Problem: Iahub is very proud of his recent discovery, propagating trees. Right now, he invented a new tree, called xor-tree. After this new revolutionary discovery, he invented a game for kids which uses xor-trees.

The game is played on a tree having n nodes, numbered from 1 to n. Each node i has an initial value initi, which is either 0 or 1. The root of the tree is node 1.

One can perform several (possibly, zero) operations on the tree during the game. The only available type of operation is to pick a node x. Right after someone has picked node x, the value of node x flips, the values of sons of x remain the same, the values of sons of sons of x flips, the values of sons of sons of sons of x remain the same and so on.

The goal of the game is to get each node i to have value goali, which can also be only 0 or 1. You need to reach the goal of the game by using minimum number of operations.

Input

The first line contains an integer n (1 ≤ n ≤ 105). Each of the next n - 1 lines contains two integers ui and vi (1 ≤ ui, vi ≤ n; ui ≠ vi) meaning there is an edge between nodes ui and vi. 

The next line contains n integer numbers, the i-th of them corresponds to initi (initi is either 0 or 1). The following line also contains n integer numbers, the i-th number corresponds to goali (goali is either 0 or 1).

Output

In the first line output an integer number cnt, representing the minimal number of operations you perform. Each of the next cnt lines should contain an integer xi, representing that you pick a node xi.

Examples

Input

10
2 1
3 1
4 2
5 1
6 2
7 5
8 6
9 8
10 5
1 0 1 1 0 1 0 1 0 1
1 0 1 0 0 1 1 1 0 1


Output

2
4
7

Solution (in JAVA):

