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
import java.util.*;
import java.io.*;
import java.math.BigInteger;

public class Solution
{

    static int mod = (int) (1e9+7);
    static InputReader in;
    static PrintWriter out;
    static BigInteger[][] dp;
    static int[] sum;
    static ArrayList<Integer>[] g;
    static int n;

    static void dfs(int u, int p){
        sum[u] = 1;
        for(int i = 0; i <= n; i++){
                dp[u][i] = BigInteger.ONE;
        }
        for(int v: g[u]){
            if(v == p)  continue;
            dfs(v,u);
            sum[u] += sum[v];
            for(int a = sum[u]-sum[v]; a >= 0; a--){
                for(int b = sum[v];b >= 0;b--){
                    dp[u][a+b] = dp[u][a + b].max(dp[u][a].multiply(dp[v][b]));
                }
            }
        }
        for(int i = 1; i <= sum[u]; i++){
            dp[u][0] = dp[u][0].max(dp[u][i].multiply(new BigInteger(i+"")));
        }
    }
    
    public static void main(String[] args)
    {
        in = new InputReader(System.in);
        out = new PrintWriter(System.out);            
        
        
        n = in.nextInt();
        dp = new BigInteger[n][n + 1];
        sum = new int[n + 1];
        g = new ArrayList[n];
        
        for(int i = 0; i < n; i++)
            g[i] = new ArrayList<>();
        
        for(int i = 0; i < n - 1; i++){
            int u = in.nextInt() - 1;
            int v = in.nextInt() - 1;
            g[u].add(v);
            g[v].add(u);
        }
        dfs(0,-1);

        out.println(dp[0][0]);
        
        out.close();

    }


    static void debug(Object... o)
    {
            System.out.println(Arrays.deepToString(o));
    }

    static class Pair implements Comparable<Pair>
    {

        int x,y;
        
        
        Pair (int x,int y)
        {
		this.x = x;
                this.y = y;
	}
        
	public int compareTo(Pair o)
        {
            return Integer.compare(this.x,o.x);
		//return 0;
	}

        public boolean equals(Object o)
        {
            if (o instanceof Pair)
            {
                Pair p = (Pair)o;
                return p.x == x && p.y==y;
            }
            return false;
        }

        @Override
        public String toString()
        {
            return x + " "+ y;
        }
        
        public int hashCode()
        {
            return new Long(x).hashCode() * 31 + new Long(y).hashCode();
        }
    
    } 

    static long gcd(long x,long y)
    {
        if(y==0)
                return x;
        else
                return gcd(y,x%y);
    }

    static int gcd(int x,int y)
    {
        if(y==0)
                return x;
        else 
                return gcd(y,x%y);
    }

    static long pow(long n,long p,long m)
    {
         long  result = 1;
          if(p==0)
            return 1;

        while(p!=0)
        {
            if(p%2==1)
                result *= n;
            if(result>=m)
            result%=m;
            p >>=1;
            n*=n;
            if(n>=m)
            n%=m;
        }
        return result;
    }

    static long pow(long n,long p)
    {
        long  result = 1;
          if(p==0)
            return 1;

        while(p!=0)
        {
            if(p%2==1)
                result *= n;	    
            p >>=1;
            n*=n;	    
        }
        return result;
    }

    static class InputReader
    {

        private final InputStream stream;
        private final byte[] buf = new byte[8192];
        private int curChar, snumChars;
        private SpaceCharFilter filter;

        public InputReader(InputStream stream)
        {
                this.stream = stream;
        }

        public int snext()
        {
                if (snumChars == -1)
                        throw new InputMismatchException();
                if (curChar >= snumChars)
                {
                        curChar = 0;
                        try
                        {
                                snumChars = stream.read(buf);
                        } catch (IOException e)
                        {
                                throw new InputMismatchException();
                        }
                        if (snumChars <= 0)
                                return -1;
                }
                return buf[curChar++];
        }

        public int nextInt()
        {
                int c = snext();
                while (isSpaceChar(c))
                {
                        c = snext();
                }
                int sgn = 1;
                if (c == '-')
                {
                        sgn = -1;
                        c = snext();
                }
                int res = 0;
                do
                {
                        if (c < '0' || c > '9')
                                throw new InputMismatchException();
                        res *= 10;
                        res += c - '0';
                        c = snext();
                } while (!isSpaceChar(c));
                return res * sgn;
        }

        public long nextLong()
        {
                int c = snext();
                while (isSpaceChar(c))
                {
                        c = snext();
                }
                int sgn = 1;
                if (c == '-')
                {
                        sgn = -1;
                        c = snext();
                }
                long res = 0;
                do
                {
                        if (c < '0' || c > '9')
                                throw new InputMismatchException();
                        res *= 10;
                        res += c - '0';
                        c = snext();
                } while (!isSpaceChar(c));
                return res * sgn;
        }

        public int[] nextIntArray(int n)
        {
                int a[] = new int[n];
                for (int i = 0; i < n; i++)
                {
                        a[i] = nextInt();
                }
                return a;
        }

        public long[] nextLongArray(int n)
        {
                long a[] = new long[n];
                for (int i = 0; i < n; i++)
                {
                        a[i] = nextLong();
                }
                return a;
        }

        public String readString()
        {
                int c = snext();
                while (isSpaceChar(c))
                {
                        c = snext();
                }
                StringBuilder res = new StringBuilder();
                do
                {
                        res.appendCodePoint(c);
                        c = snext();
                } while (!isSpaceChar(c));
                return res.toString();
        }

        public String nextLine()
        {
                int c = snext();
                while (isSpaceChar(c))
                        c = snext();
                StringBuilder res = new StringBuilder();
                do
                {
                        res.appendCodePoint(c);
                        c = snext();
                } while (!isEndOfLine(c));
                return res.toString();
        }

        public boolean isSpaceChar(int c)
        {
                if (filter != null)
                        return filter.isSpaceChar(c);
                return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        private boolean isEndOfLine(int c)
        {
                return c == '\n' || c == '\r' || c == -1;
        }

        public interface SpaceCharFilter
        {
                public boolean isSpaceChar(int ch);
        }

    }
}    