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.
n=int(input())
a=list(map(int,input().split()))
b=list(map(int,input().split()))
flag=0
tf=True
t1f=False
t2f=False
t3f=False
t=[0]*n
for i in range(n-1):
    if (a[i]==0 and b[i]!=0) or (a[i]!=3 and b[i]==3) or (a[i]==1 and b[i]>1) or (a[i]==2 and b[i]==1):
        flag=1
        break
    else:
        if i==0:
            if a[i]==b[i]:
                t[0],t[1]=a[i],a[i]
            elif abs(a[i]-b[i])<3:
                t1=[0]*n
                t1f=True
                t1[0],t1[1]=a[i],b[i]
                t[0],t[1]=b[i],a[i]
            else:
                t2f=True
                t1f=True
                t3f=True
                t1=[0]*n
                t2=[0]*n
                t3=[0]*n
                t1[0],t1[1]=a[i],b[i]
                t2[0],t2[1]=b[i],a[i]
                t3[0],t3[1]=max(a[i],b[i])-1, min(a[i],b[i])-1
                t[1],t[0]=max(a[i],b[i])-1, min(a[i],b[i])-1
        else:
            if not t1f:
                if a[i]==b[i]:
                    if t[i]==a[i]:
                        t[i+1]=a[i]
                    else:
                        flag=1
                        break
                elif abs(a[i]-b[i])<2:
                    if t[i]==a[i]:
                        t[i+1]=b[i]
                    elif t[i]==b[i]:
                        t[i+1]=a[i]
                    else:
                        flag=1
                        break
                else:
                    t[i+1]=3-t[i]
            elif not t2f:
                if a[i]==b[i]:
                    if t[i]==a[i]:
                        t[i+1]=a[i]
                    else:
                        tf=False
                    if t1[i]==a[i]:
                        t1[i+1]=a[i]
                    else:t1f=False
                    if tf==False and t1f==False:
                        flag=1
                        break
                    elif tf==False and t1f==True:
                        t=copy(t1)
                        tf,t1f=t1f,tf                    
                elif abs(a[i]-b[i])<3:
                    if t[i]==a[i]:
                        t[i+1]=b[i]
                    elif t[i]==b[i]:
                        t[i+1]=a[i]
                    elif t1[i]==a[i]:
                        t1[i+1]=b[i]
                        tf=False
                    elif t1[i]==b[i]:
                        t1[i+1]=a[i]
                    else:t1f=False
                    if tf==False and t1f==False:
                        flag=1
                        break
                    elif tf==False and t1f==True:
                        t=copy(t1)
                        tf,t1f=t1f,tf
                else:
                    t[i+1]=3-t[i]
                    t1[i+1]=3-t1[i]
            elif not t3f:
                if a[i]==b[i]:
                    if t[i]==a[i]:
                        t[i+1]=a[i]
                    else: tf=False
                    if t1[i]==a[i]:
                        t1[i+1]=a[i]
                    else:t1f=False
                    if t2[i]==a[i]:
                        t2[i+1]=a[i]
                    else:t2f=False
                    if tf==False:
                        if t2f==True:
                            t=copy(t2)
                            tf,t2f=t2f,tf
                        elif t1f==True:
                            t=copy(t1)
                            tf,t1f=t1f,tf
                        else:
                            flag=1
                            break
                elif abs(a[i]-b[i])<3:
                    if t[i]==a[i]:
                        t[i+1]=b[i]
                    elif t[i]==b[i]:
                        t[i+1]=a[i]
                    elif t1[i]==a[i]:
                        t1[i+1]=b[i]
                        tf=False
                    elif t1[i]==b[i]:
                        t1[i+1]=a[i]
                    elif 2[i]==a[i]:
                        t2[i+1]=b[i]
                        t1f=False
                    elif t1[i]==b[i]:
                        t2[i+1]=a[i]
                    else:t2f=False
                    if tf==False:
                        if t2f==True:
                            t=copy(t2)
                            tf,t2f=t2f,tf
                        elif t1f==True:
                            t=copy(t1)
                            tf,t1f=t1f,tf
                        else:
                            flag=1
                            break
                else:
                    t[i+1]=3-t[i]
                    t1[i+1]=3-t1[i]
                    t2[i+1]=3-t2[i]
            else:
                if a[i]==b[i]:
                    if t[i]==a[i]:
                        t[i+1]=a[i]
                    else: tf=False
                    if t1[i]==a[i]:
                        t1[i+1]=a[i]
                    else:t1f=False
                    if t2[i]==a[i]:
                        t2[i+1]=a[i]
                    else:t2f=False
                    if t3[i]==a[i]:
                        t3[i+1]=a[i]
                    else:t3f=False
                    if tf==False:
                        if t3f==True:
                            t=copy(t3)
                            tf,t3f=t3f,tf
                        elif t2f==True:
                            t=copy(t2)
                            tf,t2f=t2f,tf
                        elif t1f==True:
                            t=copy(t1)
                            tf,t1f=t1f,tf
                        else:
                            flag=1
                            break
                    if t1f==False:
                        if t3f==True:
                            t=copy(t3)
                            t1f,t3f=t3f,t1f
                        elif t2f==True:
                            t=copy(t2)
                            t1f,t2f=t2f,t1f
                    if t2f==False:
                        if t3f==True:
                            t=copy(t3)
                            t2f,t3f=t3f,t2f
                elif abs(a[i]-b[i])<3:
                    if t[i]==a[i]:
                        t[i+1]=b[i]
                    elif t[i]==b[i]:
                        t[i+1]=a[i]
                    elif t1[i]==a[i]:
                        t1[i+1]=b[i]
                        tf=False
                    elif t1[i]==b[i]:
                        t1[i+1]=a[i]
                    elif 2[i]==a[i]:
                        t2[i+1]=b[i]
                        t1f=False
                    elif t2[i]==b[i]:
                        t2[i+1]=a[i]
                    elif 3[i]==a[i]:
                        t3[i+1]=b[i]
                        t2f=False
                    elif t3[i]==b[i]:
                        t3[i+1]=a[i]
                    else:t3f=False
                    if tf==False:
                        if t3f==True:
                            t=copy(t3)
                            tf,t3f=t3f,tf
                        elif t2f==True:
                            t=copy(t2)
                            tf,t2f=t2f,tf
                        elif t1f==True:
                            t=copy(t1)
                            tf,t1f=t1f,tf
                        else:
                            flag=1
                            break
                    if t1f==False:
                        if t3f==True:
                            t=copy(t3)
                            t1f,t3f=t3f,t1f
                        elif t2f==True:
                            t=copy(t2)
                            t1f,t2f=t2f,t1f
                    if t2f==False:
                        if t3f==True:
                            t=copy(t3)
                            t2f,t3f=t3f,t2f
                else:
                    t[i+1]=3-t[i]
                    t1[i+1]=3-t1[i]
                    t2[i+1]=3-t2[i]
                    t3[i+1]=3-t3[i]
if flag==0:
    print('YES')
    print(*t)
else:
    print('NO')
