When Masha came to math classes today, she saw two integer sequences of length n - 1 on the blackboard. Let's denote the elements of the first sequence as a_i (0 ≤ a_i ≤ 3), and the elements of the second sequence as b_i (0 ≤ b_i ≤ 3).

Masha became interested if or not there is an integer sequence of length n, which elements we will denote as t_i (0 ≤ t_i ≤ 3), so that for every i (1 ≤ i ≤ n - 1) the following is true: 

  * a_i = t_i | t_{i + 1} (where | denotes the [bitwise OR operation](https://en.wikipedia.org/wiki/Bitwise_operation#OR)) and 
  * b_i = t_i \& t_{i + 1} (where \& denotes the [bitwise AND operation](https://en.wikipedia.org/wiki/Bitwise_operation#AND)). 



The question appeared to be too difficult for Masha, so now she asked you to check whether such a sequence t_i of length n exists. If it exists, find such a sequence. If there are multiple such sequences, find any of them.

Input

The first line contains a single integer n (2 ≤ n ≤ 10^5) — the length of the sequence t_i. 

The second line contains n - 1 integers a_1, a_2, …, a_{n-1} (0 ≤ a_i ≤ 3) — the first sequence on the blackboard.

The third line contains n - 1 integers b_1, b_2, …, b_{n-1} (0 ≤ b_i ≤ 3) — the second sequence on the blackboard.

Output

In the first line print "YES" (without quotes), if there is a sequence t_i that satisfies the conditions from the statements, and "NO" (without quotes), if there is no such sequence.

If there is such a sequence, on the second line print n integers t_1, t_2, …, t_n (0 ≤ t_i ≤ 3) — the sequence that satisfies the statements conditions.

If there are multiple answers, print any of them.

Examples

Input

4
3 3 2
1 2 0


Output

YES
1 3 2 0 

Input

3
1 3
3 2


Output

NO

Note

In the first example it's easy to see that the sequence from output satisfies the given conditions: 

  * t_1 | t_2 = (01_2) | (11_2) = (11_2) = 3 = a_1 and t_1 \& t_2 = (01_2) \& (11_2) = (01_2) = 1 = b_1; 
  * t_2 | t_3 = (11_2) | (10_2) = (11_2) = 3 = a_2 and t_2 \& t_3 = (11_2) \& (10_2) = (10_2) = 2 = b_2; 
  * t_3 | t_4 = (10_2) | (00_2) = (10_2) = 2 = a_3 and t_3 \& t_4 = (10_2) \& (00_2) = (00_2) = 0 = b_3. 



In the second example there is no such sequence.
    //    A Computer is Like a mischievous genie.
    //    It will give you exactly what you ask for,
    //    but not always what you want
    //    A code by Rahul Verma


    import java.io.BufferedOutputStream;
    import java.io.BufferedReader;
    import java.io.IOException;
    import java.io.InputStreamReader;
    import java.io.PrintWriter;
    import java.math.BigInteger;
    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.LinkedHashSet;
    import java.util.LinkedList;
    import java.util.List;
    import java.util.PriorityQueue;
    import java.util.Queue;
    import java.util.Set;
    import java.util.Stack;
    import java.util.StringTokenizer;
    import java.util.TreeMap;
    import java.util.TreeSet;


    public class Main {


        static class Clock {

            protected long start, stop;

            public void start() {

                start = System.currentTimeMillis();
            }

            public void stop() {
                stop = System.currentTimeMillis();
            }

            public String getTime() {

                return ((stop - start) + " ms");
            }
        }


        public static PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));

        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 nextInt() {
                return Integer.parseInt(next());
            }

            long nextLong() {
                return Long.parseLong(next());
            }

            double nextDouble() {
                return Double.parseDouble(next());
            }

            String[] nextSArray() {
                String sr[] = null;
                try {
                    sr = br.readLine().trim().split(" ");
                } catch (IOException e) {
                    e.printStackTrace();
                }
                return sr;
            }

            String nextLine() {
                String str = "";
                try {
                    str = br.readLine();
                } catch (IOException e) {
                    e.printStackTrace();
                }

                return str;
            }
        }


        static long powmodulo(long a, long p) {
            if (p == 0) {
                return 1 % mod;
            }
            if (p == 1) {
                return a % mod;
            }
            long ans = 1;
            while (p > 0) {
                if ((p & 1) > 0) {
                    ans = (ans * a) % mod;
                }
                a = (a * a) % mod;
                p = p >> 1;
            }
            return ans % mod;
        }


        static long mod = 1000000007;

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

        static long fast_powerNumbers(long a, long n) {
            if (n == 1) {
                return a;
            }
            long ans = fast_powerNumbers(a, n / 2);
            if (n % 2 == 0) {
                return (ans * ans);
            } else {
                return ((ans * ans) * (a));
            }
        }


        static void dfs_helper(int[][] arr, int i, int j, int team, int n, int m) {
            arr[i][j] = team;
            if (i - 1 >= 0 && arr[i - 1][j] == 1) {
                dfs(arr, i - 1, j, team, n, m);
            }
            if (j - 1 >= 0 && arr[i][j - 1] == 1) {
                dfs(arr, i, j - 1, team, n, m);
            }
            if (i + 1 < n && arr[i + 1][j] == 1) {
                dfs(arr, i + 1, j, team, n, m);
            }
            if (j + 1 < m && arr[i][j + 1] == 1) {
                dfs(arr, i, j + 1, team, n, m);
            }

