I found an interesting problem on https://codeforces.com/problemset/problem/1031/B:
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 $a_i$ ($0 \le a_i \le 3$), and the elements of the second sequence as $b_i$ ($0 \le b_i \le 3$).

Masha became interested if or not there is an integer sequence of length $n$, which elements we will denote as $t_i$ ($0 \le t_i \le 3$), so that for every $i$ ($1 \le i \le n - 1$) the following is true:   $a_i = t_i | t_{i + 1}$ (where $|$ denotes the bitwise OR operation) and  $b_i = t_i \& t_{i + 1}$ (where $\&$ denotes the bitwise AND operation). 

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 $n$ ($2 \le n \le 10^5$) — the length of the sequence $t_i$. 

The second line contains $n - 1$ integers $a_1, a_2, \ldots, a_{n-1}$ ($0 \le a_i \le 3$) — the first sequence on the blackboard.

The third line contains $n - 1$ integers $b_1, b_2, \ldots, b_{n-1}$ ($0 \le b_i \le 3$) — 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 $t_1, t_2, \ldots, t_n$ ($0 \le t_i \le 3$) — 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) \&...

I tried it in Python, but could not do it. Can you solve it?
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')