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.
d={
    (0,0):(0,0),
    (1,0):(0,1),
    (1,1):(1,1),
    (2,0):(0,2),
    (2,2):(2,2),
    (3,0):(0,3),
    (3,1):(1,3),
    (3,2):(2,3),
    (3,3):(3,3),
}
n=input()
a=map(int,raw_input().split())
b=map(int,raw_input().split())
p=[]
for i in range(n-1):
    q=(a[i],b[i])
    if q not in d:
        print "NO"
        exit(0)
    else:
        p.append(d[q])
ans=[]
if n==2:
    print "YES"
    for i in p[0]:
        print i,
    exit(0)
if p[0][0] == p[1][0]:
    ans=[p[0][1],p[0][0],p[1][1]]
elif p[0][0] == p[1][1]:
    ans=[p[0][1],p[0][0],p[1][0]]
elif p[0][1] == p[1][0]:
    ans=[p[0][0],p[0][1],p[1][1]]
elif p[0][1] == p[1][1]:
    ans=[p[0][0],p[0][1],p[1][0]]
else:
    print "NO"
    exit(0)
for i in range(2,n-1):
    if ans[-1] == p[i][0]:
        ans.append(p[i][1])
    elif ans[-1] == p[i][1]:
        ans.append(p[i][0])
    else:
        print "NO"
        exit(0)
print "YES"
for i in ans:
    print i,