C. Timofey and a tree

time limit per test:2 seconds

memory limit per test:256 megabytes

input:standard input

output:standard output

Each New Year Timofey and his friends cut down a tree of n vertices and bring it home. After that they paint all the n its vertices, so that the i-th vertex gets color ci.

Now it’s time for Timofey birthday, and his mother asked him to remove the tree. Timofey removes the tree in the following way: he takes some vertex in hands, while all the other vertices move down so that the tree becomes rooted at the chosen vertex. After that Timofey brings the tree to a trash can.

Timofey doesn’t like it when many colors are mixing together. A subtree annoys him if there are vertices of different color in it. Timofey wants to find a vertex which he should take in hands so that there are no subtrees that annoy him. He doesn’t consider the whole tree as a subtree since he can’t see the color of the root vertex.

A subtree of some vertex is a subgraph containing that vertex and all its descendants.

Your task is to determine if there is a vertex, taking which in hands Timofey wouldn’t be annoyed.

Input

The first line contains single integer n (2?≤?n?≤?105) — the number of vertices in the tree.

Each of the next n?-?1 lines contains two integers u and v (1?≤?u,?v?≤?n, u?≠?v), denoting there is an edge between vertices u and v. It is guaranteed that the given graph is a tree.

The next line contains n integers c1,?c2,?…,?cn (1?≤?ci?≤?105), denoting the colors of the vertices.

Output

PRint “NO” in a single line, if Timofey can’t take the tree in such a way that it doesn’t annoy him.

Otherwise print “YES” in the first line. In the second line print the index of the vertex which Timofey should take in hands. If there are multiple answers, print any of them.

Examples

Input 4 1 2 2 3 3 4 1 2 1 1

Output YES 2

Input 3 1 2 2 3 1 2 3

Output YES 2

Input 4 1 2 2 3 3 4 1 2 1 2

Output NO 題意：給你一個n個節點n-1條邊的樹。每個節點有顏色ci。問是否存在一個點，將它看為根后，所有子樹的顏色相同（子樹和子樹之間可以不同） 題解：我們將顏色相同的并相連的點進行縮點。最后就會形成類似這樣的圖，如果有解的話就像圖上紅色圈內樣，與其他都相連（則它的度為染色數-1.） 代碼：