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.
#include<stdio.h>
#include<string>
short int a[100000],b[100000],n;
std::string ss="",jj;
void son (int k,std::string s)
{
	int t=0,kk=0;
		if(k==n-1)
		{
			
		   	ss=s;
		   	return;
		}
		for(int j=0;j<4;j++)
		{kk=0;
			if((int(s[k]-'0')|j)==a[k]&&(int(s[k]-'0')&j)==b[k])
			{	if(k<n-1)
				{
					for(int e=0;e<4;e++)
					{
						if((e|j)==a[k+1]&&(e&j)==b[k+1])
						{
							kk=1;
						}
					}
				}
				if(kk==1)
				{
				 s=s+char(j+'0');
			     son(k+1,s);
			    t++;	
				}
				else if(k==n-1)
				{
					s=s+char(j+'0');
			     son(k+1,s);
			    t++;
				}
			}
		}
		if(t==0)
	return ;
	
	
}
main ()
{
	scanf("%d",&n);
	//std::cin>>n;
	for(int i=0;i<n-1;i++)
	scanf("%d",&a[i]);
	//std::cin>>a[i];
	for(int i=0;i<n-1;i++)
	scanf("%d",&b[i]);
	//std::cin>>b[i];
	for(int i=0;i<4;i++)
	{		
	for(int j=i;j<4;j++)
	if((i|j)==a[0]&&(i&j)==b[0])
	{
		//cerr<<ii<<"  "<<jj<<endl;
		jj=char(i+'0');
		son(0,jj);
		jj=char(j+'0');
		son(0,jj);
		if(n==1)
		{
			printf("YES\n");
			//std::cout<<"YES"<<endl;
			printf("%d %d",i,j);
			//std::cout<<i<<" "<<j;
			return 0;
		}
	}
  }
	if(ss!="")
	{
		printf("YES\n");
		//std::cout<<"YES"<<endl;
	for(int i=0;i<n;i++)
	printf("%c ",ss[i]);
	//std::cout<<ss[i]<<" ";
	}
	else printf("NO");
	//std::cout<<"NO";
	
}