B. Curiosity Has No Limitstime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputWhen 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.InputThe 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.OutputIn 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.ExamplesInput43 3 21 2 0OutputYES1 3 2 0 Input31 33 2OutputNONoteIn 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.
Input43 3 21 2 0
OutputYES1 3 2 0 
['*1500']