#include <bits/stdc++.h>
using namespace std;
template <class T>
void _R(T &x) {
  cin >> x;
}
void _R(int &x) { scanf("%d", &x); }
void _R(int64_t &x) { scanf("%lld", &x); }
void _R(double &x) { scanf("%lf", &x); }
void _R(char &x) { scanf(" %c", &x); }
void _R(char *x) { scanf("%s", x); }
void R() {}
template <class T, class... U>
void R(T &head, U &...tail) {
  _R(head);
  R(tail...);
}
template <class T>
void _W(const T &x) {
  cout << x;
}
void _W(const int &x) { printf("%d", x); }
void _W(const int64_t &x) { printf("%lld", x); }
void _W(const double &x) { printf("%.16f", x); }
void _W(const char &x) { putchar(x); }
void _W(const char *x) { printf("%s", x); }
template <class T, class U>
void _W(const pair<T, U> &x) {
  _W(x.first);
  putchar(' ');
  _W(x.second);
}
template <class T>
void _W(const vector<T> &x) {
  for (auto i = x.begin(); i != x.end(); _W(*i++))
    if (i != x.cbegin()) putchar(' ');
}
void W() {}
template <class T, class... U>
void W(const T &head, const U &...tail) {
  _W(head);
  putchar(sizeof...(tail) ? ' ' : '\n');
  W(tail...);
}
int MOD = 998244353;
void ADD(long long &x, long long v) {
  x = (x + v) % MOD;
  if (x < 0) x += MOD;
}
const int SIZE = 1 << 20;
long long mypow(long long x, long long y) {
  long long res = 1;
  while (y) {
    if (y & 1) res = res * x % MOD;
    y >>= 1;
    x = x * x % MOD;
  }
  return res;
}
void add(int &a, int b) {
  a += b;
  if (a >= MOD) a -= MOD;
}
void sub(int &a, int b) {
  a -= b;
  if (a < 0) a += MOD;
}
int mult(int a, int b) { return (long long)a * b % MOD; }
const int inv2 = (MOD + 1) / 2;
namespace NTT {
using T = int;
const int MAXB = 21;
const int MAXN = 1 << MAXB;
int rev[MAXN];
void ntt(T *a, int K, bool inv) {
  const int n = 1 << K;
  rev[0] = 0;
  for (int i = (1); i < (n); ++i) {
    rev[i] = (rev[i >> 1] >> 1) ^ ((i & 1) << (K - 1));
  }
  for (int i = 0; i < (n); ++i) {
    if (i < rev[i]) {
      swap(a[i], a[rev[i]]);
    }
  }
  for (int len = 1; len < n; len *= 2) {
    vector<T> roots(len);
    roots[0] = 1;
    if (len > 1) {
      roots[1] = mypow(3, (MOD - 1) / (2 * len));
    }
    for (int i = (2); i < (len); ++i) {
      roots[i] = mult(roots[i >> 1], roots[(i + 1) >> 1]);
    }
    for (int i = 0; i < n; i += len * 2) {
      for (int j = 0; j < (len); ++j) {
        const auto &w = roots[j];
        const auto x = a[i + j];
        const auto y = mult(a[i + len + j], w);
        a[i + j] = x;
        add(a[i + j], y);
        a[i + len + j] = x;
        sub(a[i + len + j], y);
        if (inv) {
          a[i + j] = mult(a[i + j], inv2);
          a[i + len + j] = mult(a[i + j + len], inv2);
        }
      }
    }
  }
  if (inv) {
    reverse(a + 1, a + n);
  }
}
vector<int> brut_mult(const vector<int> &a, const vector<int> &b) {
  vector<int> c(((int)(a).size()) + ((int)(b).size()));
  for (int i = 0; i < (((int)(a).size())); ++i) {
    for (int j = 0; j < (((int)(b).size())); ++j) {
      add(c[i + j], ::mult(a[i], b[j]));
    }
  }
  return c;
}
vector<int> powr(const vector<int> &a, int m) {
  if (!m) return {1};
  int K = 0;
  while ((1 << K) < ((int)(a).size()) * m) {
    ++K;
  }
  ++K;
  vector<T> A(1 << K);
  for (int i = 0; i < (((int)(a).size())); ++i) {
    A[i] = a[i];
  }
  ntt(A.data(), K, false);
  for (int i = 0; i < (((int)(A).size())); ++i) {
    A[i] = mypow(A[i], m);
  }
  ntt(A.data(), K, true);
  vector<int> res(((int)(A).size()));
  for (int i = 0; i < (((int)(res).size())); ++i) {
    res[i] = A[i];
  }
  int len = ((int)(res).size());
  while (len > 1 && res[len - 1] == 0) len--;
  res.resize(len);
  return res;
}
vector<int> mult(const vector<int> &a, const vector<int> &b) {
  int K = 0;
  while ((1 << K) < max(((int)(a).size()), ((int)(b).size()))) {
    ++K;
  }
  ++K;
  vector<T> A(1 << K);
