As you know, Bob's brother lives in Flatland. In Flatland there are n cities, connected by n - 1 two-way roads. The cities are numbered from 1 to n. You can get from one city to another moving along the roads.

The «Two Paths» company, where Bob's brother works, has won a tender to repair two paths in Flatland. A path is a sequence of different cities, connected sequentially by roads. The company is allowed to choose by itself the paths to repair. The only condition they have to meet is that the two paths shouldn't cross (i.e. shouldn't have common cities).

It is known that the profit, the «Two Paths» company will get, equals the product of the lengths of the two paths. Let's consider the length of each road equals 1, and the length of a path equals the amount of roads in it. Find the maximum possible profit for the company.

Input

The first line contains an integer n (2 ≤ n ≤ 200), where n is the amount of cities in the country. The following n - 1 lines contain the information about the roads. Each line contains a pair of numbers of the cities, connected by the road ai, bi (1 ≤ ai, bi ≤ n).

Output

Output the maximum possible profit.

Examples

Input

4
1 2
2 3
3 4


Output

1


Input

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


Output

0


Input

6
1 2
2 3
2 4
5 4
6 4


Output

4
import java.io.*;
    import java.math.BigInteger;
import java.text.DecimalFormat;
import java.util.*;
 
 
 
     
     
    public  class Main {
    	public static InputReader in;
        public static PrintWriter pw;
     
     
     
    	public static void main(String args[]) 
    	{
    		new Thread(null, new Runnable() {
                public void run() {
                    try{
                        solve();
                    }
                    catch(Exception e){
                        e.printStackTrace();
                    }
                }
            }, "1", 1 << 26).start();
        }
    	static ArrayList<Integer> g[];
    	static ArrayList<Integer> h[];
    	static boolean visited[];
    	static int[] parent;
    	static int par[];
    	static int degree[];
    	static int edjes=0;
    	static int start=-1;
    	static int end=-1;
    	static int Total=0;
    	static int time1[];
    	static int time2[];
    	static int glob=0;
    	static int[] ans;
    	static boolean vis2[][];
    	//static long sum1=0;
    	//static long val[];
        static ArrayList<Integer> levels[];
        static int max=0;
        static int lev=1;
        static ArrayList<Integer> nodes[];
        static ArrayList<Integer> values[];
        static int depth[];
        static boolean found=false;
       // static long sm[];
        static int sum1=0;
        static int pre[][];
        static int subtree[];
       static  int cnt=0;
       static  HashMap<String,Integer> hm;
       static int sm[];
       static int size[];
       static long mul[];
       static long d[]=new long[1000000];
       static int tot=0;
       static long highest=(long)1e9;
       static boolean bit=false;
        static Stack<Integer> tt=new Stack();
       static HashSet<String> set=new HashSet<String>();
 	   static long fact[],num[];
 	   static long MOD=1000000007;
 	   static int value[];static int premen[];
 	   static int count=0,index=0;
 	   static double ans11[];
 	   static int price[];
 	   static ArrayList<String> hp[][];
 	   static boolean visit[][];
 	   static int cnu[]=new int[1000001];
 	   static int label=1;
 	   static int his[][];
 	   static int size1=0;
 	   static int up[],down[];
 	   static int TotalUp=0;
 	   static long dist[];
 	//   static HashMap<String,Integer> hm1=new HashMap();
 	  // static HashMap<Integer,Integer> hm2=new HashMap();
 	   static TreeSet<Long> set1=new TreeSet();
 	  static  long DP[][][]=new long[20][200][1500];
 	 	static int t=-1,n=-1;
 	 	static int two[],min[],r[];
 	 	static int total[];static int black[];
 	 	static int Parent[];
 	 	static int subtree1[][];
 	 	static int tin[],tout[],a[];
 	 public static void solve() throws FileNotFoundException{
    		
    	
    		 in = new InputReader(System.in);
    		 pw = new PrintWriter(System.out);  
    	/*	 String p=in.readString();
    	     char c[]=p.toCharArray();
    	     int z[]=new int[p.length()];
    	     z[0]=0;
    	     int left=0;
    	     int right=0;
    	     for(int i=1;i<p.length();i++)
    	     {
    	    	 if(i>right)
    	    	 {
    	    		 
