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.math.*;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;

     //--------------->>>>IF YOU ARE HERE FOR QUICKSORT HACK THEN SORRY NO HACK FOR YOU<<<-------------------

public class a{ 
     static long[] count,count1,count2;
     static boolean[] prime;
     static Node[] nodes,nodes1,nodes2;
     static NodeInt[] nodesInt,nodesInt1;
     static long[] arr;
     static long[][] cost;
     static int[] arrInt,darrInt,farrInt;
     static long[][] dp;
     static char[] ch,ch1;
     static long[] darr,farr;
     static long[][] mat,mat1;
     static boolean[] vis;
     static long x,h;
     static long maxl;
     static double dec;
     static long mx = (long)1e7;
     static long inf = (long)1e15;
     static String s,s1,s2,s3,s4;
     static long minl;   
     static long mod = ((long)(1e9))+7;
     // static int minl = -1;
     // static long n;
     static int n,n1,n2,q,r1,c1,r2,c2;
     static int arr_size = (int)2e5+10;
     static long a;
     static long b;
     static long c;
     static long d;
     static long y,z;
     static int m;
     static int ans;
     static long k;
     static FastScanner sc;
     static String[] str,str1;
     static Set<Integer> set,set1,set2;
     static SortedSet<Long> ss;
     static List<Integer> list,list1,list2,list3;
     static PriorityQueue<Node> pq,pq1;
     static LinkedList<Node> ll,ll1,ll2;
     static Map<Integer,List<Integer>> map1;
     static Map<Integer,List<Integer>> map;
     static StringBuilder sb,sb1,sb2;
     static int index;
     static long[] sum;
     static int[] dx = {0,-1,0,1,-1,1,-1,1};
     static int[] dy = {-1,0,1,0,-1,-1,1,1};

     // public static void solve(){

     //    FastScanner sc = new FastScanner();
     //    // int t = sc.nextInt();
     //    int t = 1;
     //    for(int tt = 0 ; tt < t ; tt++){

     //        // s = sc.next();
     //        // s1 = sc.next();

     //        n = sc.nextInt();

     //        m = sc.nextInt();

     //        // int k = sc.nextInt();

     //        // sb = new StringBuilder();

     //        map = new HashMap<>();
     //        map1 = new HashMap<>();

     //        // q = sc.nextInt();
     //        // sb = new StringBuilder();
     //        // long k = sc.nextLong();

     //        // ch = sc.next().toCharArray();

     //        // count = new int[200002];
           
     //        // m = sc.nextInt();

     //        for(int o = 0 ; o < m ; o++){

     //            int l = sc.nextInt()-1;
     //            int r = sc.nextInt()-1;

     //        }

     //    }
        
     // }

     //--------------->>>>IF YOU ARE HERE FOR QUICKSORT HACK THEN SORRY NO HACK FOR YOU<<<-------------------

     public static void solve(){

        map = new HashMap<>();
        sb = new StringBuilder();
        if(n != 1){
            for(int i = 0 ; i < n-1 ; i++){
                int u = sc.nextInt();
                int v = sc.nextInt();
                if(!map.containsKey(u))
                    map.put(u,new ArrayList<>());
                if(!map.containsKey(v))
                    map.put(v,new ArrayList<>());
                map.get(u).add(v);
                map.get(v).add(u);
            }
        }

        arrInt = new int[n+1];
        darrInt = new int[n+1];

        for(int i = 0 ; i < n ; i++){
            arrInt[i+1] = sc.nextInt();
        }

        for(int i = 0 ; i < n ; i++){
            darrInt[i+1] = sc.nextInt();
        }

        if(n == 1){
            if(arrInt[1] == darrInt[1]){
                System.out.println("0");
            }
            else{
                System.out.println("1");
                System.out.print("1"); 
            }
            return;
        }

        ans = 0;
        vis = new boolean[n+1];
        Arrays.fill(vis,false);
        dfs(1,0,0,0);
        System.out.println(ans);
        System.out.print(sb);
     }

     public static void dfs(int i,int odd,int even,int hyt){

        vis[i] = true;
        int curr = arrInt[i];

        if(hyt%2 == 0 && even%2 == 1)
            curr = 1 - curr;

        if(hyt%2 == 1 && odd%2 == 1)
            curr = 1 - curr;