Solution:
import java.io.*;
import java.math.*;
import java.security.KeyStore.Entry;
import java.util.*;
/* 
                                                                yash jobanputra
                                                                    DA-IICT
*/
public class yash {
    private static InputStream stream;
    private static byte[] buf = new byte[1024];
    private static int curChar;
    private static int numChars;
    private static SpaceCharFilter filter;
    private static PrintWriter pw;
    private static long mod = 1000000000 + 7;
    private static long mod1 = 1000000000 + 9;
    private static int MAX=1000001;
    private static int block;
    private static int[] level;
    private static long[] cost;
    private static long[] costm;
    private static int times;
    private static long ans;
    private static long max;
    private static boolean[] vis;
    private static long[] sa;
    private static long count;
    private static boolean ff;
    private static int odd;
    private static int even;
    private static ArrayList<Integer> ansa;
    public static void soln()
    {
    	int n=ni();
    	ArrayList<Integer>[] g=new ArrayList[n+1];
    	for(int i=0;i<=n;i++)
    		g[i]=new ArrayList<>();
    	for(int i=0;i<n-1;i++)
    	{
    		int a=ni();int b=ni();
    		g[a].add(b);g[b].add(a);
    	}
    	int[] ini=nia(n);
    	int[] goal=nia(n);
    	level=new int[n+1];
    	vis=new boolean[n+1];
    	odd=0;even=0;level[1]=0;
    	ansa=new ArrayList<>();
    	dfs(g,1,ini,goal,0,0);
    	pl(ansa.size());
    	for(int i=0;i<ansa.size();i++)
    		pl(ansa.get(i));
    }
    public static void dfsp(ArrayList<Pair>[] gr,int v,int[] a)
    {
        vis[v]=true;
        ArrayList<Pair> arr=gr[v];
        for(int i=0;i<arr.size();i++)
        {
            if(!vis[arr.get(i).v])
            {
            		dfsp(gr,arr.get(i).v,a);
           	}
        }
    }
    public static void dfs(ArrayList<Integer>[] gr,int v,int[] ini,int[] goal,int odd,int even)
    {
        vis[v]=true;
        ArrayList<Integer> arr=gr[v];
        if(level[v]%2==0 && ((ini[v-1]+even)%2)!=goal[v-1])
        {
        	ansa.add(v);
        	even++;
        }
        if(level[v]%2==1 && ((ini[v-1]+odd)%2)!=goal[v-1])
        {
        	ansa.add(v);
        	odd++;
        }
        for(int i=0;i<arr.size();i++)
        {
            if(!vis[arr.get(i)])
            {
            	level[arr.get(i)]=level[v]+1;
           		dfs(gr,arr.get(i),ini,goal,odd,even);
           	}
        }
    }
    public static class lca{
    	int[] e;
    	int[] l;
    	int[] h;
    	int[] level;
    	boolean[] vis;
    	int time;
    	int[] tree=new int[10000000];
        int[] lazy=new int[10000000];
        int n;
    	public lca(ArrayList<Integer>[] g)
    	{
    		n=g.length-1;
    		pw.println(n);
    		e=new int[2*n];
    		l=new int[2*n];
    		h=new int[n+1];
    		vis=new boolean[n+1];
    		level=new int[n+1];
    		level[1]=0;
    		dfs(g,1);
    		Arrays.fill(lazy, 0);
    		build(l,0,0,2*n-1);
    	}
    	public int lf(int u,int v)
    	{
    		int a=h[u];int b=h[v];
    		if(h[u]>h[v])
    			{a=h[v];b=h[u];}
    		int p=query(l,0,0,2*n-1,a,b);
    		return e[p];
    	}
    	public void dfs(ArrayList<Integer>[] gr,int v)
        {
             vis[v]=true;
             time++;
             e[time]=v;
             l[time]=level[v];
             h[v]=time;
             ArrayList<Integer> arr=gr[v];
             for(int i=0;i<arr.size();i++)
             {
                 if(!vis[arr.get(i)])
                 {
                	 level[arr.get(i)]=level[v]+1;
                	 dfs(gr,arr.get(i));
                	 time++;e[time]=v;l[time]=level[v];
                 }
             }
         }
    	 public void build(int[] arr,int node,int l,int r)
         {
             if(l==r)
             {
                 tree[node]=l;
             }
             else
             {
                 int m=(l+r)/2;
                 build(arr,(2*node)+1,l,m);
                 build(arr,(2*node)+2,m+1,r);
                 if(arr[tree[2*node+1]]<arr[tree[2*node+2]])
                	 tree[node]=tree[2*node+1];
                 else
                	 tree[node]=tree[2*node+2];
             }
         }
    	 public int query(int[] arr,int node,int l,int r,int s,int e)
         {
             if(e<l || r<s)
                 return -1;
             if(s<=l && e>=r)
                 return tree[node];
             int m=(l+r)/2;
             int p1=query(arr,(2*node+1),l,m,s,e);
             int p2=query(arr,(2*node+2),m+1,r,s,e);
             if(p1==-1)
            	 return p2;
             else if(p2==-1)
            	 return p1;
             else
             {
            	 if(arr[p1]<arr[p2])
            		 return p1;
            	 else
            		 return p2;
             }
         }
    }
    public static long[] reverse(long[] arr, int l, int r)
      {
          int d = (r-l+1)/2;
          for(int i=0;i<d;i++)
          {
             long t = arr[l+i];
             arr[l+i] = arr[r-i];
             arr[r-i] = t;
          }
          return arr;
      }
    private static class graph{
        public static void arti(boolean[] ap,int[] parent,int[] disc,int[] low,ArrayList<Integer>[] gr,boolean[] vis,int ver)
        {
            int child=0;
            vis[ver]=true;
            ArrayList<Integer> arr=gr[ver];
            times++;
            disc[ver]=low[ver]=times;
            for(int i=0;i<arr.size();i++)
            {
                if(!vis[arr.get(i)])
                {
                    child++;
                    parent[arr.get(i)]=ver;
                    arti(ap,parent,disc,low,gr,vis,arr.get(i));
                    low[ver]=Math.min(low[ver], low[arr.get(i)]);
                    if(parent[ver]!=0 && low[arr.get(i)]>=disc[ver])
                        ap[ver]=true;
                    if(parent[ver]==0 && child>1)
                        ap[ver]=true;
                }
                else if(parent[ver]!=arr.get(i))
                    low[ver]=Math.min(low[ver], disc[arr.get(i)]);
            }
        }
        public static void floyd(Pair[] arr,int n,int m,int[][] dist)
        {
            for(int i=0;i<=n;i++)
            {
                Arrays.fill(dist[i], Integer.MAX_VALUE);
            }
            for(int c=0;c<m;c++)
            {
                int w=arr[c].v;
                int a=arr[c].j.v;
                int b=arr[c].j.i;
                dist[a][b]=w;
            }
            for(int i=0;i<=n;i++)
                dist[i][i]=0;
            for(int k=1;k<=n;k++)
            {
                for(int i=1;i<=n;i++)
                {
                    for(int j=1;j<=n;j++)
                    {
                        if(dist[i][k]!=Integer.MAX_VALUE && dist[k][j]!=Integer.MAX_VALUE)
                        dist[i][j]=Math.min(dist[i][j], dist[i][k]+dist[k][j]);
                    }
                }
            }
        }
        public static boolean bfs(ArrayList<Integer>[] gr,int v,int n)
        {
            
