The Fox and the Complete Tree Traversal

Description:

Input:

The first line contains one integer $$$n$$$ ($$$2 \le n \le 2 \cdot 10^5$$$) —the number of vertices of the tree.

Each of the following $$$n - 1$$$ lines contains two integers $$$u$$$ and $$$v$$$ ($$$1 \le u, v \le n$$$, $$$u \ne v$$$) — vertices connected by an edge. It is guaranteed that these edges form a tree.

Output:

On the first line, print "Yes" (without quotes) if the required route of the tree exists, or "No" (without quotes) otherwise.

If the required tree traversal exists, on the second line print $$$n$$$ integers of different integers $$$v_1, v_2, \ldots, v_n$$$ ($$$1 \le v_i \le n$$$) — the vertices of the tree in traversal order.

If there are several correct traversals, output any of them.

Sample Input:

5
1 2
1 3
3 4
3 5

Sample Output:

Yes
4 5 1 2 3 

Sample Input:

3
1 2
1 3

Sample Output:

Yes
1 2 3

Sample Input:

15
1 2
1 3
2 4
2 5
3 6
3 7
4 8
4 9
5 10
5 11
6 12
6 13
7 14
7 15

Sample Output:

No

Note:

The tree from the first example is shown below. The bold arrows indicate the fox's route.

In the second example, any sequence of three different vertices is a correct route, because the fox can jump from any vertex to any vertex.

The tree from the third example is shown below. It can be shown that there is no required route for it.