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()))
ways = {(0,0): [(0,0)], (1,0):[(0,1),(1,0)], (1,1):[(1,1)], (2,0):[(2,0),(0,2)], (2,2):[(2,2)], (3,0):[(3,0),(0,3),(2,1),(1,2)],(3,1):[(3,1),(1,3)],(3,2):[(3,2),(2,3)], (3,3):[(3,3)]}
ans = []
ddl = []
s= {0,1,2,3}
for i in range(n-2,-1,-1):
    if (a[i],b[i]) not in ways:
        print("NO")
        exit()
    d = ways[(a[i],b[i])]
    ns = set()
    dd = {None: None}
    for st, en in d:
        if (en in s):
            ns.add(st)
            dd[st] = en
    if i == 0:
        if len(ns) == 0:
            print("NO")
            exit()
        k = ns.pop()
        ans = [k, dd[k]]
    else:
        ddl.append(dd)
    s = ns
        
for i in range(1,n-1):
    dd = ddl.pop()
    ans.append(dd[ans[-1]])



if ans[0] == None:
    print('NO')
else:
    print('YES')
    print(' '.join(map(str,ans)))