  vector<T> B(1 << K);
  for (int i = 0; i < (((int)(a).size())); ++i) {
    A[i] = a[i];
  }
  for (int i = 0; i < (((int)(b).size())); ++i) {
    B[i] = b[i];
  }
  ntt(A.data(), K, false);
  ntt(B.data(), K, false);
  for (int i = 0; i < (((int)(A).size())); ++i) {
    A[i] = ::mult(A[i], B[i]);
  }
  ntt(A.data(), K, true);
  vector<int> res(((int)(A).size()));
  for (int i = 0; i < (((int)(A).size())); ++i) {
    res[i] = A[i];
  }
  int len = ((int)(res).size());
  while (len > 1 && res[len - 1] == 0) len--;
  res.resize(len);
  return res;
}
};  // namespace NTT
int n;
vector<int> e[SIZE];
vector<int> gg;
vector<int> AA;
void dfs(int x, int lt) {
  int deg = 0;
  for (int y : e[x]) {
    if (y == lt) continue;
    dfs(y, x);
    deg++;
  }
  if (deg) AA.push_back(deg);
}
vector<int> poly[SIZE];
void build(int L, int R, int id) {
  if (L == R) {
    poly[id] = {1, AA[L]};
    return;
  }
  int mm = (L + R) / 2;
  build(L, mm, id * 2);
  build(mm + 1, R, id * 2 + 1);
  poly[id] = NTT::mult(poly[id * 2], poly[id * 2 + 1]);
}
const int COMBINATION_SIZE = 1 << 21;
long long mypow(long long x, long long y, long long mod = MOD) {
  long long res = 1;
  while (y) {
    if (y & 1) {
      res = res * x % mod;
    }
    y >>= 1;
    x = x * x % mod;
  }
  return res;
}
long long fac[SIZE];
void solve() {
  dfs(1, 1);
  build(0, ((int)(AA).size()) - 1, 1);
  long long an = 0;
  int ng = 1;
  for (int i = 0; i < (((int)(poly[1]).size())); ++i) {
    ADD(an, ng * (long long)poly[1][i] * fac[n - i]);
    ng = -ng;
  }
  W(an);
}
void input() {
  R(n);
  fac[0] = 1;
  for (int i = (1); i <= (n); ++i) fac[i] = fac[i - 1] * i % MOD;
  for (int i = (1); i < (n); ++i) {
    int x, y;
    R(x, y);
    e[x].push_back(y);
    e[y].push_back(x);
  }
}
int main() {
  input();
  solve();
  return 0;
}

### Prompt

Construct a cpp code solution to the problem outlined:

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

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
template <class T>
void _R(T &x) {
  cin >> x;
}
void _R(int &x) { scanf("%d", &x); }
void _R(int64_t &x) { scanf("%lld", &x); }
void _R(double &x) { scanf("%lf", &x); }
void _R(char &x) { scanf(" %c", &x); }
void _R(char *x) { scanf("%s", x); }
void R() {}
template <class T, class... U>
void R(T &head, U &...tail) {
  _R(head);
  R(tail...);
}
template <class T>
void _W(const T &x) {
  cout << x;
}
void _W(const int &x) { printf("%d", x); }
void _W(const int64_t &x) { printf("%lld", x); }
void _W(const double &x) { printf("%.16f", x); }
void _W(const char &x) { putchar(x); }
void _W(const char *x) { printf("%s", x); }
template <class T, class U>
void _W(const pair<T, U> &x) {
  _W(x.first);
  putchar(' ');
  _W(x.second);
}
template <class T>
void _W(const vector<T> &x) {
  for (auto i = x.begin(); i != x.end(); _W(*i++))
    if (i != x.cbegin()) putchar(' ');
}
void W() {}
template <class T, class... U>
void W(const T &head, const U &...tail) {
  _W(head);
  putchar(sizeof...(tail) ? ' ' : '\n');
  W(tail...);
}
int MOD = 998244353;
void ADD(long long &x, long long v) {
  x = (x + v) % MOD;
  if (x < 0) x += MOD;
}
const int SIZE = 1 << 20;
long long mypow(long long x, long long y) {
  long long res = 1;
  while (y) {
    if (y & 1) res = res * x % MOD;
    y >>= 1;
    x = x * x % MOD;
  }
  return res;
}
void add(int &a, int b) {
  a += b;
  if (a >= MOD) a -= MOD;
}
void sub(int &a, int b) {
  a -= b;
  if (a < 0) a += MOD;
}
int mult(int a, int b) { return (long long)a * b % MOD; }
const int inv2 = (MOD + 1) / 2;
namespace NTT {
using T = int;
const int MAXB = 21;
const int MAXN = 1 << MAXB;
int rev[MAXN];
void ntt(T *a, int K, bool inv) {
  const int n = 1 << K;
  rev[0] = 0;
  for (int i = (1); i < (n); ++i) {
    rev[i] = (rev[i >> 1] >> 1) ^ ((i & 1) << (K - 1));