            boolean[] vis=new boolean[n+1];
            int c2=0;
            Queue<Integer> q=new LinkedList<>();
            q.add(v);
            while(!q.isEmpty())
            {
                int x=q.poll();
                Iterator<Integer> it=gr[x].iterator();
                while(it.hasNext())
                {
                    int p=it.next();
                    if(!vis[p])
                    {
                        q.add(p);
                        c2++;
                        vis[p]=true;
                    }
                }
            }
            return c2==n;
        }
        public static ArrayList<Pair> MSTP(int n,int m,ArrayList<Pair>[] arr,int[][] arr2)
        {
            ArrayList<Pair> pp=new ArrayList<>();
            int[] par=new int[n+1];
            int[] key=new int[n+1];
            vis=new boolean[n+1];
            Arrays.fill(key, Integer.MAX_VALUE);
            key[1]=0;
            PriorityQueue<Integer> dis=new PriorityQueue<>(n+1,
                    new Comparator<Integer>()
                    {
                        public int compare(Integer p,Integer q)
                        {
                        return key[p]-key[q];
                        }
                    }
                    );
            dis.add(1);
            vis[1]=true;
            while(!dis.isEmpty())
            {
                //pw.println(dis);
                int u=dis.poll();
                    ArrayList<Pair> p=arr[u];
                    for(int i=0;i<p.size();i++)
                    {
                        if(key[u]+p.get(i).i<key[p.get(i).v])
                        {
                            key[p.get(i).v]=key[u]+p.get(i).i;
                            par[p.get(i).v]=u;
                            if(!vis[p.get(i).v])
                            {
                                dis.add(p.get(i).v);
                                vis[p.get(i).v]=true;
                            }
                        }
                    }
            }
            for(int i=1;i<=n;i++)
                pp.add(new Pair(i,par[i]));
            return pp;
        }
        public static ArrayList<Pair> MSTK(int n,int m,Pair[] arr)
        {
            ArrayList<Pair> pp=new ArrayList<>();
            long sum=0;
            Arrays.sort(arr);
            DSU x=new DSU(n+1);
            for(int c=0;(c<m);c++)
            {
                Pair p=arr[c];
                //int a=p.v;
                //int b=p.i;
                int a=p.j.v;
                int b=p.j.i;
                int w=p.v;
                if(x.find(a)!=x.find(b))
                {
                    pp.add(new Pair(w,new Pair(a,b)));
                    x.Union(a, b);
                }
            }
            return pp;
        }
        public static int[] dijkstras(ArrayList<Pair>[] gr)
        {
            int n=gr.length-1;
            int[] dist=new int[n+1];
            Arrays.fill(dist, Integer.MAX_VALUE);
            
            PriorityQueue<Integer> dis=new PriorityQueue<>(n+1,
                    new Comparator<Integer>()
                    {
                        public int compare(Integer p,Integer q)
                        {
                        return dist[p]-dist[q];
                        }
                    }
                    );
            boolean[] vis=new boolean[n+1];
            Arrays.fill(vis, false);
            
            int s=1;
            dist[s]=0;
            dis.add(s);
            vis[s]=true;
            while(!dis.isEmpty())
            {
                int p=dis.poll();
                for(int i=0;i<gr[p].size();i++)
                {
                    int y=gr[p].get(i).v;
                    int w=gr[p].get(i).i;
                    if(!vis[y])
                    {
                        dist[y]=dist[p]+w;
                        dis.add(y);
                        vis[y]=true;
                    }
                    else
                    {
                        if(dist[p]+w<dist[y])
                        {
                            dist[y]=dist[p]+w;
                        }
                    }
                }
            }
            return dist;
        }
    }
    
