CF1031B.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) 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.

今天玛莎来到数学课时，发现黑板上有两个长度为 $n - 1$ 的整数序列。我们记第一个序列的元素为 $a_i$（$0 \le a_i \le 3$），第二个序列的元素为 $b_i$（$0 \le b_i \le 3$）。

玛莎开始好奇：是否存在一个长度为 $n$ 的整数序列，其元素记为 $t_i$（$0 \le t_i \le 3$），使得对每个 $i$（$1 \le i \le n - 1$）均满足以下条件：

• $a_i = t_i | t_{i + 1}$（其中 $|$ 表示按位或运算），且
• $b_i = t_i \& t_{i + 1}$（其中 $\&$ 表示按位与运算）。

这个问题对玛莎来说太难了，因此她请你帮忙判断这样的序列 $t_i$ 是否存在。如果存在，请构造出一个这样的序列；如果存在多个解，则输出任意一个即可。

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.

第一行包含一个整数 $n$（$2 \le n \le 10^5$）——序列 $t_i$ 的长度。

第二行包含 $n - 1$ 个整数 $a_1, a_2, \ldots, a_{n-1}$（$0 \le a_i \le 3$）——黑板上的第一个序列。

第三行包含 $n - 1$ 个整数 $b_1, b_2, \ldots, b_{n-1}$（$0 \le b_i \le 3$）——黑板上的第二个序列。

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.

第一行输出 "YES"（不带引号），如果存在满足题目条件的序列 $t_i$；否则输出 "NO"（不带引号）。

如果存在这样的序列，则在第二行输出 $n$ 个整数 $t_1, t_2, \ldots, t_n$（其中 $0 \le t_i \le 3$）—— 即满足题目条件的序列。

若存在多个答案，输出任意一个即可。

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.

在第一个例子中，很容易看出输出序列满足给定条件：

• $t_1 | t_2 = (01_2) | (11_2) = (11_2) = 3 = a_1$，且 $t_1 \& t_2 = (01_2) \& (11_2) = (01_2) = 1 = b_1$；
• $t_2 | t_3 = (11_2) | (10_2) = (11_2) = 3 = a_2$，且 $t_2 \& t_3 = (11_2) \& (10_2) = (10_2) = 2 = b_2$；
• $t_3 | t_4 = (10_2) | (00_2) = (10_2) = 2 = a_3$，且 $t_3 \& t_4 = (10_2) \& (00_2) = (00_2) = 0 = b_3$。

在第二个例子中，不存在满足条件的序列。