Each New Year Timofey and his friends cut down a tree of n vertices and bring it home. After that they paint all the n its vertices, so that the i-th vertex gets color ci.

Now it's time for Timofey birthday, and his mother asked him to remove the tree. Timofey removes the tree in the following way: he takes some vertex in hands, while all the other vertices move down so that the tree becomes rooted at the chosen vertex. After that Timofey brings the tree to a trash can.

Timofey doesn't like it when many colors are mixing together. A subtree annoys him if there are vertices of different color in it. Timofey wants to find a vertex which he should take in hands so that there are no subtrees that annoy him. He doesn't consider the whole tree as a subtree since he can't see the color of the root vertex.

A subtree of some vertex is a subgraph containing that vertex and all its descendants.

Your task is to determine if there is a vertex, taking which in hands Timofey wouldn't be annoyed.

Input

The first line contains single integer n (2 ≤ n ≤ 105) — the number of vertices in the tree.

Each of the next n - 1 lines contains two integers u and v (1 ≤ u, v ≤ n, u ≠ v), denoting there is an edge between vertices u and v. It is guaranteed that the given graph is a tree.

The next line contains n integers c1, c2, ..., cn (1 ≤ ci ≤ 105), denoting the colors of the vertices.

Output

Print "NO" in a single line, if Timofey can't take the tree in such a way that it doesn't annoy him.

Otherwise print "YES" in the first line. In the second line print the index of the vertex which Timofey should take in hands. If there are multiple answers, print any of them.

Examples

Input

4
1 2
2 3
3 4
1 2 1 1


Output

YES
2

Input

3
1 2
2 3
1 2 3


Output

YES
2

Input

4
1 2
2 3
3 4
1 2 1 2


Output

NO
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.Hashtable;
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 q1 {
    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;
    
    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 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 queary{
    int type;
    int l;
    int r;
    int index;
    queary(int type,int l,int r,int index){
        this.type=type;
        this.l=l;
        this.r=r;
        this.index=index;
    }
}
class TaskC {
    static long mod=1000000007;
   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 TrieNode{
        int value;
        TrieNode children[];
        public TrieNode(int value,TrieNode children[] ){
            this.value=value;
            this.children=children;
        }
    }
    class Trie{
        TrieNode root;
        int count;
        public Trie(TrieNode root,int count){
            this.root=root;
            this.count=count;
        }
    }
    public void insert(Trie t,char key[]){
        t.count++;
        int length=key.length;
        int level=0;
        TrieNode current=t.root;
        if(current==null){
            t.root=new TrieNode(0, new TrieNode[26]);
            current=t.root;
        }
        for(level=0;level<length;level++){
            int index=key[level]-'a';
            if(current.children[index]==null){
                current.children[index]=new TrieNode(0,new TrieNode[26]);
            }
            current=current.children[index];
        }
        current.value=t.count;
    }
    public int search(Trie t,char key[]){
        TrieNode current=t.root;
        if(current==null){
            return 0;
        }
        int length=key.length;
        int level=0;
        for(level=0;level<length;level++){
            int index=key[level]-'a';
            if(current.children[index]==null){
                return 0;
            }
            current=current.children[index];
        }
        return current.value;
    }
    class point implements Comparable<point>{
        long x;
        long y;
        public point(long x,long y){
            this.x=x;
            this.y=y;
        }
        @Override
        public int compareTo(point o) {
            // TODO Auto-generated method stub
            if(o.x==x && o.y==y)
            return 0;
            else return (int)Math.max(x-o.x, y-o.y);
        }
        public int hashCode(){
            return (int)(x+y);
            
        }
        public boolean equals(Object z){
            if(z!=null){
                point o=(point)z;
                if(o.x==x && o.y==y)
                    return true;
            }
            return false;
        }
        