        }

        static void dfs(int[][] arr, int i, int j, int team, int n, int m) {
            dfs_helper(arr, i, j, team, n, m);

        }
        public static int arr[];


        static void seive(int n) {
            // 1 is not prime
            arr = new int[n + 1];
            arr[0] = arr[1] = 1;
            for (int i = 4; i <= n; i = i + 2) {
                arr[i] = 1;
            }
            for (int i = 3; i * i <= n; i = i + 2) {
                if (arr[i] == 0) {
                    for (int j = i * i; j <= n; j = j + i) {
                        arr[j] = 1;
                    }

                }
            }
        }


        public static HashMap<Integer,Integer> primefac(int n)
        {
            HashMap<Integer,Integer>hm=new HashMap<>();
            //int x = (int) Math.sqrt(n);
            for (int i = 2; i <=n; i++) {
                int x=0;
                while(n%i==0)
                {
                    n=n/i;
                    ++x;
                }
                if(x!=0)
                {
                    hm.put(i,x);
                }
            }
            return hm;
        }
       static long fac(int p)
       {
           if(p==0||p==1)
               return 1;
           return p*fac(p-1);
       }





        public static void main(String[] args) throws Exception {
            FastReader sc = new FastReader();

            Clock clock = new Clock();

            clock.start();
            int n=sc.nextInt()-1;
            int arr[]=new int[n];
            int brr[]=new int[n];
            for (int i = 0; i < n; i++) {
                arr[i]=sc.nextInt();
            }
            for (int i = 0; i < n; i++) {
                brr[i]=sc.nextInt();
            }
            int crr[]=new int[n+1];
            boolean ans=true;
            for (int i = 0; i < n; i++) {
                
                if((brr[i]&1)==1)
                {
                    crr[i]+=1;
                    crr[i+1]+=1;
                }
                if((brr[i]&2)==2)
                {
                    crr[i]+=2;
                    crr[i+1]+=2;
                }
            }
            for (int i = 0; i < n; i++) {
                if((arr[i]&1)==0)
                {
                    if((crr[i]&1)==0&&(crr[i+1]&1)==0)
                    {

                    }
                    else
                    {
                        ans=false;
                        break;
                    }
                }

                if((arr[i]&2)==0)
                {
                    if((crr[i]&2)==0&&(crr[i+1]&2)==0)
                    {

                    }
                    else
                    {
                        ans=false;
                        break;
                    }
                }
            }
            if (ans) {
                out.println("YES");
                for (int i = 0; i <= n; i++) {
                    out.print(crr[i] + " ");
                }
                out.close();
            } else {
                System.out.println("NO");
            }

        }}

    class Pair{

        int a,b;
        Pair(int a,int b)
        {
            this.a=a;
            this.b=b;
        }
    }

    class DSU
    {
        int parent[];
        int rank[];
        DSU(int n)
        {
            parent=new int[n];
            rank=new int[n];
            for (int i = 0; i < n; i++) {
                parent[i]=-1;
                rank[i]=1;
            }
        }

        int find(int s1)
        {
            if(parent[s1]==-1)
                return s1;
            return parent[s1]=find(parent[s1]);
        }

        void unite(int s1, int s2)
        {
            int p1=find(s1);
            int p2=find(s2);
            if(p1!=p2)
            {
                if(rank[p1]>rank[p2])
                {
                    parent[p2]=p1;
                    rank[p1]+=rank[p2];
                }
                else
                {
                    parent[p1]=p2;
                    rank[p2]+=rank[p1];
                }
            }
        }
    }

    class Gaph {

        HashMap<Integer, ArrayList<Integer>> hm;

        Gaph() {
            hm = new HashMap<>();
        }

        Gaph(int n) {

            hm = new HashMap<>();
            for (int i = 0; i < n; i++) {
                hm.put(i, new ArrayList<Integer>());
            }
        }

        // function for adding an edge.................................................
        public void addEdge(int a, int b, boolean isDir) {
            if (isDir) {
                if (hm.containsKey(a)) {
                    hm.get(a).add(b);
                } else {
                    hm.put(a, new ArrayList<>(Arrays.asList(b)));
                }
            } else {
                if (hm.containsKey(a)) {
                    hm.get(a).add(b);
                } else if (!hm.containsKey(a)) {
                    hm.put(a, new ArrayList<>(Arrays.asList(b)));
                }

                if (hm.containsKey(b)) {
                    hm.get(b).add(a);
                } else if (!hm.containsKey(b)) {
                    hm.put(b, new ArrayList<>(Arrays.asList(a)));
                }
            }
        }


    }

    // out.println(al.toString().replaceAll("[\\[|\\]|,]",""));