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 dvoi(a):
    if(a==0):
        return "00"
    elif(a==1):
        return "01"
    elif(a==2):
        return "10"
    elif(a==3):
        return "11"

def des(a):
    if(a=="00"):
        return 0
    elif(a=="01"):
        return 1
    elif(a=="10"):
        return 2
    elif(a=="11"):
        return 3

def logi(a, b):
    if(a=='0' and b=='0'):
        return '0'
    elif(a=='1' and b=='0'):
        return '0'
    elif(a=='0' and b=='1'):
        return '0'
    elif(a=='1' and b=='1'):
        return '1'

def logili(a, b):
    if(a=='0'  and b=='0'):
        return '0'
    elif(a=='1' and b=='0'):
        return '1'
    elif(a=='0' and b=='1'):
        return '1'
    elif(a=='1' and b=='1'):
        return '1'


def slogi(a, b):
    at = dvoi(a)
    bt = dvoi(b)
    ct = ""
    ct+=logi(at[0], bt[0])
    ct+=logi(at[1], bt[1])
    c = des(ct)
    return c
    
def slogili(a, b):
    at = dvoi(a)
    bt = dvoi(b)
    ct = ""
    ct+=logili(at[0], bt[0])
    ct+=logili(at[1], bt[1])
    c = des(ct)
    return c

n = int(input())
a = []
b = []
t1 = []
t2 = []
for s in input().split():
    a.append(int(s))
    
for s in input().split():
    b.append(int(s))

for ti0 in range(4):
    for ti1 in range(4):
        if a[0]==slogili(ti0, ti1) and b[0]==slogi(ti0, ti1):
            if(t1==[]):
                t1.append(ti0)
                t1.append(ti1)
            elif(t2==[]):
                t2.append(ti0)
                t2.append(ti1)
                
if t1==[] and t2==[]:
    print("NO")
    exit()

if(t1!=[]):
    for i in range(1, n-1, 1):
        for ti in range(4):
            if a[i]==slogili(t1[i], ti) and b[i]==slogi(t1[i], ti):
                t1.append(ti)
        if(len(t1)==i+1):
            if(t2!=[]):
                for j in range(1, n, 1):
                    for tj in range(4):
                        if a[i]==slogili(t2[j], tj) and b[i]==slogi(t2[j], tj):
                            t2.append(tj)
                    if(len(t2)==j+1):
                        print("NO")
                        exit()
                print("YES")
                g = ""
                for j in t2:
                    g += str(j)
                    g += " "
                print(g)
                exit()
    print("YES")
    p = ""
    for i in t1:
        p += str(i)
        p += " "
    print(p)
    exit()