        List<Integer> list = map.get(i);

        if(darrInt[i] != curr){
            ans += 1;
            sb.append(i+"\n");
            if(hyt%2 == 0)
                even += 1;
            else
                odd += 1;
        }

        for(Integer j : list){
            if(vis[j])
                continue;
            dfs(j,odd,even,hyt+1);
        }

        // System.out.println("here");

     }
        
     public static void main(String[] args) {

            sc = new FastScanner();
            // Scanner sc = new Scanner(System.in);
            // int t = sc.nextInt();
            int t = 1;
            // int l = 1;
            while(t > 0){
                
                // n = sc.nextInt();
                // n = sc.nextLong();
                // k = sc.nextLong();
                // x = sc.nextLong();
                // y = sc.nextLong();
                // z = sc.nextLong();

                // a = sc.nextLong();
                // b = sc.nextLong();
                // c = sc.nextLong();
                // d = sc.nextLong();

                // x = sc.nextLong();
                // y = sc.nextLong();
                // z = sc.nextLong();
                // d = sc.nextLong();

                n = sc.nextInt();

                // n1 = sc.nextInt();

                // m = sc.nextInt();
                // q = sc.nextInt();

                // a = sc.nextLong();
                // b = sc.nextLong();

                // k = sc.nextLong();

                // x = sc.nextLong();
                // d = sc.nextLong();

                // s = sc.next();

                // ch = sc.next().toCharArray();
                // ch1 = sc.next().toCharArray();

                // m = sc.nextInt();
                // n = 6;

                // arr = new long[n];
                // for(int i = 0 ; i < n ; i++){
                //     arr[i] = sc.nextLong();
                // }

                // arrInt = new int[n];
                // for(int i = 0 ; i < n ; i++){
                //     arrInt[i] = sc.nextInt();
                // }
                // x = sc.nextLong();
                // y = sc.nextLong();
                // ch = sc.next().toCharArray();
                // m = n;
                // m = sc.nextInt();
                // darr = new long[m];
                // for(int i = 0 ; i < m ; i++){
                //     darr[i] = sc.nextLong();
                // }
                // k = sc.nextLong();
                // m = n;
                // darrInt = new int[n];
                // for(int i = 0 ; i < n ; i++){
                //     darrInt[i] = sc.nextInt();
                // }

                // farrInt = new int[m];
                // for(int i = 0; i < m ; i++){
                //     farrInt[i] = sc.nextInt();
                // }

                // m = n;
                // mat = new long[n][m];
                // for(int i = 0 ; i < n ; i++){
                //     for(int j = 0 ; j < m ; j++){
                //         mat[i][j] = sc.nextLong();
                //     }
                // }

                // m = n;
                // mat = new char[n][m];
                // for(int i = 0 ; i < n ; i++){
                //     String s = sc.next();
                //     for(int j = 0 ; j < m ; j++){
                //         mat[i][j] = s.charAt(j);
                //     }
                // }

                // str = new String[n];
                // for(int i = 0 ; i < n ; i++)
                //     str[i] = sc.next();

                // nodes = new Node[n];
                // for(int i = 0 ; i < n ;i++)
                //     nodes[i] = new Node(sc.nextLong(),sc.nextLong());

                // nodesInt = new NodeInt[n];
                // for(int i = 0 ; i < n ;i++)
                //     nodesInt[i] = new NodeInt(sc.nextInt(),sc.nextInt(),i);

                 solve();       
                 t -= 1;
            }

     }

    public static int log(long n,long base){

         if(n == 0 || n == 1)
             return 0;

         if(n == base)
             return 1;

         double num = Math.log(n);
         double den = Math.log(base);

         if(den == 0)
             return 0;

         return (int)(num/den);
     }

    public static boolean isPrime(long n) { 
    // Corner cases 
        if (n <= 1)  
            return false; 

        if (n <= 3)  
            return true; 
      
        // This is checked so that we can skip  
        // middle five numbers in below loop 
        if (n%2 == 0 || n%3 == 0) 
            return false; 
      
        for (int i=5; i*i<=n; i=i+6) 
            if (n%i == 0 || n%(i+2) == 0) 
               return false; 
      
        return true; 
    } 

    public static long gcd(long a, long b)
    {
      if (b == 0)
        return a;
      return gcd(b, a % b); 
    }

    public static long lcm(long a, long b)
    {
      return (b/gcd(b, a % b)) * a; 
    }

     public static long mod_inverse(long a,long mod){
        long x1=1,x2=0;
        long p=mod,q,t;
        while(a%p!=0){
          q = a/p;
          t = x1-q*x2;
          x1=x2; x2=t;
          t=a%p;
          a=p; p=t;
        }
        return x2<0 ? x2+mod : x2;
    }

