#include <bits/stdc++.h>
using namespace std;
const long long INF = 1e9;
const long long MOD = 1e9 + 7;
const int MAXN = 705;
const int bignumlen = 17;
const int Blen = 8;
const long long base = 100000000;
struct bignum {
  int len;
  long long data[bignumlen];
  long long &operator[](int x) { return (data[x]); }
  const long long &operator[](int x) const { return (data[x]); }
  bignum() {
    memset(data, 0, sizeof(data));
    len = 0;
  }
  void clear() {
    for (int i = len; i >= 1; --i) data[i] = 0;
    len = 0;
  }
  int check(const bignum &a, const bignum &b) {
    if (a.len > b.len) return (0);
    if (b.len > a.len) return (1);
    for (int i = a.len; i >= 1; --i) {
      if (a.data[i] < b.data[i]) return (1);
      if (b.data[i] < a.data[i]) return (0);
    }
    return 2;
  }
  bool operator<(const bignum &b) { return (check(*this, b) == 1); }
  bool operator>(const bignum &b) { return (check(*this, b) == 0); }
  bool operator<=(const bignum &b) { return (check(*this, b) >= 1); }
  bool operator>=(const bignum &b) { return (check(*this, b) % 2 == 0); }
  bool operator!=(const bignum &b) { return (check(*this, b) != 2); }
  bool operator==(const bignum &b) { return (check(*this, b) == 2); }
  bignum operator=(const bignum &x) {
    for (int i = x.len + 1; i <= len; ++i) data[i] = 0;
    for (int i = 1; i <= x.len; ++i) data[i] = x.data[i];
    len = x.len;
    return *this;
  }
  bignum operator=(long long x) {
    for (int i = len; i >= 0; --i) data[i] = 0;
    len = 0;
    while (x) {
      data[++len] = x % base;
      x /= base;
    }
    return *this;
  }
  bignum(long long x) {
    memset(data, 0, sizeof(data));
    len = 0;
    (*this) = x;
  }
  bignum operator*(const bignum &b) {
    int i, j;
    bignum tmp;
    for (i = 1; i <= len; ++i)
      if (data[i] != 0)
        for (j = 1; j <= b.len; ++j)
          if (b.data[j] != 0) {
            tmp.data[i + j - 1] += data[i] * b.data[j];
            tmp.data[i + j] += tmp.data[i + j - 1] / base;
            tmp.data[i + j - 1] %= base;
          }
    tmp.len = len + b.len - 1;
    while (tmp.data[tmp.len + 1]) tmp.len++;
    return tmp;
  }
  bignum operator*(long long x) {
    int i;
    bignum tmp;
    for (i = 1; i <= len; ++i) tmp[i] = data[i] * x;
    tmp.len = len;
    for (i = 1; i <= len; ++i) {
      tmp[i + 1] += tmp[i] / base, tmp[i] %= base;
      if (tmp[i + 1] && i + 1 > tmp.len) tmp.len++;
    }
    return tmp;
  }
  bignum operator/(long long x) {
    int i;
    bignum tmp;
    long long y = 0;
    for (i = len; i >= 1; --i) {
      y = y * base + data[i];
      tmp[i] = y / x;
      y %= x;
    }
    tmp.len = len;
    while (tmp[tmp.len] == 0 && tmp.len > 1) tmp.len--;
    return tmp;
  }
  bignum operator/(const bignum &b) {
    if (b.len <= 1 && b[1] == 0) {
      printf("error! ?0?!");
      for (;;)
        ;
    }
    int i, l1 = (len - 1) * Blen, l2 = (b.len - 1) * Blen;
    long long x = data[len], y = b[b.len];
    while (x) x /= 10, l1++;
    while (y) y /= 10, l2++;
    bignum tmp, chu, B;
    chu = *this;
    B = b;
    for (i = 1; i * Blen <= l1 - l2; ++i) B *= base;
    for (i = 1; i <= (l1 - l2) % Blen; ++i) B *= 10;
    for (i = l1 - l2; i >= 0; --i) {
      x = 0;
      while (chu >= B) chu -= B, x++;
      tmp[i / Blen + 1] = tmp[i / Blen + 1] * 10 + x;
      B /= 10;
    }
    tmp.len = (l1 - l2) / Blen + 1;
    while (tmp.len >= 1 && !tmp[tmp.len]) tmp.len--;
    return tmp;
  }
  bignum operator+(const bignum &b) {
    bignum tmp;
    int i, l = max(len, b.len);
    for (i = 1; i <= l; ++i) tmp[i] = data[i] + b[i];
    for (i = 1; i <= l; ++i) tmp[i + 1] += tmp[i] / base, tmp[i] %= base;
    tmp.len = l;
    if (tmp[tmp.len + 1]) tmp.len++;
    return tmp;
  }
  bignum operator+(long long x) {
    bignum tmp;
    tmp = *this;
