E. Neko and Flashbacktime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputA permutation of length k is a sequence of k integers from 1 to k containing each integer exactly once. For example, the sequence [3, 1, 2] is a permutation of length 3.When Neko was five, he thought of an array a of n positive integers and a permutation p of length n - 1. Then, he performed the following:  Constructed an array b of length n-1, where b_i = \min(a_i, a_{i+1}).  Constructed an array c of length n-1, where c_i = \max(a_i, a_{i+1}).  Constructed an array b' of length n-1, where b'_i = b_{p_i}.  Constructed an array c' of length n-1, where c'_i = c_{p_i}. For example, if the array a was [3, 4, 6, 5, 7] and permutation p was [2, 4, 1, 3], then Neko would have constructed the following arrays:  b = [3, 4, 5, 5]  c = [4, 6, 6, 7]  b' = [4, 5, 3, 5]  c' = [6, 7, 4, 6] Then, he wrote two arrays b' and c' on a piece of paper and forgot about it. 14 years later, when he was cleaning up his room, he discovered this old piece of paper with two arrays b' and c' written on it. However he can't remember the array a and permutation p he used.In case Neko made a mistake and there is no array a and permutation p resulting in such b' and c', print -1. Otherwise, help him recover any possible array a. InputThe first line contains an integer n (2 \leq n \leq 10^5) — the number of elements in array a.The second line contains n-1 integers b'_1, b'_2, \ldots, b'_{n-1} (1 \leq b'_i \leq 10^9).The third line contains n-1 integers c'_1, c'_2, \ldots, c'_{n-1} (1 \leq c'_i \leq 10^9).OutputIf Neko made a mistake and there is no array a and a permutation p leading to the b' and c', print -1. Otherwise, print n positive integers a_i (1 \le a_i \le 10^9), denoting the elements of the array a.If there are multiple possible solutions, print any of them. ExamplesInput
5
4 5 3 5
6 7 4 6
Output
3 4 6 5 7 
Input
3
2 4
3 2
Output
-1
Input
8
2 3 1 1 2 4 3
3 4 4 2 5 5 4
Output
3 4 5 2 1 4 3 2 
NoteThe first example is explained is the problem statement.In the third example, for a = [3, 4, 5, 2, 1, 4, 3, 2], a possible permutation p is [7, 1, 5, 4, 3, 2, 6]. In that case, Neko would have constructed the following arrays:  b = [3, 4, 2, 1, 1, 3, 2]  c = [4, 5, 5, 2, 4, 4, 3]  b' = [2, 3, 1, 1, 2, 4, 3]  c' = [3, 4, 4, 2, 5, 5, 4] 
5
4 5 3 5
6 7 4 6

3 4 6 5 7  
['constructive algorithms', 'dfs and similar', 'graphs', '*2400']