#include<bits/stdc++.h>

using namespace std;

struct Combination
{
  int mod;
  vector< int64_t > mfact, rfact;

  Combination(int sz, int mod) : mfact(sz + 1), rfact(sz + 1), mod(mod)
  {
    mfact[0] = 1;
    for(int i = 1; i < mfact.size(); i++) {
      mfact[i] = mfact[i - 1] * i % mod;
    }
    rfact[sz] = inv(mfact[sz]);
    for(int i = sz - 1; i >= 0; i--) {
      rfact[i] = rfact[i + 1] * (i + 1) % mod;
    }
  }

  int64_t fact(int k) const
  {
    return (mfact[k]);
  }

  int64_t pow(int64_t x, int64_t n) const
  {
    int64_t ret = 1;
    while(n > 0) {
      if(n & 1) (ret *= x) %= mod;
      (x *= x) %= mod;
      n >>= 1;
    }
    return (ret);
  }

  int64_t inv(int64_t x) const
  {
    return (pow(x, mod - 2));
  }

  int64_t P(int n, int r) const
  {
    if(r < 0 || n < r) return (0);
    return (mfact[n] * rfact[n - r] % mod);
  }

  int64_t C(int p, int q) const
  {
    if(q < 0 || p < q) return (0);
    return (mfact[p] * rfact[q] % mod * rfact[p - q] % mod);
  }

  int64_t H(int n, int r) const
  {
    if(n < 0 || r < 0) return (0);
    return (r == 0 ? 1 : C(n + r - 1, r));
  }
};

using int64 = long long;
const int INF = 1 << 30;
const int mod = 1e9 + 7;

int N;
vector< int > g[5000];
int sub[5000];
int centroid_sz = INF;
vector< int > centroid;
Combination comb(5001, mod);

int build_dfs(int idx, int par)
{
  sub[idx] = 1;
  for(auto &to : g[idx]) {
    if(to == par) continue;
    sub[idx] += build_dfs(to, idx);
  }
  return (sub[idx]);
}


void build_centroid(int idx, int par, const int all)
{
  int connect = all - sub[idx];
  for(auto &to : g[idx]) {
    if(to == par) continue;
    build_centroid(to, idx, all);
    connect = max(connect, sub[to]);
  }
  if(connect < centroid_sz) {
    centroid_sz = connect;
    centroid.clear();
  }
  if(connect == centroid_sz) {
    centroid.emplace_back(idx);
  }
}


int main()
{
  cin >> N;
  for(int i = 1; i < N; i++) {
    int x, y;
    cin >> x >> y;
    --x, --y;
    g[x].push_back(y);
    g[y].push_back(x);
  }
  build_centroid(0, -1, build_dfs(0, -1));
  assert(centroid.size() <= 2);
  if(centroid.size() == 2) {
    cout << comb.fact(N / 2) * comb.fact(N / 2) % mod << endl;
    return (0);
  }
  build_dfs(centroid[0], -1);


  int sz = 1;
  vector< int > dp1(1);
  dp1[0] = 1;
  for(auto &to : g[centroid[0]]) {
    vector< int > dp2(sz + sub[to]);
    for(int i = 0; i < sz; i++) {
      for(int j = 0; j <= sub[to]; j++) {
        (dp2[i + j] += dp1[i] * comb.P(sub[to], j) % mod * comb.C(sub[to], j) % mod) %= mod;
      }
    }
    sz += sub[to];
    dp1.swap(dp2);
  }
  int ret = 0;
  for(int i = 0; i < N; i++) {
    if(i % 2 == 0) (ret += dp1[i] * comb.fact(N - i) % mod) %= mod;
    else (ret += mod - dp1[i] * comb.fact(N - i) % mod) %= mod;
  }
  cout << ret << endl;
}


### Prompt

Please formulate a Cpp solution to the following problem:

There is a tree with N vertices. The vertices are numbered 1 through N. The i-th edge (1 \leq i \leq N - 1) connects Vertex x_i and y_i. For vertices v and w (1 \leq v, w \leq N), we will define the distance between v and w d(v, w) as "the number of edges contained in the path v-w".

A squirrel lives in each vertex of the tree. They are planning to move, as follows. First, they will freely choose a permutation of (1, 2, ..., N), p = (p_1, p_2, ..., p_N). Then, for each 1 \leq i \leq N, the squirrel that lived in Vertex i will move to Vertex p_i.

Since they like long travels, they have decided to maximize the total distance they traveled during the process. That is, they will choose p so that d(1, p_1) + d(2, p_2) + ... + d(N, p_N) will be maximized. How many such ways are there to choose p, modulo 10^9 + 7?