    public static class sieve{
        public static ArrayList<Integer> sieves(int n)
        {
            ArrayList<Integer> arr=new ArrayList<>();
            boolean[] bol=new boolean[n+1];
            Arrays.fill(bol, true);
            //arr.add(1);
            for(int i=2;i<=n;i++)
            {
                if(bol[i])
                {
                    arr.add(i);
                    for(int j=2;j*i<=n;j++)
                    {
                        bol[i*j]=false;
                    }
                }
            }
            return arr;
        }
    }
    public static class isprime{
        public static boolean check(int n)
        {
            if(n==2)
                return true;
            else if(n==3)
                return true;
            else if(n%2==0)
                return false;
            else if(n%3==0)
                return false;
            else
            {
                for(int i=6;;i+=6)
                {
                    if(i>Math.sqrt(n))
                        break;
                    if(n%(i-1)==0)
                    {
                        return false;
                    }
                    else if(n%(i+1)==0)
                        return false;
                                    }
                return true;
            }
        }
    }
    private static class DSU{
        int[] parent;
        int[] rank;
        int cnt;
        public DSU(int n){
            parent=new int[n];
            rank=new int[n];
            for(int i=0;i<n;i++){
                parent[i]=i;
                rank[i]=1;
            }
            cnt=n;
        }
        int find(int i){
            while(parent[i] !=i){
                parent[i]=parent[parent[i]];
                i=parent[i];
            }
            return i;
        }
        int Union(int x, int y){
            int xset = find(x);
            int yset = find(y);
            if(xset!=yset)
                cnt--;
            if(rank[xset]<rank[yset]){
                parent[xset] = yset;
                rank[yset]+=rank[xset];
                rank[xset]=0;
                return yset;
            }else{
                parent[yset]=xset;
                rank[xset]+=rank[yset];
                rank[yset]=0;
                return xset;
            }
        }
    }
    private static class Pair implements Comparable<Pair>{
        int v,i;Pair j;
        public Pair(int a,int b){
            v=a;
            i=b;
        }
        public Pair(int a,Pair b)
        {
            v=a;
            j=b;
        }
        @Override
        public int compareTo(Pair arg0) {
            {
                return this.v-arg0.v;
            }
        }
    }
    private static class Pairl implements Comparable<Pairl>{
        long v,i;Pairl j;
        public Pairl(long a,long b){
            v=a;
            i=b;
        }
        public Pairl(long a,Pairl b)
        {
            v=a;
            j=b;
        }
        @Override
        public int compareTo(Pairl arg0) {
            {
                if(this.v>arg0.v)
                    return 1;
                else
                    return -1;
            }
        }
    }
    public static long f(long number,long m) {
          if (number <= 1) return 1;
          else return (number * f(number - 1,m))%m;
       }
    public static long mmi(long a, long m) 
    { 
        long m0 = m; 
        long y = 0, x = 1; 
      
        if (m == 1) 
          return 0; 
      
        while (a > 1) 
        { 
            // q is quotient 
            long q = a / m; 
            long t = m; 
      
            // m is remainder now, process same as 
            // Euclid's algo 
            m = a % m; a = t; 
            t = y; 
      
            // Update y and x 
            y = x - q * y; 
            x = t; 
        } 
      
        // Make x positive 
        if (x < 0) 
           x += m0; 
      
        return x; 
    } 
    public static class segtree{ 
        static int[] tree=new int[10000000];
        static int[] lazy=new int[10000000];
        public static void initial()
        {
            Arrays.fill(lazy, 0);
        }
        public static void build(int[] arr,int node,int l,int r)
        {
            if(l==r)
            {
                tree[node]=arr[l];
            }
            else
            {
                int m=(l+r)/2;
                build(arr,(2*node)+1,l,m);
                build(arr,(2*node)+2,m+1,r);
                tree[node]=tree[2*node+1]+tree[(2*node)+2];
            }
        }
        public static void updater(int[] arr,int node,int l,int r,int s,int e,int val)
        {
            if(lazy[node]!=0)
            {
                tree[node]+=(r-l+1)*lazy[node];
                if(l!=r)
                {
                    lazy[2*node+1]+=lazy[node];
                    lazy[2*node+2]+=lazy[node];
                }
                lazy[node]=0;
            }
            if(s<=l && e>=r)
            {
                tree[node]+=(r-l+1)*val;
                if(l!=r)
                {
                    lazy[2*node+1]+=val;
                    lazy[2*node+2]+=val;
                }
            }
            else if(!(e<l || r<s))
            {
                int m=(l+r)/2;
                updater(arr,2*node+1,l,m,s,e,val);
                updater(arr,2*node+2,m+1,r,s,e,val);
                tree[node]=tree[2*node+1]+tree[2*node+2];
            }
        }
        public static void update(int[] arr,int node,int l,int r,int ind,int val)
        {
            if(l==r)
            {
                arr[ind]+=val;
                tree[node]+=val;
            }
            else
            {
                int m=(l+r)/2;
                if(l<=ind && ind<=m)
                {
                    update(arr,(2*node+1),l,m,ind,val);
                }
                else
                {
                    update(arr,(2*node+2),m+1,r,ind,val);
                }
                tree[node]=tree[2*node+1]+tree[2*node+2];
            }
        }
        public static int query(int node,int l,int r,int s,int e)
        {
            if(lazy[node]!=0)
            {
                tree[node]+=(r-l+1)*lazy[node];
                if(l!=r)
                {
                    lazy[2*node+1]+=lazy[node];
                    lazy[2*node+2]+=lazy[node];
                }
                lazy[node]=0;
            }
            if(e<l || r<s)
                return 0;
            if(s<=l && e>=r)
                return tree[node];
            int m=(l+r)/2;
            int p1=query((2*node+1),l,m,s,e);
            int p2=query((2*node+2),m+1,r,s,e);
            return (p1+p2);
        }
    }
    
