Andrew and Jerry are playing a game with Harry as the scorekeeper. The game consists of three rounds. In each round, Andrew and Jerry draw randomly without replacement from a jar containing n balls, each labeled with a distinct positive integer. Without looking, they hand their balls to Harry, who awards the point to the player with the larger number and returns the balls to the jar. The winner of the game is the one who wins at least two of the three rounds.

Andrew wins rounds 1 and 2 while Jerry wins round 3, so Andrew wins the game. However, Jerry is unhappy with this system, claiming that he will often lose the match despite having the higher overall total. What is the probability that the sum of the three balls Jerry drew is strictly higher than the sum of the three balls Andrew drew?

Input

The first line of input contains a single integer n (2 ≤ n ≤ 2000) — the number of balls in the jar.

The second line contains n integers ai (1 ≤ ai ≤ 5000) — the number written on the ith ball. It is guaranteed that no two balls have the same number.

Output

Print a single real value — the probability that Jerry has a higher total, given that Andrew wins the first two rounds and Jerry wins the third. Your answer will be considered correct if its absolute or relative error does not exceed 10 - 6. 

Namely: let's assume that your answer is a, and the answer of the jury is b. The checker program will consider your answer correct, if <image>.

Examples

Input

2
1 2


Output

0.0000000000


Input

3
1 2 10


Output

0.0740740741

Note

In the first case, there are only two balls. In the first two rounds, Andrew must have drawn the 2 and Jerry must have drawn the 1, and vice versa in the final round. Thus, Andrew's sum is 5 and Jerry's sum is 4, so Jerry never has a higher total.

In the second case, each game could've had three outcomes — 10 - 2, 10 - 1, or 2 - 1. Jerry has a higher total if and only if Andrew won 2 - 1 in both of the first two rounds, and Jerry drew the 10 in the last round. This has probability <image>.
import java.awt.Point;
import java.awt.geom.Line2D;
import java.io.BufferedReader;
import java.io.File;
import java.io.FileInputStream;
import java.io.FileReader;
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.security.GuardedObject;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.InputMismatchException;
import java.util.LinkedList;
import java.util.List;
import java.util.Map;
import java.util.PriorityQueue;
import java.util.Queue;
import java.util.Random;
import java.util.Scanner;
import java.util.Stack;
import java.util.StringTokenizer;
import java.util.TreeMap;
import java.util.TreeSet;
import java.io.InputStream;
import java.math.BigInteger;






/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */

public class Main {
    public static void main(String[] args) throws IOException {
        InputStream inputStream = System.in;
        
        OutputStream outputStream = System.out;
        FastScanner in;
        PrintWriter out;
        
           in=new FastScanner(System.in);
            out=new PrintWriter(System.out);
        //in=new FastScanner(new FileInputStream(new File("C://Users//KANDARP//Desktop//coding_contest_creation (1).txt")));
        
        TaskC solver = new TaskC();
        long var=System.currentTimeMillis();
        solver.solve(1, in, out);
        /*if(System.getProperty("ONLINE_JUDGE")==null){
            out.println("["+(double)(System.currentTimeMillis()-var)/1000+"]");
        }*/
        out.close();
    }
}
class Pair {
	
    long x,y,index;
    long  r1,r2;
    HashMap<Double,Long> map=new HashMap<>();
    Pair(long x,long y,int index){
        this.x=x;
        this.y=y;
        this.index=index;
    }
    public String toString(){
        return this.x+" "+this.y+" ";
    }
    
}
class tupple{
    long x,y,z;
    ArrayList<String> list=new ArrayList<>();
    tupple(long x,long y,long z){
        this.x=x;
        this.y=y;
        this.z=z;
    }
    tupple(tupple cl){
        this.x=cl.x;
        this.y=cl.y;
        this.z=cl.z;
        this.list=cl.list;
    }
}
class Edge implements  Comparable<Edge>{
    int u;
    int v;
    int time;
    long cost;
    long wcost;
    public Edge(int u,int v,long cost,long wcost){
        this.u=u;
        this.v=v;
        this.cost=cost;
        this.wcost=wcost;
        time=Integer.MAX_VALUE;
    }
    public int other(int x){
        if(u==x)return v;
        return u;
    }
    @Override
    public int compareTo(Edge o) {
        // TODO Auto-generated method stub
        return Long.compare(cost, o.cost);
    }
}
class Ss{
    Integer a[]=new Integer[3];
    Ss(Integer a[]){
        this.a=a;
        
