A12027 | Curiosity Has No Limits

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.