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()))

for i in range(n-1):
    if a[i] == 3:
        a[i] = '11'
    elif a[i] == 2:
        a[i] = '10'
    elif a[i] == 1:
        a[i] = '01'
    elif a[i] == 0:
        a[i] = '00'

for i in range(n-1):
    if b[i] == 3:
        b[i] = '11'
    elif b[i] == 2:
        b[i] = '10'
    elif b[i] == 1:
        b[i] = '01'
    elif b[i] == 0:
        b[i] = '00'


def Checker(z, x, y):
    if z == '0':
        if x == '0' and y == '0':
            return '0'
        elif x == '0' and y == '1':
            return None
        elif x == '1' and y == '0':
            return '1'
        elif x == '1' and y == '1':
            return None
    elif z == '1':
        if x == '0' and y == '0':
            return None
        elif x == '0' and y == '1':
            return None
        elif x == '1' and y == '0':
            return '0'
        elif x == '1' and y == '1':
            return '1'


s = []
flag = True

for ti in ['00', '01', '10', '11']:
    t = ti
    if len(s) == n:
        break
    elif (Checker(t[0], a[0][0], b[0][0]) is not None) and (Checker(t[1], a[0][1], b[0][1]) is not None):
        s.append(t)
        for i in range(n-1):
            c = Checker(t[0], a[i][0], b[i][0])
            e = Checker(t[1], a[i][1], b[i][1])
            if (c is not None) and (e is not None):
                k = ''.join([c, e])
                s.append(k)
                t = k
            else:
                s.clear()
                break
    elif t == '11':
        flag = False
if flag and s:
    print('YES')
    for i in range(n):
        if s[i] == '11':
            print(3, end=' ')
        elif s[i] == '10':
            print(2, end=' ')
        elif s[i] == '01':
            print(1, end=' ')
        elif s[i] == '00':
            print(0, end=' ')
else:
    print('NO')