    private static long pow(long a, long b, long c) {
        if (b == 0)
            return 1;
        long p = pow(a, b / 2, c);
        p = (p * p) % c;
        return (b % 2 == 0) ? p : (a * p) % c;
    }
    private static long gcd(long n, long l) {
        if (l == 0)
            return n;
        return gcd(l, n % l);
    }
    private static int gcd(int n, int l) {
        if (l == 0)
            return n;
        return gcd(l, n % l);
    }
    private static long max(long a, long b) {
        if (a > b)
            return a;
        return b;
    }
    private static long min(long a, long b) {
        if (a < b)
            return a;
        return b;
    }
    public static void merge(int arr[], int l, int m, int r) 
    { 
        // Find sizes of two subarrays to be merged 
        int n1 = m - l + 1; 
        int n2 = r - m; 
  
        /* Create temp arrays */
        int L[] = new int [n1]; 
        int R[] = new int [n2]; 
  
        /*Copy data to temp arrays*/
        for (int i=0; i<n1; ++i) 
            L[i] = arr[l + i]; 
        for (int j=0; j<n2; ++j) 
            R[j] = arr[m + 1+ j]; 
  
  
        /* Merge the temp arrays */
  
        // Initial indexes of first and second subarrays 
        int i = 0, j = 0; 
  
        // Initial index of merged subarry array 
        int k = l; 
        while (i < n1 && j < n2) 
        { 
            if (L[i] <= R[j]) 
            { 
                arr[k] = L[i]; 
                i++; 
            } 
            else
            { 
                arr[k] = R[j]; 
                j++; 
            } 
            k++; 
        } 
  
        /* Copy remaining elements of L[] if any */
        while (i < n1) 
        { 
            arr[k] = L[i]; 
            i++; 
            k++; 
        } 
  
        /* Copy remaining elements of R[] if any */
        while (j < n2) 
        { 
            arr[k] = R[j]; 
            j++; 
            k++; 
        } 
    } 
    public static void merge(long arr[], int l, int m, int r) 
    { 
        // Find sizes of two subarrays to be merged 
        int n1 = m - l + 1; 
        int n2 = r - m; 
  
        /* Create temp arrays */
        long L[] = new long [n1]; 
        long R[] = new long [n2]; 
  
        /*Copy data to temp arrays*/
        for (int i=0; i<n1; ++i) 
            L[i] = arr[l + i]; 
        for (int j=0; j<n2; ++j) 
            R[j] = arr[m + 1+ j]; 
  
  
        /* Merge the temp arrays */
  
        // Initial indexes of first and second subarrays 
        int i = 0, j = 0; 
  
        // Initial index of merged subarry array 
        int k = l; 
        while (i < n1 && j < n2) 
        { 
            if (L[i] <= R[j]) 
            { 
                arr[k] = L[i]; 
                i++; 
            } 
            else
            { 
                arr[k] = R[j]; 
                j++; 
            } 
            k++; 
        } 
  
        /* Copy remaining elements of L[] if any */
        while (i < n1) 
        { 
            arr[k] = L[i]; 
            i++; 
            k++; 
        } 
  
        /* Copy remaining elements of R[] if any */
        while (j < n2) 
        { 
            arr[k] = R[j]; 
            j++; 
            k++; 
        } 
    } 
    public static void sort(long arr[])
    {
    	sort(arr,0,arr.length-1);
    }
    public static void sort(int arr[])
    {
    	sort(arr,0,arr.length-1);
    }
    public static void sort(int arr[], int l, int r) 
    { 
        if (l < r) 
        { 
            // Find the middle point 
            int m = (l+r)/2; 
  
