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 = int(input())
A = list(map(int,input().split()))
B = list(map(int,input().split()))
i = 0
p = True
C1 = []
C2 = []
m = True
D1 = []
D2 = []
n = True
E1 = []
E2 = []
l = True
F1 = []
F2 = []
o = True
while i!= a-1 and p == True:
    if A[i] == 0:
        a1 = 0
        a2 = 0
    elif A[i] == 1:
        a1 = 0
        a2 = 1
    elif A[i] == 2:
        a1 = 1
        a2 = 0
    elif A[i] == 3:
        a1 = 1
        a2 = 1
    if B[i] == 0:
        b1 = 0
        b2 = 0
    elif B[i] == 1:
        b1 = 0
        b2 = 1
    elif B[i] == 2:
        b1 = 1
        b2 = 0
    elif B[i] == 3:
        b1 = 1
        b2 = 1
    if a1 < b1 or a2 < b2:
        p = False
    else:
        
        if i == 0:
            if b1 == 0:
                d1 = 0
                if a1 == 0:
                    c1 = 0
                else:
                    c1 = 1
            else:
                c1 = 1
                d1 = 1
            if b2 == 0:
                d2 = 0
                if a2 == 0:
                    c2 = 0
                else:
                    c2 = 1
               
            else:
                c2 = 1
                d2 = 1
            x = 2*d1+1*d2
            y = 2*c1+1*c2
            C1.append(x)
            C1.append(y)
            C2.append([d1,d2])
            C2.append([c1,c2])
            D1.append(y)
            D1.append(x)
            D2.append([c1,c2])
            D2.append([d1,d2])
            x = 2*d1+1*c2
            y = 2*c1+1*d2
            E1.append(x)
            E1.append(y)
            E2.append([d1,c2])
            E2.append([c1,d2])
            F1.append(y)
            F1.append(x)
            F2.append([c1,D2])
            F2.append([d1,c2])
            
        else:
            if m == True:
                if b1 == 0:
                    if C2[i][0] == 0:
                        if a1 == 0:
                            c1 = 0
                        else:
                            c1 = 1
                    else:
                        c1 = 0
                else:
                    if C2[i][0] == 1:
                        c1 = 1
                    else:
                        m = False
                if b2 == 0:
                    if C2[i][1] == 0:
                        if a2 == 0:
                            c2 = 0
                        else:
                            c2 = 1
                    else:
                        c2 = 0
                else:
                    if C2[i][1] == 1:
                        c2 = 1
                    else:
                        m = False
                if m == True:
                    C1.append(2*c1+1*c2)
                    C2.append([c1,c2])
            if n == True:
                if b1 == 0:
                    if D2[i][0] == 0:
                        if a1 == 0:
                            c1 = 0
                        else:
                            c1 = 1
                    else:
                        c1 = 0
                else:
                    if D2[i][0] == 1:
                        c1 = 1
                    else:
                        n = False
                if b2 == 0:
                    if D2[i][1] == 0:
                        if a2 == 0:
                            c2 = 0
                        else:
                            c2 = 1
                    else:
                        c2 = 0
                else:
                    if D2[i][1] == 1:
                        c2 = 1
                    else:
                        n = False
                if n == True:
                    D1.append(2*c1+1*c2)
                    D2.append([c1,c2])
            if l == True:
                if b1 == 0:
                    if E2[i][0] == 0:
                        if a1 == 0:
                            c1 = 0
                        else:
                            c1 = 1
                    else:
                        c1 = 0
                else:
                    if E2[i][0] == 1:
                        c1 = 1
                    else:
                        l = False
                if b2 == 0:
                    if E2[i][1] == 0:
                        if a2 == 0:
                            c2 = 0
                        else:
                            c2 = 1
                    else:
                        c2 = 0
                else:
                    if E2[i][1] == 1:
                        c2 = 1
                    else:
                        l = False
                if l == True:
                    E1.append(2*c1+1*c2)
                    E2.append([c1,c2])
            if o == True:
                if b1 == 0:
                    if F2[i][0] == 0:
                        if a1 == 0:
                            c1 = 0
                        else:
                            c1 = 1
                    else:
                        c1 = 0
                else:
                    if F2[i][0] == 1:
                        c1 = 1
                    else:
                        o = False
                if b2 == 0:
                    if F2[i][1] == 0:
                        if a2 == 0:
                            c2 = 0
                        else:
                            c2 = 1
                    else:
                        c2 = 0
                else:
                    if F2[i][1] == 1:
                        c2 = 1
                    else:
                        o = False
                if o == True:
                    F1.append(2*c1+1*c2)
                    F2.append([c1,c2])            
        
    i+=1
if p == False:
    print('NO')
else:
    print('YES')
    if m == True:
        print(*C1)
    elif n == True:
        print(*D1)
    elif l == True:
        print(*E1)
    else:
        print(*F1)
                    
                
                        
        
            
    
    