Neko and Flashback

A 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 $$$a$$$.