    	    		 left=right=i;
    	    		 while(right<p.length()&&c[right]==c[right-left])
    	    			 right++;
    	    		 z[i]=right-left;
    	    		 right--;
    	    	 }
    	    	 else
    	    	 {
    	    		 int k=i-left;
    	    		 if(z[k]<right-i+1)
    	    		 {
    	    			 z[i]=z[k];
    	    		 }
    	    		 else
    	    		 {
    	    			 left=i;
    	    			 while(right<p.length()&&c[right]==c[right-left])
        	    			 right++;
        	    		 z[i]=right-left;
        	    		 right--;
    	    		 }
    	    	 }
    	    	  
    	     }*/
             int n=in.nextInt();
             g=new ArrayList[n+1];
             for(int i=1;i<=n;i++)
            	 g[i]=new ArrayList<Integer>();
             int u[]=new int[n];int v[]=new int[n];
             for(int i=1;i<n;i++)
             {
            	 u[i]=in.nextInt();v[i]=in.nextInt();
            	 g[u[i]].add(v[i]);g[v[i]].add(u[i]);
             }
             visited=new boolean[n+1];
              Height(1,0);        
              Arrays.fill(visited, false);
              Diameter(1,0);
              int ans=0;
              g[1].add(0);
              for(int i=1;i<=n;i++)
              {
            	  if(i!=1)
            	  {
            		  int parent=Par[i];
            		  g[parent].remove(g[parent].indexOf(i));
            		  g[i].remove(g[i].indexOf(parent));
            		  int pt[]=Arrays.copyOf(Par,n+1);
            		  int hight[]=Arrays.copyOf(high,n+1);
            		  int diat[]=Arrays.copyOf(dia,n+1);
            		  int mx1=dia[i];
            		  Arrays.fill(high,0);
            		  Arrays.fill(visited,false);
            		  Height(1,0);
            		  Arrays.fill(visited, false);
                      Arrays.fill(dia,0);
            		  Diameter(1,0);
            		  int mx2=0;
            		  for(int j=1;j<=n;j++)
            			  mx2=Math.max(mx2,dia[j]);
            		  ans=Math.max(ans, mx1*mx2);
            		  
            		  for(int j=1;j<=n;j++)
                	  {
                		  Par[j]=pt[j];
                		  high[j]=hight[j];
                		  dia[j]=diat[j];
                	  }
            	  }
            	  
            	  g=new ArrayList[n+1];
            	  for(int j=1;j<=n;j++)
            		  g[j]=new ArrayList<Integer>();
            	  for(int j=1;j<n;j++)
            	  {
            		  g[u[j]].add(v[j]);g[v[j]].add(u[j]);
            	  }
            	 
              }
              System.out.println(ans);
 	 }
 	 static int Par[]=new int[202];
 	 public static void Height(int cur,int par){
 		 Par[cur]=par;
 		 visited[cur]=true;
 		 int t=0;
 		 for(int x:g[cur])
 		 {
 			 if(!visited[x])
 			 {
 				 t++;
 				 Height(x,cur);
 				 high[cur]=Math.max(high[cur], high[x]+1);
 			 }
 		 }
 		 if(t==0)
 		 {
 			 high[cur]=0;
 		 }
 	 }
 	 static int dia[]=new int[202];
 	 static int high[]=new int[292];
 	 public static void Diameter(int curr,int parent)
 	 {
 		visited[curr]=true;
 		int trees=0;
 		ArrayList<Integer> set=new ArrayList();
 		for(int x:g[curr])
 		{
 			if(!visited[x])
 			{
 				trees++;
 				Diameter(x,curr);
 				dia[curr]=Math.max(dia[curr],high[x]);
 				set.add(high[x]);
 			}
 		}
 		if(set.size()>=2)
 		{
 			Collections.sort(set,Collections.reverseOrder());
 			dia[curr]=Math.max(dia[curr],set.get(0)+set.get(1)+2);
 		}
 		else if(set.size()>0)
 		{
 			dia[curr]=Math.max(dia[curr],set.get(0)+1);
 		}
 		if(trees==0)
 		{
 			dia[curr]=0;
 		}

