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.

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.