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.util.*;
import java.io.*;
import java.math.BigInteger;
 public class Solution
{
     static class Pair<A,B>{
        A parent;
        B rank;
        Pair(A parent,B rank)
        {
            this.rank=rank;
            this.parent=parent;
        }
    }
//    static int find(Pair pr[],int i)
//    {
//        if(i==pr[i].parent)
//            return i;
//        else
//        {
//            pr[i].parent=find(pr,pr[i].parent);
//            return pr[i].parent;
//        }
//    }
//    static void join(Pair[] pr,int i,int j)
//    {
//        i=find(pr,i);
//        j=find(pr,j);
//        if(i==j)
//            return;
//        if(pr[i].rank>=pr[j].rank)
//        {
//            pr[j].parent=i;
//            pr[i].rank+=pr[j].rank;
//        }
//        else
//        {
//            pr[i].parent = j;
//            pr[j].rank+=pr[i].rank;
//        }
//    }
    static void swap(char ar[],int i,int j)
    {
        char f = ar[i];
        ar[i]=ar[j];
        ar[j]=f;
    }
     static long powers(long n) 
    { 
        int MOD=1000000007;
        if (n <= 1) { 
            return 1; 
        }
        n--;
  
        // This is an identity matrix. 
        long res[][] = { { 1, 0 }, { 0, 1 } }; 
  
        // this is Transformation matrix. 
        long tMat[][] = { { 2, 2 }, { 1, 0 } };
        while (n > 0) { 
            if (n % 2 == 1) { 
                long tmp[][] = new long[2][2]; 
                tmp[0][0] = ((res[0][0] * tMat[0][0])%MOD 
                             + (res[0][1] * tMat[1][0])%MOD) 
                            %MOD;
                tmp[0][1] = ((res[0][0] * tMat[0][1])%MOD 
                             + (res[0][1] * tMat[1][1])%MOD) 
                            %MOD; 
                tmp[1][0] = ((res[1][0] * tMat[0][0])%MOD 
                             + (res[1][1] * tMat[1][0])%MOD) 
                            % MOD; 
                tmp[1][1] = ((res[1][0] * tMat[0][1])%MOD 
                             + (res[1][1] * tMat[1][1])%MOD) 
                            % MOD;
                res[0][0] = tmp[0][0]; 
                res[0][1] = tmp[0][1]; 
                res[1][0] = tmp[1][0]; 
                res[1][1] = tmp[1][1]; 
            } 
  
            n = n / 2; 
            long tmp[][] = new long[2][2]; 
            tmp[0][0] = ((tMat[0][0] * tMat[0][0])%MOD 
                         + (tMat[0][1] * tMat[1][0])%MOD) 
                        % MOD; 
            tmp[0][1] = ((tMat[0][0] * tMat[0][1])%MOD 
                         + (tMat[0][1] * tMat[1][1])%MOD) 
                        % MOD; 
            tmp[1][0] = ((tMat[1][0] * tMat[0][0])%MOD 
                         + (tMat[1][1] * tMat[1][0])%MOD) 
                        % MOD; 
            tmp[1][1] = ((tMat[1][0] * tMat[0][1])%MOD 
                         + (tMat[1][1] * tMat[1][1])%MOD) 
                        % MOD; 
            tMat[0][0] = tmp[0][0]; 
            tMat[0][1] = tmp[0][1]; 
            tMat[1][0] = tmp[1][0]; 
            tMat[1][1] = tmp[1][1]; 
        }
        return ((res[0][0]*6)%MOD + (res[0][1] * 2) % MOD)%MOD; 
    }
     static ArrayList<Integer> flip = new ArrayList<>();
     static int ans=0;
    public static void main (String[] args) throws IOException
    {
        StringBuilder sb = new StringBuilder();
        FastReader s1 = new FastReader();
        int n=s1.I();
//        int k=s1.I();
        ArrayList<Integer> map[] = new ArrayList[n];
        for(int i=0;i<n;i++)
            map[i]=new ArrayList<Integer>();
        for(int i=0;i<n-1;i++)
        {
            int u=s1.I()-1;
            int v=s1.I()-1;
            map[u].add(v);
            map[v].add(u);
        }
        int given[] = new int[n];
        int req[] = new int[n];
        for(int i=0;i<n;i++)
        {
            given[i]=s1.I();
        }
        for(int i=0;i<n;i++)
        {
            req[i]=s1.I();
        }
        boolean visited[] = new boolean[n];
        boolean gp[] = new boolean[n];
        int parent[] = new int[n];
        parent[0]=-1;
        dfs(0,visited,map,req,given,parent,gp);
        sb.append(ans+"\n");
        for(int i:flip)
        {
            sb.append((i+1)+"\n");
        }
        System.out.println(sb);
    }
    static void dfs(int index,boolean visited[],ArrayList<Integer> ar[],int req[],int given[],int parent[],boolean gp[])
    {
        visited[index]=true;
//        System.out.println("here "+index+" "+parent[index]+" "+req[index]+" "+given[index]);
        int papa = parent[index];
        if(papa!=0 && papa!=-1)
        {
//            System.out.println("oooo "+gp[parent[papa]]);
            if(gp[parent[papa]])
            {
                given[index]=(given[index]^1);
                gp[index]=true;
            }
        }
//        System.out.println("okk "+req[index]+" "+given[index]+" "+gp[index]);
        if(req[index]!=given[index])
        {
            ans++;
            flip.add(index);
            gp[index]=(gp[index]^true);
//            System.out.println("inside "+gp[index]);
        }
        for(int i:ar[index])
        {
            if(!visited[i])
            {
                parent[i]=index;
                dfs(i,visited,ar,req,given,parent,gp);
            }
        }
    }
       static long computeXOR(long n) 
    { 
        // If n is a multiple of 4 
        if (n % 4 == 0) 
            return n; 
       