    tmp[1] += x;
    for (int i = 1; i <= len && tmp[i] >= base; ++i)
      tmp[i + 1] += tmp[i] / base, tmp[i] %= base;
    while (tmp[tmp.len + 1]) tmp.len++;
    return tmp;
  }
  bignum operator-(const bignum &b) {
    int i;
    bignum tmp;
    for (i = 1; i <= len; ++i) tmp.data[i] = data[i] - b.data[i];
    for (i = 1; i <= len; ++i) {
      if (tmp[i] < 0) tmp.data[i] += base, tmp.data[i + 1]--;
    }
    tmp.len = len;
    while (tmp[tmp.len] == 0 && tmp.len > 1) tmp.len--;
    return tmp;
  }
  bignum operator-(long long x) {
    bignum tmp;
    tmp = *this;
    tmp[1] -= x;
    for (int i = 1; i <= len && tmp[i] < 0; ++i) {
      tmp[i + 1] += (tmp[i] + 1) / base - 1;
      tmp[i] = (tmp[i] + 1) % base + base - 1;
    }
    while (!tmp[tmp.len] && tmp.len > 1) tmp.len--;
    return tmp;
  }
  long long operator%(long long x) {
    int i;
    long long y = 0;
    for (i = len; i >= 1; --i) y = (y * base + data[i]) % x;
    return y;
  }
  bignum operator%(const bignum &b) {
    if (b.len <= 1 && b[1] == 0) {
      printf("error! ?0 mod!");
      for (;;)
        ;
    }
    int i, l1 = (len - 1) * Blen, l2 = (b.len - 1) * Blen;
    long long x = data[len], y = b[b.len];
    while (x) x /= 10, l1++;
    while (y) y /= 10, l2++;
    bignum chu, B;
    chu = *this;
    B = b;
    for (i = 1; i * Blen <= l1 - l2; ++i) B *= base;
    for (i = 1; i <= (l1 - l2) % Blen; ++i) B *= 10;
    for (i = l1 - l2; i >= 0; --i) {
      while (chu >= B) chu -= B;
      B /= 10;
    }
    return chu;
  }
  bignum operator+=(const bignum &b) { return *this = (*this + b); }
  bignum operator*=(const bignum &b) { return *this = (*this * b); }
  bignum operator-=(const bignum &b) { return *this = (*this - b); }
  bignum operator/=(const bignum &b) { return *this = (*this / b); }
  bignum operator%=(const bignum &b) { return *this = (*this % b); }
  bignum operator*=(long long x) { return (*this = (*this * x)); }
  bignum operator+=(long long x) { return (*this = (*this + x)); }
  bignum operator-=(long long x) { return (*this = (*this - x)); }
  bignum operator/=(long long x) { return (*this = (*this / x)); }
  void read() {
    char c[bignumlen * Blen + 10];
    scanf("%s", c + 1);
    int l = strlen(c + 1);
    (*this).clear();
    long long x;
    for (int i = 1; i <= (l - 1) / Blen + 1; ++i) {
      x = 0;
      for (int j = l - Blen * i + 1; j <= l - Blen * i + Blen; ++j)
        if (j >= 1) x = x * 10 + c[j] - 48;
      data[++len] = x;
    }
  }
  void write() {
    printf("%I64d", data[len]);
    for (int i = len - 1; i >= 1; --i) printf("%0*I64d", Blen, data[i]);
  }
};
int n;
vector<bignum> DP[MAXN];
vector<int> v[MAXN];
int sz[MAXN];
int dfs(int now, int p) {
  DP[now].push_back(0);
  DP[now].push_back(1);
  sz[now] = 1;
  for (int ea = 0; ea < v[now].size(); ea++) {
    int sek = v[now][ea];
    if (sek == p) continue;
    sz[now] += dfs(sek, now);
    vector<bignum> ans(MAXN);
    for (int j = 0; j < MAXN; j++) ans[j] = -1;
    for (int i = 1; i <= DP[now].size() - 1; i++) {
      for (int j = 1; j <= DP[sek].size() - 1; j++) {
        bignum tmp = DP[now][i] / i * DP[sek][j] / j * (i + j);
        if (tmp > ans[i + j]) ans[i + j] = tmp;
        tmp = DP[now][i] * DP[sek][j];
        if (tmp > ans[i]) ans[i] = tmp;
      }
    }
    ans[0] = 0;
    DP[now].clear();
    for (int j = 0; j < MAXN; j++) {
      if (ans[j] == -1) break;
      DP[now].push_back(ans[j]);
    }
  }
  return sz[now];
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cin >> n;
  for (int i = 0; i < n - 1; i++) {
    int a, b;
    cin >> a >> b;
    a--, b--;
    v[a].push_back(b);
    v[b].push_back(a);
  }
  dfs(0, -1);
  bignum res = DP[0][1];
  for (int i = 2; i <= DP[0].size() - 1; i++)
    if (DP[0][i] > res) res = DP[0][i];
  res.write();
}

