c0; i++) bas.pop_back();
      int c = bas[0], inum = fastpow(bas[0], mod - 2);
      for (auto &x : bas) x = 1LL * x * inum % mod;
      bas = log(bas);
      for (auto &x : bas) x = 1LL * x * (n % mod) % mod;
      bas = exp(bas);
      c = fastpow(c, n2);
      for (auto &x : bas) x = 1LL * x * c % mod;
      auto safepow = [](int x, long long n, long long lim) -> int {
        if (x == 1) return min(1LL, lim);
        if (x == 0) return 0;
        long long res = 1;
        for (int i = 0; i < n; i++) {
          res *= x;
          if (res > lim) break;
        }
        res = min(res, lim);
      };
      c0 = safepow(c0, n, bas.size());
      for (int i = c0; i < (int)bas.size(); i++) {
        bas[i] = bas[i - c0];
      }
      for (int i = 0; i < c0; i++) bas[i] = 0;
      return bas;
    }
    NTT() {
      w[0] = 1;
      int ur = fastpow(root, (mod - 1) >> LogN);
      fac[0] = 1;
      for (int i = 1; i <= MaxN; i++) {
        w[i] = 1LL * w[i - 1] * ur % mod;
        fac[i] = 1LL * fac[i - 1] * i % mod;
      }
      ifac[MaxN] = fastpow(fac[MaxN], mod - 2);
      for (int i = MaxN - 1; i >= 0; i--) {
        ifac[i] = 1LL * ifac[i + 1] * (i + 1) % mod;
      }
      for (int i = 1; i <= MaxN; i++) {
        inum[i] = 1LL * ifac[i] * fac[i - 1] % mod;
      }
    }
  };
  namespace combinatorics {
  int *fac;
  int *ifac;
  int __Tmod;
  inline int add(int a, int b) { return (a + b) % __Tmod; }
  inline int sub(int a, int b) { return (a - b + __Tmod) % __Tmod; }
  inline int mult(int a, int b) { return (1LL * a * b) % __Tmod; }
  inline int fastpow(int basic, int x) {
    chmod(x, __Tmod - 1);
    if (x == 0) return 1;
    int res = 1;
    while (x) {
      if (x & 1) res = mult(res, basic);
      basic = mult(basic, basic);
      x >>= 1;
    }
    return res;
  }
  inline int inv(int x) { return fastpow(x, __Tmod - 2); }
  inline int div(int a, int b) { return mult(a, inv(b)); }
  void init(int n, int tmod) {
    __Tmod = tmod;
    fac = new int[n + 5];
    ifac = new int[n + 5];
    fac[0] = 1;
    for (int i = 1; i <= n; i++) {
      fac[i] = mult(fac[i - 1], i);
    }
    ifac[n] = inv(fac[n]);
    for (int i = n - 1; i >= 0; i--) {
      ifac[i] = mult(ifac[i + 1], i + 1);
    }
  }
  inline int C(int n, int m) {
    if (n < m || n < 0 || m < 0) return 0;
    return mult(mult(fac[n], ifac[m]), ifac[n - m]);
  }
  inline int Cat(int x) { return mult(C(x * 2, x), inv(x + 1)); }
  }  // namespace combinatorics
  using namespace std;
  int n;
  vector<int> edges[250005];
  int s;
  map<int, int> degs;
  vector<int> F[250005];
  NTT<mod, 3, 19> ntt;
  int vis[250005];
  void dfs(int x, int par) {
    int deg = 0;
    for (auto u : edges[x]) {
      if (u == par) continue;
      dfs(u, x);
      deg++;
    }
    degs[deg]++;
  }
  inline int fastpow(long long basic, int x) {
    long long res = 1;
    while (x) {
      if (x & 1) (res *= basic) %= mod;
      (basic *= basic) %= mod;
      x >>= 1;
    }
    return res;
  }
  int pw[250005];
  int main() {
    combinatorics::init(250000, mod);
    cin >> n;
    for (int i = 0; i < n - 1; i++) {
      int x, y;
      scanf("%d%d", &x, &y);
      x--;
      y--;
      edges[x].emplace_back(y);
      edges[y].emplace_back(x);
    }
    dfs(0, -1);
    int m = 0;
    int l = 0;
    for (auto [d, s] : degs) {
      if (d == 0) {
        l = s;
        continue;
      }
      F[m].resize(s + 1);
      pw[0] = 1;
      for (int i = 1; i <= s; i++) pw[i] = 1LL * pw[i - 1] * d % mod;
      for (int i = 0; i <= s; i++)
        F[m][i] = 1LL * combinatorics::C(s, i) * pw[s - i] % mod;
      m++;
    }
    for (int i = 0; i < m - 1; i++) {
      int t1 = -1, t2 = -1;
      for (int j = 0; j < m; j++) {
        if (vis[j]) continue;
        if (t1 == -1)
          t1 = j;
        else if (t2 == -1)
          t2 = j;
        else {
          if (F[j].size() < F[t2].size()) t2 = j;
        }
        if (t2 != -1 && F[t2].size() < F[t1].size()) swap(t1, t2);
      }
      if (t1 > t2) swap(t1, t2);
      ntt.multiply(F[t1], F[t2], F[t1]);
      vis[t2] = 1;
    }
    int res = 0;
    for (int i = 0; i <= n - l; i++) {
      int v = 1LL * F[0][i] * combinatorics::fac[i + l] % mod;
      if ((n - l - i) & 1)
        chadd(res, mod - v);
      else
        chadd(res, v);
    }
    cout << res << endl;
    return 0;
  }
  