    }
    public int hashCode(){
        return a[0].hashCode()+a[1].hashCode()+a[2].hashCode();
    }
    public boolean equals(Object o){
        Ss x=(Ss)o;
        for(int i=0;i<3;i++){
            if(x.a[i]!=this.a[i]){
                return false;
            }
        }
        return true;
        
    }
}
class queary{
    int type;
    int l;
    int r;
    int index;
    queary(int type,int l,int r){
        this.type=type;
        this.l=l;
        this.r=r;
    }
}
class boat implements Comparable<boat>{
    int capacity;
    int index;
    boat(int capacity,int index)
    {
        this.capacity=capacity;
        this.index=index;
    }
    @Override
    public int compareTo(boat o) {
        // TODO Auto-generated method stub
        return this.capacity-o.capacity;
    }
}
class angle{
    double x,y,angle;
    int index;
    angle(int x,int y,double angle){
        this.x=x;
        this.y=y;
        this.angle=angle;
    }
}
class TaskC {
    static long mod=1000000007;
//    SegTree tree;
    //    int min[];
 /*   static int prime_len=1000010;
    static int prime[]=new int[prime_len];
    static long n_prime[]=new long[prime_len];
    static ArrayList<Integer> primes=new ArrayList<>();
    static{ 
        for(int i=2;i<=Math.sqrt(prime.length);i++){
            for(int j=i*i;j<prime.length;j+=i){
                
                prime[j]=i;
                
            }
        }
        for(int i=2;i<prime.length;i++){
            n_prime[i]=n_prime[i-1];
            if(prime[i]==0){
               n_prime[i]++;
            }
            
        }
    //  System.out.println("end");
        
    //  prime[0]=true;
    //  prime[1]=1;
    }
    /*
     *  long pp[]=new long[10000001];
            pp[0]=0;
            pp[1]=1;
            for(int i=2;i<pp.length;i++){
                if(prime[i]!=0){
                    int gcd=(int)greatestCommonDivisor(i/prime[i], prime[i]);
                    pp[i]=(pp[i/prime[i]]*pp[prime[i]]*gcd)/pp[(int)gcd];
                }
                else
                    pp[i]=i-1;
            }
        

}
     * */
    class Rmq {

		  int[] logTable;
		  int[][] rmq;
		  int[] a;

		  public Rmq(int[] a) {
		    this.a = a;
		    int n = a.length;

		    logTable = new int[n + 1];
		    for (int i = 2; i <= n; i++)
		      logTable[i] = logTable[i >> 1] + 1;

		    rmq = new int[logTable[n] + 1][n];

		    for (int i = 0; i < n; ++i)
		      rmq[0][i] = i;

		    for (int k = 1; (1 << k) < n; ++k) {
		      for (int i = 0; i + (1 << k) <= n; i++) {
		        int x = rmq[k - 1][i];
		        int y = rmq[k - 1][i + (1 << k - 1)];
		        rmq[k][i] = a[x] <= a[y] ? x : y;
		      }
		    }
		  }

		  public int minPos(int i, int j) {
		    int k = logTable[j - i];
		    int x = rmq[k][i];
		    int y = rmq[k][j - (1 << k) + 1];
		    return a[x] <= a[y] ? a[x] : a[y];
		  }

	}
    	

	
   public void solve(int testNumber, FastScanner in, PrintWriter out) throws IOException {
	int n=in.nextInt();
	int a[]=new int[n];
	for(int i=0;i<n;i++){
		a[i]=in.nextInt();
	}
	Arrays.sort(a);
	long fre[]=new long[5010];
	for(int i=0;i<n;i++){
		for(int j=i+1;j<n;j++){
			fre[a[j]-a[i]]++;
		}
	}
	long fre2[]=new long[10020];
	for(int i=0;i<fre.length;i++){
		for(int j=0;j<fre.length;j++){
			fre2[i+j]+=fre[i]*fre[j];
		}
	}
	long ans=0;
	for(int i=0;i<fre2.length;i++){
		int index=0;
		for(int j=0;j<n;j++){
			while(index<n && a[index]-a[j]<=i){
				index++;
			}
			ans+=fre2[i]*(n-index);
		}
	}
	long nc2=(n*(n-1))/2;
	double pow=Math.pow(nc2, 3);
	out.println(ans*1.0/(pow));
   }
   
   static long greatestCommonDivisor (long m, long n){
       long x;
       long y;
       while(m%n != 0){
           x = n;
           y = m%n;
           m = x;
           n = y;
       }
       return n;
   }