 	 }
 	 
      	 
 	 public static boolean IsPal(String s)
 	 {
 		 char c[]=s.toCharArray();
 		 for(int i=0;i<c.length/2;i++)
 		 {
 			 if(c[i]!=c[s.length()-1-i])
 				 return false;
 		 }
 		 return true;
 	 }
 	public static void Merge(long[] a,int p,int r){
        if(p<r){
            int q = (p+r)/2;
            Merge(a,p,q);
            Merge(a,q+1,r);
            Merge_Array(a,p,q,r);
        }
    }
    public static void Merge_Array(long a[],int p,int q,int r){
       long b[] = new long[q-p+1];
        long c[] = new long[r-q];
        for(int i=0;i<b.length;i++)
            b[i] = a[p+i];
        for(int i=0;i<c.length;i++)
            c[i] = a[q+i+1];
        int i = 0,j = 0;
        for(int k=p;k<=r;k++){
            if(i==b.length){
                a[k] = c[j];
                j++;
            }
            else if(j==c.length){
                a[k] = b[i];
                i++;
            }
            else if(b[i]<c[j]){
                a[k] = b[i];
                i++;
            }
            else{
                a[k] = c[j];
                j++;
            }
        }
    }
 	 
 	 
 	 
 	
 	
       
 	  public static void dfs1(int curr,int parent)
 	  {
 		  visited[curr]=true;
 		  
 		  for(int x:g[curr])
 		  {
 			  
 			  if(x==parent)continue;
 			  depth[x]=depth[curr]+1;
 			  up[x]=up[curr];
 			  if(h[x].contains(curr)){
 				  up[x]++;
 				  TotalUp++;
 			  }
 			  dfs1(x,curr);
 		  }
 	  }
 	 
        
        
        public static void dfs(int curr,int Parent)
        {
        	visited[curr]=true;
        	size[curr]=1;
        	parent[curr]=Parent;
        	count++;
        	if(value[curr]>0)
        	{
        		index=value[curr];
        	}
        	for(int x:g[curr])
        	{
        		if(!visited[x])
        		{
        			dfs(x,curr);
        			size[curr]+=size[x];
        		}
        	}
        }
        static long ncr(long a, long b){
			if(b>a || b<0) return 0;
			long f = (fact[(int) a]*modInverse(((fact[(int) b]*fact[(int) (a-b)])%MOD), MOD))%MOD;
			return f;
		}
		static long modInverse(long a, long mOD2){
            return  power(a, mOD2-2, mOD2);
}
static long power(long x, long y, long m)
{
    if (y == 0)
        return 1;
    long p = power(x, y/2, m) % m;
    p = (p * p) % m;
 
    return (y%2 == 0)? p : (x * p) % m;
}
 
        public static long gcd(long x, long y) {
    		if (x == 0)
    			return y;
    		else
    			return gcd( y % x,x);
    	}	
        public static long power(long a,long b)
		{
			long result=1;
			while(b>0)
			{
				if(b%2==1)
					result*=a;
				a=a*a;
				b/=2;
			}
			return result;
		}
        static class Pair implements Comparable<Pair>{
        	//int index;
        		int s;
        		int m;
        		//int index;
        		int h;
        		Pair(int index,int value,int y){
        	     	this.s=index;
        			this.m=value;
                    	this.h=y;
        		}
        		@Override
        		public int compareTo(Pair o) {
return 1;
        		}
        				
        	}
    	static class InputReader {
     
    		private InputStream stream;
    		private 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 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 boolean isSpaceChar(int c) {
    			if (filter != null)
    				return filter.isSpaceChar(c);
    			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
    		}
     
    		public interface SpaceCharFilter {
    			public boolean isSpaceChar(int ch);
    		}
    	}
    }
 