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.util.*;
import java.io.*;
public class candy{
    public static void main(String args[])throws IOException
{
InputStreamReader read=new InputStreamReader(System.in);
BufferedReader in=new BufferedReader(read);
     Scanner ob=new Scanner(System.in);
     int n=ob.nextInt();
     int a[]=new int[n];
     int b[]=new int[n];
     int c[]=new int[n],f=0,flag=0;
int x=-1,y=-1,w=-1,z=-1;
     for(int i=0;i<n-1;i++)
    a[i]=ob.nextInt();
     for(int i=0;i<n-1;i++)
    b[i]=ob.nextInt();
for(int i=0;i<4;i++)
for(int j=0;j<4;j++)
if((i&j)==b[n-2] && (i|j)==a[n-2])
{
if(flag==1)
{
w=i;
z=j;
}
else
{
x=i;
y=j;
}
flag=1;
}
if(flag==1)
{
if(w!=-1&&n!=2)
for(int i=0;i<4;i++)
if((i&w)==b[n-3] && (i|w)==a[n-3])
{
x=w;
y=z;
}

c[n-1]=y;
c[n-2]=x;
for(int i=n-3;i>=0;i--)
{
int k=0;
for(int j=0;j<4;j++)
if(b[i]==(j&c[i+1]) && a[i]==(j|c[i+1]))
{
f++;
k=1;
c[i]=j;
break;
}
if(k==0)
break;
}
if(f==n-2)
{
System.out.println("YES");
for(int i=0;i<n;i++)
System.out.print(c[i]+" ");
}
else
System.out.println("NO");
}
else
System.out.println("NO");
}}