 }
	   		   
    /*
     * 	   long res[]=new long[m];
    	   int cl=1;
    	   int cr=0;
    	   for(int i=0;i<m;i++){
    		   int l=(int)q[i].x;
    		   int r=(int)q[i].y;
    		   while(cl>l){
    			   cl--;
    			   ans+=add(cl);
    			   
    		   }
    		   while(cl<l){
    			   ans-=remove(cl);
    			   cl++;
    			  
    		   }
    		   while(cr>r){
    			   ans-=remove(cr);
    			   cr--;
    		   }
    		   while(cr<r){
    			   cr++;
    			   ans+=add(cr);
    		   }
    		   res[(int)q[i].index]=ans;
    	   }
    	   for(int i=0;i<m;i++)
    		   out.println(res[i]);	         
     */
	   	 class SegmentTree2D {
          public  long max(int[][] t, int x1, int y1, int x2, int y2) {
            int n = t.length >> 1;
            x1 += n;
            x2 += n;
            int m = t[0].length >> 1;
            y1 += m;
            y2 += m;
            long res = 0;
            for (int lx = x1, rx = x2; lx <= rx; lx = (lx + 1) >> 1, rx = (rx - 1) >> 1)
              for (int ly = y1, ry = y2; ly <= ry; ly = (ly + 1) >> 1, ry = (ry - 1) >> 1) {
                if ((lx & 1) != 0 && (ly & 1) != 0) res = (res+ t[lx][ly]);
                if ((lx & 1) != 0 && (ry & 1) == 0) res = (res+ t[lx][ry]);
                if ((rx & 1) == 0 && (ly & 1) != 0) res =(res+t[rx][ly]);
                if ((rx & 1) == 0 && (ry & 1) == 0) res = (res+ t[rx][ry]);
              }
            return res;
          }

          public  void add(int[][] t, int x, int y, int value) {
            x += t.length >> 1;
            y += t[0].length >> 1;
            t[x][y] += value;
            for (int tx = x; tx > 0; tx >>= 1)
              for (int ty = y; ty > 0; ty >>= 1) {
                if (tx > 1) t[tx >> 1][ty] = (t[tx][ty]+t[tx ^ 1][ty]);
                if (ty > 1) t[tx][ty >> 1] = (t[tx][ty]+ t[tx][ty ^ 1]);
              }

//          for (int ty = y; ty > 1; ty >>= 1)
//            t[x][ty >> 1] = Math.max(t[x][ty], t[x][ty ^ 1]);
//          for (int tx = x; tx > 1; tx >>= 1)
//            for (int ty = y; ty > 0; ty >>= 1)
//              t[tx >> 1][ty] = Math.max(t[tx][ty], t[tx ^ 1][ty]);

//          for (int lx=x; lx> 0; lx >>= 1) {
//            if (lx > 1)
//              t[lx >> 1][y] = Math.max(t[lx][y], t[lx ^ 1][y]);
//            for (int ly = y; ly > 1; ly >>= 1)
//              t[lx][ly >> 1] = Math.max(t[lx][ly], t[lx][ly ^ 1]);
//          }
          }
    }
     class SegmentTree {

          // Modify the following 5 methods to implement your custom operations on the tree.
          // This example implements Add/Max operations. Operations like Add/Sum, Set/Max can also be implemented.
          long modifyOperation(long x, long y) {
            return  y;
          }

          // query (or combine) operation
          long queryOperation(long leftValue, long rightValue) {
            return (leftValue| rightValue);
          }

          long deltaEffectOnSegment(long delta, long segmentLength) {
            // Here you must write a fast equivalent of following slow code:
            // int result = delta;
            // for (int i = 1; i < segmentLength; i++) result = queryOperation(result, delta);
            // return result;
            return delta;
          }

          int getNeutralDelta() {
            return 0;
          }

          int getInitValue() {
            return 0;
          }

          // generic code
          int n;
          long[] value;
          long[] delta; // delta[i] affects value[i], delta[2*i+1] and delta[2*i+2]

          long joinValueWithDelta(long value, long delta) {
            if (delta == getNeutralDelta()) return value;
            return modifyOperation(value, delta);
          }

