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()))
lst = [[[(0, 0)], [], [], []], [[(0, 1), (1, 0)], [(1, 1)], [], []], [[(0, 2), (2, 0)], [], [(2, 2)], []], [[(0, 3), (1, 2), (2, 1), (3, 0)], [(1, 3), (3, 1)], [(2, 3), (3, 2)], [(3, 3)]]]
ans = []

prev = [0, 1, 2, 3]
res = []
for i in range(n - 1):
    if len(lst[a[i]][b[i]]) != 0:
        ans.append(lst[a[i]][b[i]])
    else:
        print("NO")
        exit()
    prev2 = []
    res.append([])
    for j in prev:
        for x in ans[-1]:
            if x[0] == j:
                prev2.append(x[1])
                res[-1].append((x[1], x[0]))
    prev = prev2

    if len(prev) == 0:
        print("NO")
        exit()

ans = [res[-1][0][0]]
prev = res[-1][0][1]
for i in range(len(res) - 2, -1, -1):

    for j in range(len(res[i])):
        if res[i][j][0] == prev:
            ans.append(res[i][j][0])
            prev = res[i][j][1]
            break
ans.append(prev)
ans.reverse()
print("YES")
print(*ans)