        // If n%4 gives remainder 1 
        if (n % 4 == 1) 
            return 1; 
       
        // If n%4 gives remainder 2 
        if (n % 4 == 2) 
            return n + 1; 
       
        // If n%4 gives remainder 3 
        return 0; 
    }
    static ArrayList<Integer> primeFactor(int n)
    {
        ArrayList<Integer> ans = new ArrayList<>();
        if(n%2==0)
            ans.add(2);
        while (n%2==0)
        {   
            n /= 2;
        }
        for (int i = 3; i <= Math.sqrt(n); i+= 2)
        {
            if(n%i==0)
                ans.add(i);
            while (n%i == 0)
            {
                n /= i;
            }
        }
        if (n > 2)
            ans.add(n);
        return ans;
    }
    static class FastReader{
        BufferedReader br;
        StringTokenizer st;
        public FastReader()
        {
            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 I()
        {
            return Integer.parseInt(next());
        }
        
        long L()
        {
            return Long.parseLong(next());
        }
        
        double D()
        {
            return Double.parseDouble(next());
        }
        
        String nextLine()
        {
            String str = "";
            try
            {
                str = br.readLine();
            }
            catch (IOException e)
            {
                e.printStackTrace();
            }
            return str;
        }
    }
    static long gcd(long a,long b)
    {
        if(a%b==0)
            return b;
        return gcd(b,a%b);
    }
    static float power(float x, int y)
    {
        float temp;
        if( y == 0)
            return 1;
        temp = power(x, y/2);
        
        if (y%2 == 0)
            return temp*temp;
        else
        {
            if(y > 0)
                return x * temp * temp;
            else
                return (temp * temp) / x;
        }
    }
    static long pow(long x, long y)
    {
        int p =  1000000007;
        long res = 1;
        x = x % p;
        if(x<0)
            x+=p;
        while (y > 0)
        {
            if((y & 1)==1){
                res = (res * x) % p;
                if(res<0)
                    res+=p;
            }
            y = y >> 1;
            x = (x * x) % p;
        }
        return res;
    }
    static void sieveOfEratosthenes(int n)
    {
        ArrayList<Integer> prime=new ArrayList<Integer>();
        boolean Prime[] = new boolean[n+1];
        for(int i=2;i<n;i++)
            Prime[i] = true;
        
        for(int p = 2; p*p <=n; p++)
        {
            if(Prime[p] == true)
            {
                prime.add(p);
                for(int i = p*p; i <= n; i += p)
                    Prime[i] = false;
            }
        }
    }
}