          long joinDeltas(long delta1, long delta2) {
            if (delta1 == getNeutralDelta()) return delta2;
            if (delta2 == getNeutralDelta()) return delta1;
            return modifyOperation(delta1, delta2);
          }

          void pushDelta(int root, int left, int right) {
            value[root] = joinValueWithDelta(value[root], deltaEffectOnSegment(delta[root], right - left + 1));
            delta[2 * root + 1] = joinDeltas(delta[2 * root + 1], delta[root]);
            delta[2 * root + 2] = joinDeltas(delta[2 * root + 2], delta[root]);
            delta[root] = getNeutralDelta();
          }

          public SegmentTree(int n) {
            this.n = n;
            value = new long[4 * n];
            delta = new long[4 * n];
            init(0, 0, n - 1);
          }

          void init(int root, int left, int right) {
            if (left == right) {
              value[root] = getInitValue();
              delta[root] = getNeutralDelta();
            } else {
              int mid = (left + right) >> 1;
              init(2 * root + 1, left, mid);
              init(2 * root + 2, mid + 1, right);
              value[root] = queryOperation(value[2 * root + 1], value[2 * root + 2]);
              delta[root] = getNeutralDelta();
            }
          }

          public long query(int from, int to) {
            return query(from, to, 0, 0, n - 1);
          }

          long query(int from, int to, int root, int left, int right) {
            if (from == left && to == right)
              return joinValueWithDelta(value[root], deltaEffectOnSegment(delta[root], right - left + 1));
            pushDelta(root, left, right);
            int mid = (left + right) >> 1;
            if (from <= mid && to > mid)
              return queryOperation(
                  query(from, Math.min(to, mid), root * 2 + 1, left, mid),
                  query(Math.max(from, mid + 1), to, root * 2 + 2, mid + 1, right));
            else if (from <= mid)
              return query(from, Math.min(to, mid), root * 2 + 1, left, mid);
            else if (to > mid)
              return query(Math.max(from, mid + 1), to, root * 2 + 2, mid + 1, right);
            else
              throw new RuntimeException("Incorrect query from " + from + " to " + to);
          }

          public void modify(int from, int to, long delta) {
            modify(from, to, delta, 0, 0, n - 1);
          }

          void modify(int from, int to, long delta, int root, int left, int right) {
            if (from == left && to == right) {
              this.delta[root] = joinDeltas(this.delta[root], delta);
              return;
            }
            pushDelta(root, left, right);
            int mid = (left + right) >> 1;
            if (from <= mid)
              modify(from, Math.min(to, mid), delta, 2 * root + 1, left, mid);
            if (to > mid)
              modify(Math.max(from, mid + 1), to, delta, 2 * root + 2, mid + 1, right);
            value[root] = queryOperation(
                joinValueWithDelta(value[2 * root + 1], deltaEffectOnSegment(this.delta[2 * root + 1], mid - left + 1)),
                joinValueWithDelta(value[2 * root + 2], deltaEffectOnSegment(this.delta[2 * root + 2], right - mid)));
          }
    }

 	
 
    class LcaSparseTable {

          int len;
          int[][] up;
          int[][] max;
          int[] tin;
          int[] tout;
          int time;
          int []lvel;
          
          void dfs(List<Integer>[] tree, int u, int p) {
            tin[u] = time++;
            lvel[u]=lvel[p]+1;
            up[0][u] = p;
            if(u!=p)
            //max[0][u]=weight(u,p);
            for (int i = 1; i < len; i++)
              {
                up[i][u] = up[i - 1][up[i - 1][u]];
                max[i][u]=Math.max(max[i-1][u],max[i-1][up[i-1][u]]);
              }
            for (int v : tree[u])
              if (v != p)
                dfs(tree, v, u);
            tout[u] = time++;
          }

          public LcaSparseTable(List<Integer>[] tree, int root) {
            int n = tree.length;
            len = 1;
            while ((1 << len) <= n) ++len;
            up = new int[len][n];
            max=new int[len][n];
            tin = new int[n];
            tout = new int[n];
            lvel=new int[n];
            lvel[root]=0;
            dfs(tree, root, root);
          }

          boolean isParent(int parent, int child) {
            return tin[parent] <= tin[child] && tout[child] <= tout[parent];
          }