Constraints

* 2 \leq N \leq 5,000
* 1 \leq x_i, y_i \leq N
* The input graph is a tree.

Input

Input is given from Standard Input in the following format:


N
x_1 y_1
x_2 y_2
:
x_{N - 1} y_{N - 1}


Output

Print the number of the ways to choose p so that the condition is satisfied, modulo 10^9 + 7.

Examples

Input

3
1 2
2 3


Output

3


Input

4
1 2
1 3
1 4


Output

11


Input

6
1 2
1 3
1 4
2 5
2 6


Output

36


Input

7
1 2
6 3
4 5
1 7
1 5
2 3


Output

396

### Response

```cpp
#include<bits/stdc++.h>

using namespace std;

struct Combination
{
  int mod;
  vector< int64_t > mfact, rfact;

  Combination(int sz, int mod) : mfact(sz + 1), rfact(sz + 1), mod(mod)
  {
    mfact[0] = 1;
    for(int i = 1; i < mfact.size(); i++) {
      mfact[i] = mfact[i - 1] * i % mod;
    }
    rfact[sz] = inv(mfact[sz]);
    for(int i = sz - 1; i >= 0; i--) {
      rfact[i] = rfact[i + 1] * (i + 1) % mod;
    }
  }

  int64_t fact(int k) const
  {
    return (mfact[k]);
  }

  int64_t pow(int64_t x, int64_t n) const
  {
    int64_t ret = 1;
    while(n > 0) {
      if(n & 1) (ret *= x) %= mod;
      (x *= x) %= mod;
      n >>= 1;
    }
    return (ret);
  }

  int64_t inv(int64_t x) const
  {
    return (pow(x, mod - 2));
  }

  int64_t P(int n, int r) const
  {
    if(r < 0 || n < r) return (0);
    return (mfact[n] * rfact[n - r] % mod);
  }

  int64_t C(int p, int q) const
  {
    if(q < 0 || p < q) return (0);
    return (mfact[p] * rfact[q] % mod * rfact[p - q] % mod);
  }

  int64_t H(int n, int r) const
  {
    if(n < 0 || r < 0) return (0);
    return (r == 0 ? 1 : C(n + r - 1, r));
  }
};

using int64 = long long;
const int INF = 1 << 30;
const int mod = 1e9 + 7;

int N;
vector< int > g[5000];
int sub[5000];
int centroid_sz = INF;
vector< int > centroid;
Combination comb(5001, mod);

int build_dfs(int idx, int par)
{
  sub[idx] = 1;
  for(auto &to : g[idx]) {
    if(to == par) continue;
    sub[idx] += build_dfs(to, idx);
  }
  return (sub[idx]);
}


void build_centroid(int idx, int par, const int all)
{
  int connect = all - sub[idx];
  for(auto &to : g[idx]) {
    if(to == par) continue;
    build_centroid(to, idx, all);
    connect = max(connect, sub[to]);
  }
  if(connect < centroid_sz) {
    centroid_sz = connect;
    centroid.clear();
  }
  if(connect == centroid_sz) {
    centroid.emplace_back(idx);
  }
}


int main()
{
  cin >> N;
  for(int i = 1; i < N; i++) {
    int x, y;
    cin >> x >> y;
    --x, --y;
    g[x].push_back(y);
    g[y].push_back(x);
  }
  build_centroid(0, -1, build_dfs(0, -1));
  assert(centroid.size() <= 2);
  if(centroid.size() == 2) {
    cout << comb.fact(N / 2) * comb.fact(N / 2) % mod << endl;
    return (0);
  }
  build_dfs(centroid[0], -1);


  int sz = 1;
  vector< int > dp1(1);
  dp1[0] = 1;
  for(auto &to : g[centroid[0]]) {
    vector< int > dp2(sz + sub[to]);
    for(int i = 0; i < sz; i++) {
      for(int j = 0; j <= sub[to]; j++) {
        (dp2[i + j] += dp1[i] * comb.P(sub[to], j) % mod * comb.C(sub[to], j) % mod) %= mod;
      }
    }
    sz += sub[to];
    dp1.swap(dp2);
  }
  int ret = 0;
  for(int i = 0; i < N; i++) {
    if(i % 2 == 0) (ret += dp1[i] * comb.fact(N - i) % mod) %= mod;
    else (ret += mod - dp1[i] * comb.fact(N - i) % mod) %= mod;
  }
  cout << ret << endl;
}


```