### Prompt

In Cpp, your task is to solve the following problem:

Recently Bob invented a new game with a tree (we should remind you, that a tree is a connected graph without cycles): he deletes any (possibly, zero) amount of edges of the tree, and counts the product of sizes of the connected components left after the deletion. Your task is to find out the maximum number that Bob can get in his new game for a given tree.

Input

The first input line contains integer number n (1 ≤ n ≤ 700) — amount of vertices in the tree. The following n - 1 lines contain the description of the edges. Each line contains the pair of vertices' indexes, joined by an edge, ai, bi (1 ≤ ai, bi ≤ n). It's guaranteed that the graph described in the input is a tree.

Output

Output the only number — the maximum product of sizes of the connected components, that Bob can get after deleting some of the tree's edges.

Examples

Input

5
1 2
2 3
3 4
4 5


Output

6

Input

8
1 2
1 3
2 4
2 5
3 6
3 7
6 8


Output

18

Input

3
1 2
1 3


Output

3

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
const long long INF = 1e9;
const long long MOD = 1e9 + 7;
const int MAXN = 705;
const int bignumlen = 17;
const int Blen = 8;
const long long base = 100000000;
struct bignum {
  int len;
  long long data[bignumlen];
  long long &operator[](int x) { return (data[x]); }
  const long long &operator[](int x) const { return (data[x]); }
  bignum() {
    memset(data, 0, sizeof(data));
    len = 0;
  }
  void clear() {
    for (int i = len; i >= 1; --i) data[i] = 0;
    len = 0;
  }
  int check(const bignum &a, const bignum &b) {
    if (a.len > b.len) return (0);
    if (b.len > a.len) return (1);
    for (int i = a.len; i >= 1; --i) {
      if (a.data[i] < b.data[i]) return (1);
      if (b.data[i] < a.data[i]) return (0);
    }
    return 2;
  }
  bool operator<(const bignum &b) { return (check(*this, b) == 1); }
  bool operator>(const bignum &b) { return (check(*this, b) == 0); }
  bool operator<=(const bignum &b) { return (check(*this, b) >= 1); }
  bool operator>=(const bignum &b) { return (check(*this, b) % 2 == 0); }
  bool operator!=(const bignum &b) { return (check(*this, b) != 2); }
  bool operator==(const bignum &b) { return (check(*this, b) == 2); }
  bignum operator=(const bignum &x) {
    for (int i = x.len + 1; i <= len; ++i) data[i] = 0;
    for (int i = 1; i <= x.len; ++i) data[i] = x.data[i];
    len = x.len;
    return *this;
  }
  bignum operator=(long long x) {
    for (int i = len; i >= 0; --i) data[i] = 0;
    len = 0;
    while (x) {
      data[++len] = x % base;
      x /= base;
    }
    return *this;
  }
  bignum(long long x) {
    memset(data, 0, sizeof(data));
    len = 0;
    (*this) = x;
  }
  bignum operator*(const bignum &b) {
    int i, j;
    bignum tmp;
    for (i = 1; i <= len; ++i)
      if (data[i] != 0)
        for (j = 1; j <= b.len; ++j)