    }
    class Edge {
        int t, rev, cap, f;

        public Edge(int t, int rev, int cap) {
          this.t = t;
          this.rev = rev;
          this.cap = cap;
        }
      }

    class MaxFlowDinic {

          
          public  List<Edge>[] createGraph(int nodes) {
            List<Edge>[] graph = new List[nodes];
            for (int i = 0; i < nodes; i++)
              graph[i] = new ArrayList<>();
            return graph;
          }

          public  void addEdge(List<Edge>[] graph, int s, int t, int cap) {
            graph[s].add(new Edge(t, graph[t].size(), cap));
            graph[t].add(new Edge(s, graph[s].size() - 1, 0));
          }

           boolean dinicBfs(List<Edge>[] graph, int src, int dest, int[] dist) {
            Arrays.fill(dist, -1);
            dist[src] = 0;
            int[] Q = new int[graph.length];
            int sizeQ = 0;
            Q[sizeQ++] = src;
            for (int i = 0; i < sizeQ; i++) {
              int u = Q[i];
              for (Edge e : graph[u]) {
                if (dist[e.t] < 0 && e.f < e.cap) {
                  dist[e.t] = dist[u] + 1;
                  Q[sizeQ++] = e.t;
                }
              }
            }
            return dist[dest] >= 0;
          }

           int dinicDfs(List<Edge>[] graph, int[] ptr, int[] dist, int dest, int u, int f) {
            if (u == dest)
              return f;
            for (; ptr[u] < graph[u].size(); ++ptr[u]) {
              Edge e = graph[u].get(ptr[u]);
              if (dist[e.t] == dist[u] + 1 && e.f < e.cap) {
                int df = dinicDfs(graph, ptr, dist, dest, e.t, Math.min(f, e.cap - e.f));
                if (df > 0) {
                  e.f += df;
                  graph[e.t].get(e.rev).f -= df;
                  return df;
                }
              }
            }
            return 0;
          }

          public  int maxFlow(List<Edge>[] graph, int src, int dest) {
            int flow = 0;
            int[] dist = new int[graph.length];
            while (dinicBfs(graph, src, dest, dist)) {
              int[] ptr = new int[graph.length];
              while (true) {
                int df = dinicDfs(graph, ptr, dist, dest, src, Integer.MAX_VALUE);
                if (df == 0)
                  break;
                flow += df;
              }
            }
            return flow;
          }
    }
        //int arr[]=new int[1000000000];
      int n;
      ArrayList<Integer> list[];
      int c[];
    public void solve(int testNumber, FastScanner in, PrintWriter out) throws IOException {
    	 n=in.nextInt();
    	list=new ArrayList[n];
    	for(int i=0;i<n;i++){
    		list[i] = new ArrayList<>();
    	}
    	c = new int[n];
    	for(int i=0;i<n-1;i++){
    		int u = in.nextInt()-1;
    		int v = in.nextInt()-1;
    		list[u].add(v);
    		list[v].add(u);
    	}
    	for(int i=0;i<n;i++){
    		c[i]= in.nextInt();
    	}
    	for(int i=0;i<n;i++){
    		
    		for(int x:list[i]){
    			if(c[x]!=c[i]){
    				if(check(x)){
    					out.println("YES");
    					out.println((x+1));
    				}
    				else if(check(i)){
    					out.println("YES");
    					out.println((i+1));
    				}
    				else{
    					out.println("NO");
    				}
    				return;
    				
    			}
    		}
    	}
    	out.println("YES");
    	out.println(1);
    	
    }
    public  boolean check(int index){
    	boolean ans =true;
    	for(int x:list[index]){
    		ans &= dfs(x,index);
    	}
    	return ans;
    }
    public boolean dfs(int index, int parent){
    	int color = c[index];
    	boolean ans =true;
    	for(int x:list[index]){
    		if(x!=parent){
    			if(c[x]==color){
    				ans &= dfs(x,index);
    			}
    			else{
    				return false;
    			}
    		}
    	}
    	return ans;
    }
    public void swap(int a[],int i,int j){
    	int tmp = a[i];
    	a[i]=a[j];
    	a[j]=tmp;
    }
    
    public long[] fun(long n,int k,int a){
        long arr[]=new long[k];
        for(int i=0;i<k;i++){
            
            arr[(int)(pow(i, a, k)%k)]+=((n/k)%mod+ ((i!=0  &&  i<=n%k)? 1: 0))%mod;
        }
        return arr;
    }
         
     
     public long getAns(int d[],int n){
         if(d[0]<0 && d[n-1]>0){
             
             return Math.min(-2*d[0]+d[n-1], 2*d[n-1]-d[0]);
             
             
          }
          else{
              if(d[0]<0){
                     return d[0]*-1;
              }
              else{
                     return(d[n-1]*1);
              }
          }
         
