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.
def test_a():
    k = 0
    ordic = [[[0, 0]],
             [[0, 1], [1, 0], [1, 1]],
             [[0, 2], [2, 0], [2, 2]],
             [[0, 3], [1, 2], [1, 3], [2, 1], [2, 3], [3, 0], [3, 1], [3, 2],
              [3, 3]]]
    anddic = [[[0, 0], [0, 1], [0, 2], [0, 3], [1, 0], [1, 2], [2, 0], [2, 1],
               [3, 0]],
              [[1, 1], [1, 3], [3, 1]],
              [[2, 2], [2, 3], [3, 2]],
              [[3, 3]]]
    n = int(input())
    orl = list(map(int, input().split()))
    andl = list(map(int, input().split()))
    seqnotnor = [True] * (n - 1)
    ans = []
    for i in ordic[orl[0]]:
        for k in anddic[andl[0]]:
            if i == k:
                ans.append(i[0])
                ans.append(i[1])
                seqnotnor[0] = False
                break
        if i == k:
            break
    if seqnotnor[0] is True:
        print("NO")
    else:
        for digit in range(1, n - 1):
            for i in ordic[orl[digit]]:
                for k in anddic[andl[digit]]:
                    if (ans[-1] == i[0]) and (i == k):
                        ans.append(i[1])
                        seqnotnor[digit] = False
                        break
                if i == k:
                    break
        if True in seqnotnor:
            print("NO")
        else:
            print("YES")
            print(*ans)


test_a()