          public int lca(int a, int b) {
            if (isParent(a, b))
              return a;
            if (isParent(b, a))
              return b;
            for (int i = len - 1; i >= 0; i--)
              if (!isParent(up[i][a], b))
                a = up[i][a];
            return up[0][a];
          }
          public long max(int a,int b){
              int lca=lca(a,b);
        //    System.out.println("LCA "+lca);
              long ans=0;
              int h=lvel[a]-lvel[lca];
            //  System.out.println("Height "+h);
              int index=0;
              while(h!=0){
                  if(h%2==1){
                      ans=Math.max(ans,max[index][a]);
                      a=up[index][a];
                  }
                  h/=2;
                  index++;
              }
              h=lvel[b]-lvel[lca];
             // System.out.println("Height "+h);
              
              index=0;
              while(h!=0){ 
                  if(h%2==1){
                      ans=Math.max(ans,max[index][b]);
                      b=up[index][b];
                  }
                  h/=2;
                  index++;
              }
              return ans;
          }
          
    
    static void dfs(List<Integer>[] graph, boolean[] used, List<Integer> res, int u,int parent,List<Integer> collection) {
        
        used[u] = true;
        Integer uu=new Integer(u);
        collection.add(uu);
        for (int v : graph[u]){
          if (!used[v]){
            dfs(graph, used, res, v,u,collection);
            
          }
          else if(collection.contains(v)){
              System.out.println("Impossible");
              System.exit(0);
          }
        }
        collection.remove(uu);
        res.add(u);
      }
        
      public static List<Integer> topologicalSort(List<Integer>[] graph) {
        int n = graph.length;
        boolean[] used = new boolean[n];
        List<Integer> res = new ArrayList<>();
        for (int i = 0; i < n; i++)
          if (!used[i])
            dfs(graph, used, res, i,-1,new ArrayList<Integer>());
        Collections.reverse(res);
        return res;
      }     
  		
 
    static class pairs{
                String company,color;
                String type;
                boolean visit=false;
                pairs(String company,String color,String type){
                    this.company=company;
                    this.color=color;
                    this.type=type;
                }
            }
        
            static void dfs1(List<Integer>[] graph, boolean[] used, List<Integer> res, int u) {
            used[u] = true;
            for (int v : graph[u])
              if (!used[v])
                dfs1(graph, used, res, v);
            res.add(u);
          }

          public static List<Integer> topologicalSort1(List<Integer>[] graph) {
            int n = graph.length;
            boolean[] used = new boolean[n];
            List<Integer> res = new ArrayList<>();
            for (int i = n-1; i >0; i--)
              if (!used[i])
                dfs1(graph, used, res, i);
            Collections.reverse(res);
            return res;
          }
        
        public static long[][] mulmatrix(long m1[][],long m2[][],long mod){
            long ans[][]=new long[m1.length][m2[0].length];
            for(int i=0;i<m1.length;i++){
                for(int j=0;j<m2[0].length;j++){
                    for(int k=0;k<m1.length;k++){
                        ans[i][j]+=(m1[i][k]*m2[k][j]);
                        ans[i][j]%=mod;
                    }
                }
            }
            return ans;
        }
        public static long[][] matrixexpo(long m[][],String n,long mod){
            if(n.equals("1")){
                return m.clone(); 
            }
            if(n.equals("10")){
                return mulmatrix(m, m , mod);
            }
            else{
                long temp [][]=matrixexpo(m,n.substring(0,n.length()-1),mod);
                temp=mulmatrix(temp, temp, mod);
                if(n.charAt(n.length()-1)=='0')return temp;
                else return mulmatrix(temp, m,mod);
            }
        }
        public static boolean isCompatible(long x[],long y[]){
            
            for(int i=0;i<x.length-1;i++){
                if(x[i]==y[i] && x[i+1]==y[i+1] && x[i]==x[i+1] && y[i]==y[i+1]){
                    return false;
                }
            }
            return true;
        }
        
        int phi(int n) {
            int res = n;
            for (int i = 2; i * i <= n; ++i) {
                if (n % i == 0) {
                    while (n % i == 0) {
                        n /= i;
                    }
                    res -= res / i;
                }
            }
            if (n != 1) {
                res -= res / n;
            }
            return res;
        }
        long pow(long x,long y,long mod){
            if(y<=0){
                return 1;
            }
            if(y==1){
                return x%mod;
            }
            long temp=pow(x,y/2,mod);
            if(y%2==0){
                return (temp*temp)%mod;
            }
            else{
                return (((temp*temp)%mod)*x)%mod;
            }
        }
        