          if (b.data[j] != 0) {
            tmp.data[i + j - 1] += data[i] * b.data[j];
            tmp.data[i + j] += tmp.data[i + j - 1] / base;
            tmp.data[i + j - 1] %= base;
          }
    tmp.len = len + b.len - 1;
    while (tmp.data[tmp.len + 1]) tmp.len++;
    return tmp;
  }
  bignum operator*(long long x) {
    int i;
    bignum tmp;
    for (i = 1; i <= len; ++i) tmp[i] = data[i] * x;
    tmp.len = len;
    for (i = 1; i <= len; ++i) {
      tmp[i + 1] += tmp[i] / base, tmp[i] %= base;
      if (tmp[i + 1] && i + 1 > tmp.len) tmp.len++;
    }
    return tmp;
  }
  bignum operator/(long long x) {
    int i;
    bignum tmp;
    long long y = 0;
    for (i = len; i >= 1; --i) {
      y = y * base + data[i];
      tmp[i] = y / x;
      y %= x;
    }
    tmp.len = len;
    while (tmp[tmp.len] == 0 && tmp.len > 1) tmp.len--;
    return tmp;
  }
  bignum operator/(const bignum &b) {
    if (b.len <= 1 && b[1] == 0) {
      printf("error! ?0?!");
      for (;;)
        ;
    }
    int i, l1 = (len - 1) * Blen, l2 = (b.len - 1) * Blen;
    long long x = data[len], y = b[b.len];
    while (x) x /= 10, l1++;
    while (y) y /= 10, l2++;
    bignum tmp, chu, B;
    chu = *this;
    B = b;
    for (i = 1; i * Blen <= l1 - l2; ++i) B *= base;
    for (i = 1; i <= (l1 - l2) % Blen; ++i) B *= 10;
    for (i = l1 - l2; i >= 0; --i) {
      x = 0;
      while (chu >= B) chu -= B, x++;
      tmp[i / Blen + 1] = tmp[i / Blen + 1] * 10 + x;
      B /= 10;
    }
    tmp.len = (l1 - l2) / Blen + 1;
    while (tmp.len >= 1 && !tmp[tmp.len]) tmp.len--;
    return tmp;
  }
  bignum operator+(const bignum &b) {
    bignum tmp;
    int i, l = max(len, b.len);
    for (i = 1; i <= l; ++i) tmp[i] = data[i] + b[i];
    for (i = 1; i <= l; ++i) tmp[i + 1] += tmp[i] / base, tmp[i] %= base;
    tmp.len = l;
    if (tmp[tmp.len + 1]) tmp.len++;
    return tmp;
  }
  bignum operator+(long long x) {
    bignum tmp;
    tmp = *this;
    tmp[1] += x;
    for (int i = 1; i <= len && tmp[i] >= base; ++i)
      tmp[i + 1] += tmp[i] / base, tmp[i] %= base;
    while (tmp[tmp.len + 1]) tmp.len++;
    return tmp;
  }
  bignum operator-(const bignum &b) {
    int i;
    bignum tmp;
    for (i = 1; i <= len; ++i) tmp.data[i] = data[i] - b.data[i];
    for (i = 1; i <= len; ++i) {
      if (tmp[i] < 0) tmp.data[i] += base, tmp.data[i + 1]--;
    }
    tmp.len = len;
    while (tmp[tmp.len] == 0 && tmp.len > 1) tmp.len--;
    return tmp;
  }
  bignum operator-(long long x) {
    bignum tmp;
    tmp = *this;
    tmp[1] -= x;
    for (int i = 1; i <= len && tmp[i] < 0; ++i) {
      tmp[i + 1] += (tmp[i] + 1) / base - 1;
      tmp[i] = (tmp[i] + 1) % base + base - 1;
    }
    while (!tmp[tmp.len] && tmp.len > 1) tmp.len--;
    return tmp;
  }
  long long operator%(long long x) {
    int i;
    long long y = 0;
    for (i = len; i >= 1; --i) y = (y * base + data[i]) % x;
