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 tr(x):
    if x == "3":
        return "11"
    elif x == "2":
        return "10"
    elif x == "1":
        return "01"
    return "00"


n = int(input())
a = list(map(tr, input().split()))
b = list(map(tr, input().split()))

def cont(t):
    if len(t) == n:
        print("Yes")
        print(*list(map(lambda x: int(x, 2), t)))
        exit()
    if t == []:
        if a[0] == "00":
            t.append("00")
            t.append("00")
            cont(t)
        elif a[0] == "01":
            if b[0] == "00":
                cont(["00", "01"])
                cont(["01", "00"])
            elif b[0] == "01":
                cont(["01", "01"])
        elif a[0] == "10":
            if b[0] == "00":
                cont(["00", "10"])
                cont(["10", "00"])
            elif b[0] == "10":
                cont(["10", "10"])
        else:
            if b[0] == "00":
                cont(["00", "10"])
                cont(["00", "01"])
                cont(["00", "11"])
                cont(["10", "00"])
                cont(["01", "00"])
                cont(["11", "00"])
            elif b[0] == "10":
                cont(["10", "11"])
                cont(["11", "10"])
            elif b[0] == "11":
                cont(["11","11"])
            else:
                cont(["01", "11"])
                cont(["11", "01"])
    else:
        if a[len(t) -1] == "00":
            t.append("00")
            cont(t)
        elif a[len(t)-1] == "01":
            if b[len(t)-1] == "00":
                if t[-1] == "00":
                    cont(t + ["01"])
                elif t[-1] == "01":
                    cont(t + ["00"])
            elif b[len(t)-1] == "01":
                cont(t + ["01"])
        elif a[len(t)-1] == "10":
            if b[len(t)-1] == "00":
                if t[-1] == "00":
                    cont(t + ["10"])
                elif t[-1] == "10":
                    cont(t + ["00"])
            elif b[len(t)-1] == "10":
                cont(t + ["10"])
        else:
            if b[len(t)-1] == "00":
                if t[-1] == "00":
                    cont(t + ["10"])
                    cont(t + ["01"])
                    cont(t + ["11"])
                elif t[-1] == "10":
                    cont(t + ["00"])
                elif t[-1] == "01":
                    cont(t + ["00"])
                else:
                    cont(t + ["00"])
            elif b[len(t)-1] == "10":
                if t[-1] =="10":
                    cont(t + ["11"])
                elif t[-1] == "11":
                    cont(t + ["10"])
            elif b[len(t)-1] == "11":
                cont(t + ["11"])
            else:
                if t[-1] == "01":
                    cont(t + ["11"])
                elif t[-1] == "11":
                    cont(t + ["01"])


t = []
cont(t)
print("No")