Curiosity Has No Limits

已知两个长度为n-1的整数序列a和b，序列中每个元素都在0到3之间(包含)。 试判断是否存在满足以下条件的长度为n的整数序列t， 如存在，则输出之： - 对于1<=i<=n,ti在0到3之间(包含) - 对于1<=i<=n-1,有ai=ti|ti+1,bi=ti&ti+1 #### 输入 共三行，第一行一个整数n(2<=n<=10^5)，第二、三行各有n-1个整数，表示序列a和b。 #### 输出 如果不存在满足上述要求的t，则输出一行‘NO’。 如存在，则在第一行输出‘YES’，在第二行输出n 个整数，两个数之间用一个空格隔开，表示序列t。

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](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.

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.

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.

4
3 3 2
1 2 0

YES
1 3 2 0 

3
1 3
3 2

NO

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.