Package for this problem was not updated by the problem writer or Codeforces administration after we’ve upgraded the judging servers. To adjust the time limit constraint, solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then value 800 ms will be displayed and used to determine the verdict.

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ACM-ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

D. Ant on the Tree

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputConnected undirected graph without cycles is called a tree. Trees is a class of graphs which is interesting not only for people, but for ants too.

An ant stands at the root of some tree. He sees that there are *n* vertexes in the tree, and they are connected by *n* - 1 edges so that there is a path between any pair of vertexes. A leaf is a distinct from root vertex, which is connected with exactly one other vertex.

The ant wants to visit every vertex in the tree and return to the root, passing every edge twice. In addition, he wants to visit the leaves in a specific order. You are to find some possible route of the ant.

Input

The first line contains integer *n* (3 ≤ *n* ≤ 300) — amount of vertexes in the tree. Next *n* - 1 lines describe edges. Each edge is described with two integers — indexes of vertexes which it connects. Each edge can be passed in any direction. Vertexes are numbered starting from 1. The root of the tree has number 1. The last line contains *k* integers, where *k* is amount of leaves in the tree. These numbers describe the order in which the leaves should be visited. It is guaranteed that each leaf appears in this order exactly once.

Output

If the required route doesn't exist, output -1. Otherwise, output 2*n* - 1 numbers, describing the route. Every time the ant comes to a vertex, output it's index.

Examples

Input

3

1 2

2 3

3

Output

1 2 3 2 1

Input

6

1 2

1 3

2 4

4 5

4 6

5 6 3

Output

1 2 4 5 4 6 4 2 1 3 1

Input

6

1 2

1 3

2 4

4 5

4 6

5 3 6

Output

-1

Codeforces (c) Copyright 2010-2018 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Mar/20/2018 07:00:21 (d1).

Desktop version, switch to mobile version.

User lists

Name |
---|