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.
#print((3&3)+(3|3))
#print("| 0 1 2 3")
#print("_____"*2)
#for i in range(4):
#    print(i,"|", end=" ")
#   print(*[i|j for j in range(4)])
#print()
#print("& 0 1 2 3")
#print("______"*2)
#for i in range(4):
#    print(i,"|", end=" ")
#    print(*[(i&j) for j in range(4)])
n = int(input())
a = list(map(int, input().split()))
b = list(map(int, input().split()))
t = [-1 for i in range(n)]

def f(pos):
    for i in range(pos, n - 1):
        if (a[i] == 0 and b[i] == 0):
            t[i] = 0
            t[i + 1] = 0
        if (b[i] == 3 and a[i] == 3):
            t[i] = 3
            t[i + 1] = 3
        if (a[i] < b[i]):
            print("NO")
            exit()
        if (a[i] == b[i]):
            t[i] = a[i]
            t[i + 1] = b[i]

        if (t[i] != -1):
            if (t[i] == a[i]):
                t[i + 1] = b[i]
        if(t[i+1] == -1):
            if(t[i]==-1):
                t[i] = a[i]
                t[i] = b[i]
                if(f(i+1)):
                    return True
                t[i] = b[i]
                t[i] = a[i]
                if(f(i+1)):
                    return True
                return False
            if(a[i] == t[i]):
                t[i+1] = b[i]
            else:
                t[i+1] = a[i]
    for i in range(n-1):
        if(t[i]|t[i+1] != a[i] or t[i]&t[i+1] != b[i]):
            return False
    return True
# 1, 0 - (1,0),(0,1);2,0 - (0, 2), (2, 0); 3, 0-(0, 3); 3,1 - (3,1), (1, 3); 3,2 - (3, 2), (2, 3)

if(b[0] == 0 or a[0] == 3):
    t[0] = a[0]
    t[1] = b[0]
    if(f(1)):
        print("YES")
        print(*t)
        exit()
    t[0] = b[0]
    t[1] = a[1]
    if(f(1)):
        print("YES")
        print(*t)
        exit()
    print("NO")
if(f(0)):
    print("YES")
    print(*t)
    exit()
print("NO")