  }
  for (int i = 0; i < (n); ++i) {
    if (i < rev[i]) {
      swap(a[i], a[rev[i]]);
    }
  }
  for (int len = 1; len < n; len *= 2) {
    vector<T> roots(len);
    roots[0] = 1;
    if (len > 1) {
      roots[1] = mypow(3, (MOD - 1) / (2 * len));
    }
    for (int i = (2); i < (len); ++i) {
      roots[i] = mult(roots[i >> 1], roots[(i + 1) >> 1]);
    }
    for (int i = 0; i < n; i += len * 2) {
      for (int j = 0; j < (len); ++j) {
        const auto &w = roots[j];
        const auto x = a[i + j];
        const auto y = mult(a[i + len + j], w);
        a[i + j] = x;
        add(a[i + j], y);
        a[i + len + j] = x;
        sub(a[i + len + j], y);
        if (inv) {
          a[i + j] = mult(a[i + j], inv2);
          a[i + len + j] = mult(a[i + j + len], inv2);
        }
      }
    }
  }
  if (inv) {
    reverse(a + 1, a + n);
  }
}
vector<int> brut_mult(const vector<int> &a, const vector<int> &b) {
  vector<int> c(((int)(a).size()) + ((int)(b).size()));
  for (int i = 0; i < (((int)(a).size())); ++i) {
    for (int j = 0; j < (((int)(b).size())); ++j) {
      add(c[i + j], ::mult(a[i], b[j]));
    }
  }
  return c;
}
vector<int> powr(const vector<int> &a, int m) {
  if (!m) return {1};
  int K = 0;
  while ((1 << K) < ((int)(a).size()) * m) {
    ++K;
  }
  ++K;
  vector<T> A(1 << K);
  for (int i = 0; i < (((int)(a).size())); ++i) {
    A[i] = a[i];
  }
  ntt(A.data(), K, false);
  for (int i = 0; i < (((int)(A).size())); ++i) {
    A[i] = mypow(A[i], m);
  }
  ntt(A.data(), K, true);
  vector<int> res(((int)(A).size()));
  for (int i = 0; i < (((int)(res).size())); ++i) {
    res[i] = A[i];
  }
  int len = ((int)(res).size());
  while (len > 1 && res[len - 1] == 0) len--;
  res.resize(len);
  return res;
}
vector<int> mult(const vector<int> &a, const vector<int> &b) {
  int K = 0;
  while ((1 << K) < max(((int)(a).size()), ((int)(b).size()))) {
    ++K;
  }
  ++K;
  vector<T> A(1 << K);
  vector<T> B(1 << K);
  for (int i = 0; i < (((int)(a).size())); ++i) {
    A[i] = a[i];
  }
  for (int i = 0; i < (((int)(b).size())); ++i) {
    B[i] = b[i];
  }
  ntt(A.data(), K, false);
  ntt(B.data(), K, false);
  for (int i = 0; i < (((int)(A).size())); ++i) {
    A[i] = ::mult(A[i], B[i]);
  }
  ntt(A.data(), K, true);
  vector<int> res(((int)(A).size()));
  for (int i = 0; i < (((int)(A).size())); ++i) {
    res[i] = A[i];
  }
  int len = ((int)(res).size());
  while (len > 1 && res[len - 1] == 0) len--;
  res.resize(len);
  return res;
}
};  // namespace NTT
int n;
vector<int> e[SIZE];
vector<int> gg;
vector<int> AA;
void dfs(int x, int lt) {
  int deg = 0;
  for (int y : e[x]) {
    if (y == lt) continue;
    dfs(y, x);
    deg++;
  }
  if (deg) AA.push_back(deg);
}
vector<int> poly[SIZE];
void build(int L, int R, int id) {
  if (L == R) {
    poly[id] = {1, AA[L]};
    return;
  }
  int mm = (L + R) / 2;
  build(L, mm, id * 2);
  build(mm + 1, R, id * 2 + 1);
  poly[id] = NTT::mult(poly[id * 2], poly[id * 2 + 1]);
}
const int COMBINATION_SIZE = 1 << 21;
long long mypow(long long x, long long y, long long mod = MOD) {
  long long res = 1;
  while (y) {
    if (y & 1) {
      res = res * x % mod;
    }
    y >>= 1;
    x = x * x % mod;
  }
  return res;
}
long long fac[SIZE];
void solve() {
  dfs(1, 1);
  build(0, ((int)(AA).size()) - 1, 1);
  long long an = 0;
  int ng = 1;
  for (int i = 0; i < (((int)(poly[1]).size())); ++i) {
    ADD(an, ng * (long long)poly[1][i] * fac[n - i]);
    ng = -ng;
  }
  W(an);
}
void input() {
  R(n);
  fac[0] = 1;
  for (int i = (1); i <= (n); ++i) fac[i] = fac[i - 1] * i % MOD;
  for (int i = (1); i < (n); ++i) {
    int x, y;
    R(x, y);
    e[x].push_back(y);
    e[y].push_back(x);
  }
}
int main() {
  input();
  solve();
  return 0;
}

```