    return y;
  }
  bignum operator%(const bignum &b) {
    if (b.len <= 1 && b[1] == 0) {
      printf("error! ?0 mod!");
      for (;;)
        ;
    }
    int i, l1 = (len - 1) * Blen, l2 = (b.len - 1) * Blen;
    long long x = data[len], y = b[b.len];
    while (x) x /= 10, l1++;
    while (y) y /= 10, l2++;
    bignum chu, B;
    chu = *this;
    B = b;
    for (i = 1; i * Blen <= l1 - l2; ++i) B *= base;
    for (i = 1; i <= (l1 - l2) % Blen; ++i) B *= 10;
    for (i = l1 - l2; i >= 0; --i) {
      while (chu >= B) chu -= B;
      B /= 10;
    }
    return chu;
  }
  bignum operator+=(const bignum &b) { return *this = (*this + b); }
  bignum operator*=(const bignum &b) { return *this = (*this * b); }
  bignum operator-=(const bignum &b) { return *this = (*this - b); }
  bignum operator/=(const bignum &b) { return *this = (*this / b); }
  bignum operator%=(const bignum &b) { return *this = (*this % b); }
  bignum operator*=(long long x) { return (*this = (*this * x)); }
  bignum operator+=(long long x) { return (*this = (*this + x)); }
  bignum operator-=(long long x) { return (*this = (*this - x)); }
  bignum operator/=(long long x) { return (*this = (*this / x)); }
  void read() {
    char c[bignumlen * Blen + 10];
    scanf("%s", c + 1);
    int l = strlen(c + 1);
    (*this).clear();
    long long x;
    for (int i = 1; i <= (l - 1) / Blen + 1; ++i) {
      x = 0;
      for (int j = l - Blen * i + 1; j <= l - Blen * i + Blen; ++j)
        if (j >= 1) x = x * 10 + c[j] - 48;
      data[++len] = x;
    }
  }
  void write() {
    printf("%I64d", data[len]);
    for (int i = len - 1; i >= 1; --i) printf("%0*I64d", Blen, data[i]);
  }
};
int n;
vector<bignum> DP[MAXN];
vector<int> v[MAXN];
int sz[MAXN];
int dfs(int now, int p) {
  DP[now].push_back(0);
  DP[now].push_back(1);
  sz[now] = 1;
  for (int ea = 0; ea < v[now].size(); ea++) {
    int sek = v[now][ea];
    if (sek == p) continue;
    sz[now] += dfs(sek, now);
    vector<bignum> ans(MAXN);
    for (int j = 0; j < MAXN; j++) ans[j] = -1;
    for (int i = 1; i <= DP[now].size() - 1; i++) {
      for (int j = 1; j <= DP[sek].size() - 1; j++) {
        bignum tmp = DP[now][i] / i * DP[sek][j] / j * (i + j);
        if (tmp > ans[i + j]) ans[i + j] = tmp;
        tmp = DP[now][i] * DP[sek][j];
        if (tmp > ans[i]) ans[i] = tmp;
      }
    }
    ans[0] = 0;
    DP[now].clear();
    for (int j = 0; j < MAXN; j++) {
      if (ans[j] == -1) break;
      DP[now].push_back(ans[j]);
    }
  }
  return sz[now];
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cin >> n;
  for (int i = 0; i < n - 1; i++) {
    int a, b;
    cin >> a >> b;
    a--, b--;
    v[a].push_back(b);
    v[b].push_back(a);
  }
  dfs(0, -1);
  bignum res = DP[0][1];
  for (int i = 2; i <= DP[0].size() - 1; i++)
    if (DP[0][i] > res) res = DP[0][i];
  res.write();
}

```