C. Timofey and a tree

每年新年，蒂莫菲和他的朋友们会砍倒一棵包含 #cf_span[n] 个顶点的树并带回家。之后，他们将这 #cf_span[n] 个顶点全部涂色，使得第 #cf_span[i] 个顶点被涂成颜色 #cf_span[ci]。 现在到了蒂莫菲的生日，他的母亲让他把树拿走。蒂莫菲按照以下方式移除树：他用手握住某个顶点，其余所有顶点会向下移动，使得树以所选顶点为根。然后蒂莫菲将树扔进垃圾桶。 蒂莫菲不喜欢多种颜色混合在一起。如果一个子树中包含不同颜色的顶点，他会感到厌烦。蒂莫菲希望找到一个顶点，他用手握住该顶点后，不会有任何让他厌烦的子树。他不将整棵树视为一个子树，因为他看不到根顶点的颜色。 某个顶点的子树是指包含该顶点及其所有后代的子图。 你的任务是判断是否存在一个顶点，使得蒂莫菲握住它后不会感到厌烦。 第一行包含一个整数 #cf_span[n]（#cf_span[2 ≤ n ≤ 10^5]）——树中顶点的数量。 接下来的 #cf_span[n - 1] 行，每行包含两个整数 #cf_span[u] 和 #cf_span[v]（#cf_span[1 ≤ u, v ≤ n], #cf_span[u ≠ v]），表示顶点 #cf_span[u] 和 #cf_span[v] 之间有一条边。保证给定图是一棵树。 下一行包含 #cf_span[n] 个整数 #cf_span[c1, c2, ..., cn]（#cf_span[1 ≤ ci ≤ 10^5]），表示每个顶点的颜色。 如果蒂莫菲无法找到一个合适的顶点使得他不会感到厌烦，请在一行中输出 "_NO_"。 否则，第一行输出 "_YES_"，第二行输出蒂莫菲应握住的顶点编号。如果有多个答案，输出任意一个即可。 ## Input 第一行包含一个整数 #cf_span[n]（#cf_span[2 ≤ n ≤ 10^5]）——树中顶点的数量。接下来的 #cf_span[n - 1] 行，每行包含两个整数 #cf_span[u] 和 #cf_span[v]（#cf_span[1 ≤ u, v ≤ n], #cf_span[u ≠ v]），表示顶点 #cf_span[u] 和 #cf_span[v] 之间有一条边。保证给定图是一棵树。下一行包含 #cf_span[n] 个整数 #cf_span[c1, c2, ..., cn]（#cf_span[1 ≤ ci ≤ 10^5]），表示每个顶点的颜色。 ## Output 如果蒂莫菲无法找到一个合适的顶点使得他不会感到厌烦，请在一行中输出 "_NO_"。否则，第一行输出 "_YES_"，第二行输出蒂莫菲应握住的顶点编号。如果有多个答案，输出任意一个即可。 [samples]

**Definitions:** - Let $ T = (V, E) $ be a tree with $ |V| = n $, $ n \geq 2 $. - Let $ c: V \to \mathbb{N} $ be a coloring function, where $ c(i) $ is the color of vertex $ i $. - For a rooted tree with root $ r $, the *subtree* of a vertex $ v \neq r $ is the induced subgraph consisting of $ v $ and all its descendants. - A subtree is *annoying* if it contains vertices of more than one distinct color. - The entire tree (rooted at $ r $) is **not** considered a subtree for the purpose of annoyance. **Given:** - Tree $ T $ with $ n $ vertices. - Coloring $ c: V \to \{1, 2, \dots, 10^5\} $. - For a candidate root $ r \in V $, we require: For every vertex $ v \in V \setminus \{r\} $, the subtree rooted at $ v $ is **monochromatic** (i.e., all vertices in the subtree have the same color). **Objective:** Determine whether there exists a vertex $ r \in V $ such that, when the tree is rooted at $ r $, **all subtrees** (of all non-root vertices) are monochromatic. If such an $ r $ exists, output: ``` YES r ``` Otherwise, output: ``` NO ``` --- **Formal Condition for Valid Root $ r $:** Let $ T_r $ denote the tree rooted at $ r $. For all $ v \in V \setminus \{r\} $, let $ S_v $ be the set of vertices in the subtree rooted at $ v $. Then $ r $ is valid if and only if: $$ \forall v \in V \setminus \{r\}, \quad \forall u, w \in S_v, \quad c(u) = c(w) $$ Equivalently: For every child $ v $ of $ r $, the entire connected component of $ T \setminus \{r\} $ containing $ v $ must be monochromatic. And recursively: for every descendant $ u $ of $ v $, the subtree rooted at $ u $ must also be monochromatic — but this is implied if every *direct* subtree under $ r $ is monochromatic and the coloring is consistent downward. **Note:** The condition reduces to: When removing $ r $, each connected component (i.e., subtree of each child of $ r $) must be monochromatic. Thus, the problem reduces to: > Does there exist a vertex $ r $ such that, in the forest $ T \setminus \{r\} $, every connected component is monochromatic? This is the formal mathematical statement of the problem.