            // Sort first and second halves 
            sort(arr, l, m); 
            sort(arr , m+1, r); 
  
            // Merge the sorted halves 
            merge(arr, l, m, r); 
        } 
    } 
    public static void sort(long arr[], int l, int r) 
    { 
        if (l < r) 
        { 
            // Find the middle point 
            int m = (l+r)/2; 
  
            // Sort first and second halves 
            sort(arr, l, m); 
            sort(arr , m+1, r); 
  
            // Merge the sorted halves 
            merge(arr, l, m, r); 
        } 
    } 
    public static void main(String[] args) throws Exception {
        new Thread(null,new Runnable(){
            @Override
            public void run() {
               /* try {
                    InputReader(new FileInputStream("input.txt"));
                } catch (FileNotFoundException e) {
                    // TODO Auto-generated catch block
                    e.printStackTrace();
                }*/
                InputReader(System.in);
                pw = new PrintWriter(System.out);
                /*try {
                    pw=new PrintWriter(new FileOutputStream("output.txt"));
                } catch (FileNotFoundException e) {
                    // TODO Auto-generated catch block
                    e.printStackTrace();
                }*/
                soln(); 
                pw.close();
            }
        },"1",1<<26).start();
    }

    public static void InputReader(InputStream stream1) {
        stream = stream1;
    }

    private static boolean isWhitespace(int c) {
        return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
    }

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

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

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

    private static long nl() {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        int sgn = 1;
        if (c == '-') {
            sgn = -1;
            c = read();
        }
        long res = 0;
        do {
            if (c < '0' || c > '9')
                throw new InputMismatchException();
            res *= 10;
            res += c - '0';
            c = read();
        } while (!isSpaceChar(c));
        return res * sgn;
    }
    private static double nd()
    {
        double ret = 0, div = 1;
        int c = read();
        while (c <= ' ')
            c = read();
        boolean neg = (c == '-');
        if (neg)
            c = read();

        do {
            ret = ret * 10 + c - '0';
        }
        while ((c = read()) >= '0' && c <= '9');

        if (c == '.')
        {
            while ((c = read()) >= '0' && c <= '9')
            {
                ret += (c - '0') / (div *= 10);
            }
        }

        if (neg)
            return -ret;
        return ret;
    }
    private static String nextToken() {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        StringBuilder res = new StringBuilder();
        do {
            res.appendCodePoint(c);
            c = read();
        } while (!isSpaceChar(c));
        return res.toString();
    }

    private static String nli() {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        StringBuilder res = new StringBuilder();
        do {
            res.appendCodePoint(c);
            c = read();
        } while (!isEndOfLine(c));
        return res.toString();
    }
    
    private static int[] nia(int n) {
        int[] arr = new int[n];
        for (int i = 0; i < n; i++) {
            arr[i] = ni();
        }
        return arr;
    }

    private static long[] nla(int n) {
        long[] arr = new long[n];
        for (int i = 0; i < n; i++) {
            arr[i] = nl();
        }
        return arr;
    }

    private static void pa(int[] arr) {
        for (int i = 0; i < arr.length; i++) {
            pw.print(arr[i] + " ");
        }
        pw.println();
        return;
    }

    private static void pa(long[] arr) {
        for (int i = 0; i < arr.length; i++) {
            pw.print(arr[i] + " ");
        }
        pw.println();
        return;
    }
    private static void pl(int a)
    {
    	pw.println(a);
    }
    private static void pl(long a)
    {
    	pw.println(a);
    }
    private static void p(int a)
    {
    	pw.print(a+" ");
    }
    private static void p(long a)
    {
    	pw.print(a+" ");
    }
    private static boolean isSpaceChar(int c) {
        if (filter != null)
            return filter.isSpaceChar(c);
        return isWhitespace(c);
    }
    private static char nc() {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        char c1=(char)c;
        while(!isSpaceChar(c))
            c=read();
        return c1;
    }
    public String ns() {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        StringBuilder res = new StringBuilder();
        do {
            res.appendCodePoint(c);
            c = read();
        } while (!isSpaceChar(c));
        return res.toString();
    }
    private interface SpaceCharFilter {
        public boolean isSpaceChar(int ch);
    }
}