        // return 0;
     }
     public boolean isTriangle(int x,int y,int z){
         if(x+y>z && x+z>y && y+z>x){
             return true;
         }
         return false;
     }
     public long optimize(long x){
         long y=x;
         if(x%10<5){
             x=x-x%10;
            
         }
         else{
             x=x+(10-x%10);
         }
         return y-x;
     }
   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 long[] mul(long[] a, long[] b)
    {
        int n = Math.max(a.length, b.length);
        int h = Integer.highestOneBit(n);
        if(n > h)h *= 2;
        if(a.length < h)a = Arrays.copyOf(a, h);
        if(b.length < h)b = Arrays.copyOf(b, h);
        return mul2(a, b, 0, h, 0, h);
    }
    
    public static long[] mul2(long[] a, long[] b, int al, int ar, int bl, int br)
    {
        int n = ar-al;
        if((n&n-1) != 0)throw new RuntimeException();
        if(n <= 1<<6){
            long[] res = muln(a, b, al, ar, bl, br);
            return res;
        }
        
        long[] c0 = mul2(a, b, al+0, al+n/2, bl+0, bl+n/2);
        long[] c2 = mul2(a, b, al+n/2, al+n, bl+n/2, bl+n);
        
        long[] ab0 = new long[n/2];
        long[] ab1 = new long[n/2];
        for(int i = 0;i < n/2;i++){
            ab0[i] = a[al+i] + a[al+i+n/2];
            ab1[i] = b[bl+i] + b[bl+i+n/2];
            if(ab0[i] >= mod)ab0[i] -= mod;
            if(ab1[i] >= mod)ab1[i] -= mod;
        }
        
        int e = n+c2.length;
        long[] ret = new long[e];
        for(int i = 0;i < c0.length;i++){
            ret[i] += c0[i];
            if(ret[i] >= mod)ret[i] -= mod;
        }
        for(int i = 0;i < c2.length;i++){
            ret[i+n] += c2[i];
            if(ret[i+n] >= mod)ret[i+n] -= mod;
        }
        
        long[] c1 = mul2(ab0, ab1, 0, n/2, 0, n/2);
        for(int i = 0;i < c1.length;i++){
            c1[i] -= c0[i] + c2[i];
            if(c1[i] < 0)c1[i] += mod;
            if(c1[i] < 0)c1[i] += mod;
        }
        for(int i = 0;i < c1.length;i++){
            ret[i+n/2] += c1[i];
            if(ret[i+n/2] >= mod)ret[i+n/2] -= mod;
        }
        return ret;
    }
    
    public static long[] muln(long[] a, long[] b, int al, int ar, int bl, int br)
    {
        int n = ar - al;
        long[] ret = new long[2*n];
        for(int i = 0;i < 2*n;i++){
            long tot = 0;
            for(int j = Math.max(i-n+1, 0);j <= i && j < n;j++){
                tot += a[al+j] * b[bl+i-j];
            }
            ret[i] = tot % mod;
        }
        return ret;
    }
    
   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;
   }
   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;
       }
   }    
        
   
    

   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;
   }
   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;
     }     
     
 }
    





     
 
    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 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);
          }

        
        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;
        }
        
        
        
        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;
        }
        
        
        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 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;
    static long constt=Long.parseLong("111111111111111111111111111111",2);
    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]);
    //  System.out.println(Arrays.toString(t));
     }

     long query(int l, int r) {  // sum on interval [l, r)
         long res=constt;
         
         for (l += n, r += n; l < r; l >>= 1, r >>= 1) {
               if ((l&1)!=0) res=res&t[l++];
               if ((r&1)!=0) res=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 MyScanner {
       BufferedReader br;
       StringTokenizer st;
      
       public MyScanner() {
          br = new BufferedReader(new InputStreamReader(System.in));
       }
      
       String next() {
          while (st == null || !st.hasMoreElements()) {
             try {
                st = new StringTokenizer(br.readLine());
             } catch (IOException e) {
                e.printStackTrace();
             }
          }
          return st.nextToken();
       }
      
       int nextInt() {
          return Integer.parseInt(next());
       }
      
       long nextLong() {
          return Long.parseLong(next());
       }
      
       double nextDouble() {
          return Double.parseDouble(next());
       }
      
       String nextLine(){
          String str = "";
          try {
             str = br.readLine();
          } catch (IOException e) {
             e.printStackTrace();
          }
          return str;
       }
    
    }