/*      long DP(int id,int mask){
            //System.out.println("hi"+dp[id][mask]+" "+id+" "+Integer.toBinaryString(mask));
            if(id==0 && mask==0){
                dp[0][mask]=1;
                return 1;
            }
            else if(id==0){
                dp[0][mask]=0;
                return 0;
            }
            if(dp[id][mask]!=-1){
            
                return dp[id][mask];
            }
            long ans=0;
            for(int i=0;i<n;i++){
                if((mask & (1<<i))!=0 && c[i][id]>=1){
                        ans+=DP(id-1,mask ^ (1 << i));
                        ans%=mod;
                }
            }
            ans+=DP(id-1,mask);
            ans%=mod;
            dp[id][mask]=ans;
            return ans;
        }*/
                long no_of_primes(long m,long n,long k){
                    long count=0,i,j;
                    int primes []=new int[(int)(n-m+2)];
                       if(m==1)    primes[0] = 1;
                        for(i=2; i<=Math.sqrt(n); i++)
                        {
                            j = (m/i);    j *= i;
                            if(j<m)
                                j+=i;
                            for(; j<=n; j+=i)
                             {
                                 if(j!=i)
                                    primes[(int)(j-m)] = 1;
                             }
                        }

                for(i=0; i<=n-m; i++)
                            if(primes[(int)i]==0 && (i-1)%k==0)
                                count++;
                return count;
                }
}
class SegTree {
    int n;
    long  t[];
    long mod=(long)(1000000007);
    SegTree(int n,long  t[]){
        this.n=n;
        this.t=t;
        build();
    }
    
    void build() {  // build the tree
        
        for (int i = n - 1; i > 0; --i)
            t[i]=(t[i<<1]|t[i<<1|1]);
    }

     void modify(int p, long value) {  // set value at position p
      for (t[p += n]+=value; p > 1; p >>= 1) t[p>>1] = (t[p]|t[p^1]);
    }

     long query(int l, int r) {  // sum on interval [l, r)
      long res=0;
              
      for (l += n, r += n; l < r; l >>= 1, r >>= 1) {
            if ((l&1)!=0) res=Math.max(res,t[l++]);
            if ((r&1)!=0) res=Math.max(res,t[--r]);
          }
      return res;
    }

    
    //  
//  
//  
}
class FastScanner
{

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

    public FastScanner(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 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);
    }
}
 class UF {

    private int[] parent;  // parent[i] = parent of i
    private byte[] rank;   // rank[i] = rank of subtree rooted at i (never more than 31)
    private int count;     // number of components
    public UF(int N) {
        if (N < 0) throw new IllegalArgumentException();
        count = N;
        parent = new int[N];
        rank = new byte[N];
        for (int i = 0; i < N; i++) {
            parent[i] = i;
            rank[i] = 0;
        }
    }

    public int find(int p) {
        if (p < 0 || p >= parent.length) throw new IndexOutOfBoundsException();
        while (p != parent[p]) {
            parent[p] = parent[parent[p]];    // path compression by halving
            p = parent[p];
        }
        return p;
    }
    public int count() {
        return count;
    }

    public boolean connected(int p, int q) {
        return find(p) == find(q);
    }

    public boolean union(int p, int q) {
        int rootP = find(p);
        int rootQ = find(q);
        if (rootP == rootQ) return false;

        // make root of smaller rank point to root of larger rank
        if      (rank[rootP] < rank[rootQ]) parent[rootP] = rootQ;
        else if (rank[rootP] > rank[rootQ]) parent[rootQ] = rootP;
        else {
            parent[rootQ] = rootP;
            rank[rootP]++;
        }
        count--;
        return true;
    }
    



}
 class MyArrayList {
	 
    private int[] myStore;
    private int actSize = 0;
     
    public MyArrayList(){
        myStore = new int[2];
    }
     
    public int get(int index){
        if(index < actSize)
            return myStore[index];
         else 
            throw new ArrayIndexOutOfBoundsException();
    }
     
    public void add(int obj){
        if(myStore.length-actSize <= 1)
            increaseListSize();
        myStore[actSize++] = obj;
    }
   
    public int size(){
        return actSize;
    }
     
    private void increaseListSize(){
        myStore = Arrays.copyOf(myStore, myStore.length*2);
    }
}