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.
import java.io.BufferedOutputStream;
import java.io.DataInputStream;
import java.io.FileInputStream;
import java.io.IOException;
import java.io.OutputStream;
import java.util.ArrayList;

public class test {
	
	private static FastReader fr;
    private static OutputStream out;
    
	private static class FastReader 
    { 
        final private int BUFFER_SIZE = 1 << 16; 
        private DataInputStream din; 
        private byte[] buffer; 
        private int bufferPointer, bytesRead; 
  
        public FastReader() 
        { 
            din = new DataInputStream(System.in); 
            buffer = new byte[BUFFER_SIZE]; 
            bufferPointer = bytesRead = 0; 
        } 
  
        public FastReader(String file_name) throws IOException 
        { 
            din = new DataInputStream(new FileInputStream(file_name)); 
            buffer = new byte[BUFFER_SIZE]; 
            bufferPointer = bytesRead = 0; 
        } 
  
        public String readLine() throws IOException 
        { 
            byte[] buf = new byte[1024];
            int cnt = 0, c; 
            while ((c = read()) != -1) 
            { 
                if (c == '\n') 
                    break; 
                buf[cnt++] = (byte) c; 
            } 
            return new String(buf, 0, cnt); 
        } 
  
        public int nextInt() throws IOException 
        { 
            int ret = 0; 
            byte 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 (neg) 
                return -ret; 
            return ret; 
        } 
  
        public long nextLong() throws IOException 
        { 
            long ret = 0; 
            byte 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 (neg) 
                return -ret; 
            return ret; 
        } 
  
        public double nextDouble() throws IOException 
        { 
            double ret = 0, div = 1; 
            byte 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 void fillBuffer() throws IOException 
        { 
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE); 
            if (bytesRead == -1) 
                buffer[0] = -1; 
        } 
  
        private byte read() throws IOException 
        { 
            if (bufferPointer == bytesRead) 
                fillBuffer(); 
            return buffer[bufferPointer++]; 
        } 
  
        public void close() throws IOException 
        { 
            if (din == null) 
                return; 
            din.close(); 
        } 
        
        public int[] nextIntArray(int n) throws IOException {
        	int arr[] = new int[n];
        	for(int i=0;i<n;i++){
        		arr[i] = nextInt();
        	}
        	return arr;
        }
    } 
 
	private static void print(Object str) {
        try {
            out.write(str.toString().getBytes());
        } catch (IOException e) {
            e.printStackTrace();
        }
    }
	
	private static void println(Object str) {
        try {
            out.write((str.toString() + "\n").getBytes());
        } catch (IOException e) {
            e.printStackTrace();
        }
    }
	
	private static void printArray(int arr[]){
		for(int val: arr){
			print(val + " ");
		}
	}
	
	public static void main(String args[]) throws IOException{
		run();
	}
	
	private static void run() throws IOException{
		fr = new FastReader();
		out = new BufferedOutputStream(System.out);
		solve();
		out.flush();
		out.close();
	}
	
	private static void solve() throws IOException{
		int n = fr.nextInt();
		int a[] = fr.nextIntArray(n-1);
		int b[] = fr.nextIntArray(n-1);
		int t[] = new int[n];
		int ans[] = new int[n];
		boolean bool = true;
		boolean first = true;
		
		for(int i=0;i<4 && bool;i++){
			for(int j=0;j<4 && bool;j++){
				int x = i | j;
				int y = i & j;
				if(x == a[0] && y == b[0]){
					t[0] = i;
					t[1] = j;
					ans[0] = j;
					ans[1] = i;
					bool = false;
					break;
				}
			}
		}
		
		if(bool){
			println("NO");
		}else{
			bool = true;
			for(int count=1;count < n-1 && bool;count++){
				bool = false;
				first = false;
				for(int i=0;i<4;i++){
					int x = t[count] | i;
					int y = t[count] & i;
					if(x == a[count] && y == b[count]){
						t[count+1] = i;
						bool = true;
						first = true;
						break;
					}
				}
			}
			
			if(!bool){
				bool = true;
				for(int count=1;count < n-1 && bool;count++){
					bool = false;
					for(int i=0;i<4;i++){
						int x = ans[count] | i;
						int y = ans[count] & i;
						if(x == a[count] && y == b[count]){
							ans[count+1] = i;
							bool = true;
							break;
						}
					}
				}
			}
			
			println("YES");
			if(first){
				printArray(t);
			}else{
				printArray(ans);
			}
		}
	}
	
	private static int factorial(int n){
		int fac = 1;
		for(int i=2;i<=n;i++){
			fac *= i;
		}
		
		return fac;
	}
	
	private boolean isPrime(int n){
		if(n == 0 || n == 1){
			return false;
		}else if(n%2 == 0){
			return false;
		}else{
			int x = (int)(Math.sqrt(n)) + 1;
			for(int i=3;i<=x;i+=2){
				if(n % i == 0){
					return false;
				}
			}
			return true;
		}
	}
	
	private long pow(int base,int exp){
		if(exp == 0){
			return 1;
		}else if(exp == 1){
			return base;
		}else{
			long a = pow(base,exp/2);
			if(exp%2 == 0){
				return a * a;
			}else{
				return a * a * base;
			}
		}
		
	}

	private static int gcd(int a,int b){
		if(a == 0){
			return b;
		}
		
		return gcd(b%a,a);
	}
	
	private static int lcm(int a,int b){
		return (a * b)/gcd(a,b);
	}
	
	private static ArrayList<Integer> SieveOfEratosthenes(int n){
		boolean b[] = new boolean[n+1];
		b[0] = true;
		b[1] = true;
		for(int i=2;i<=5;i++){
			int j = 2;
			while(i * j <= n && !b[i]){
				b[i * j] = true;
				j++;
			}
		}
		
		ArrayList<Integer> arr = new ArrayList<>();
		for(int i=2;i<n+1;i++){
			if(!b[i]){
				arr.add(i);
			}
		}
		
		return arr;
	}

}