     public static void swap(long[] curr,int i,int j){
         long temp = curr[j];
         curr[j] = curr[i];
         curr[i] = temp;
     }

    static final Random random=new Random();

    static void ruffleSortLong(long[] a) {
        int n=a.length;//shuffle, then sort 
        for (int i=0; i<n; i++) {
            int oi=random.nextInt(n);
            long temp=a[oi];
            a[oi]=a[i]; a[i]=temp;
        }
        Arrays.sort(a);
    }

    static void ruffleSortInt(int[] a) {
        int n=a.length;//shuffle, then sort 
        for (int i=0; i<n; i++) {
            int oi=random.nextInt(n);
            int temp=a[oi];
            a[oi]=a[i]; a[i]=temp;
        }
        Arrays.sort(a);
    }
    
    static void ruffleSortChar(char[] a) {
        int n=a.length;//shuffle, then sort 
        for (int i=0; i<n; i++) {
            int oi=random.nextInt(n);
            char temp=a[oi];
            a[oi]=a[i]; a[i]=temp;
        }
        Arrays.sort(a);
    }

    static long binomialCoeff(long n, long k){ 

        long res = 1; 
  
        // Since C(n, k) = C(n, n-k) 
        if (k > n - k) 
            k = n - k; 
  
        // Calculate value of 
        // [n * (n-1) *---* (n-k+1)] / [k * (k-1) *----* 1] 
        for (long i = 0; i < k; ++i) { 
            res = (res*(n - i)); 
            res = (res/(i + 1)); 
        } 

        return res; 
    } 

    static long[] fact;

    public static long inv(long n){
        return power(n, mod-2);
    }

    public static void fact(int n){
        fact = new long[n+1];
        fact[0] = 1;
        for(int j = 1;j<=n;j++)
            fact[j] = (fact[j-1]*(long)j)%mod;               
    }

    public static long binom(int n, int k){
        fact(n+1);
        long prod = fact[n];
        prod*=inv(fact[n-k]);
        prod%=mod;
        prod*=inv(fact[k]);
        prod%=mod;
        return prod;    
    }

    static long power(long x, long y){
        if (y == 0)
            return 1;
        if (y%2 == 1)
            return (x*power(x, y-1))%mod;
        return power((x*x)%mod, y/2)%mod;
    }

    public static long pow(long n,long p,long m){
     long  result = 1;
      if(p==0)
        return 1;
          
    while(p!=0)
    {
        if(p%2==1)
            result *= n;
        if(result>=m)
        result%=m;
        p >>=1;
        n*=n;
        if(n>=m)
        n%=m;
    }
    return result;
    }

    static void sieve(int n){ 

        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) 
            { 
                for(int i = p*p; i <= n; i += p) 
                    prime[i] = false; 
            } 
        } 

    }

    static class Node{
        int first;
        int second;
        Node(int f,int s){
            this.first = f;
            this.second = s;
        }
    }

    static class NodeInt{
        int first;
        int second;
        int third;
        NodeInt(int f,int s,int third){
            this.first = f;
            this.second = s;
            this.third = third;
        }
    }

    static long abs(long a){
        return Math.abs(a);
    }

    static int abs(int a){
        return Math.abs(a);
    }

    static int max(int a,int b){
    if(a>b)
            return a;
    else
            return b;
    }
 
    static int min(int a,int b){
    if(a>b)
            return b;
    else 
            return a;
    }
 
    static long max(long a,long b){
    if(a>b)
            return a;
    else
            return b;
    }
 
    static long min(long a,long b){
    if(a>b)
            return b;
    else 
            return a;
    }

    static long sq(long num){
        return num*num;
    }

     static class FastScanner {

                BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
                StringTokenizer st=new StringTokenizer("");
                String next() {
                        while (!st.hasMoreTokens())
                                try {
                                        st=new StringTokenizer(br.readLine());
                                } catch (IOException e) {
                                        e.printStackTrace();
                                }
                        return st.nextToken();
                }
                
                int nextInt() {
                        return Integer.parseInt(next());
                }
                int[] readArray(int n) {
                        int[] a=new int[n];
                        for (int i=0; i<n; i++) a[i]=nextInt();
                        return a;
                }
                long nextLong() {
                        return Long.parseLong(next());
                }
        }

}