A. Timofey and a tree

每年新年，蒂莫菲和他的朋友们会砍倒一棵有 #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] 个顶点获得颜色 #cf_span[ci]。 现在到了蒂莫菲的生日，他的母亲让他把树移走。蒂莫菲移除树的方式如下：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。之后，蒂莫菲将树扔进垃圾桶。 蒂莫菲不喜欢多种颜色混杂在一起。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，他用手握住它后，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，蒂莫菲握住它后就不会感到厌烦。 第一行包含一个整数 #cf_span[n] (#cf_span[2 ≤ n ≤ 105]) —— 树的顶点数。 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。保证给定的图是一棵树。 下一行包含 #cf_span[n] 个整数 #cf_span[c1, c2, ..., cn] (#cf_span[1 ≤ ci ≤ 105])，表示各个顶点的颜色。 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 ≤ 105]) —— 树的顶点数。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。保证给定的图是一棵树。下一行包含 #cf_span[n] 个整数 #cf_span[c1, c2, ..., cn] (#cf_span[1 ≤ ci ≤ 105])，表示各个顶点的颜色。 ## 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 $ n $ vertices, $ V = \{1, 2, \dots, n\} $. - Let $ c: V \to \mathbb{N} $ be a coloring function, where $ c_i $ is the color of vertex $ i $. **Given:** - The tree $ T $ is undirected and connected. - For any vertex $ v \in V $, when $ v $ is chosen as the root, the tree becomes rooted at $ v $. - A *subtree* of a vertex $ u \neq v $ (i.e., any non-root vertex) is the subgraph induced by $ u $ and all its descendants under the rooting at $ v $. - A subtree is *annoying* if it contains at least two vertices of different colors. - Timofey is *not annoyed* if **no subtree** (of any non-root vertex) is annoying. **Objective:** Determine whether there exists a vertex $ r \in V $ such that, when $ r $ is chosen as the root, **every subtree** (i.e., the subtree rooted at every child of $ r $, and recursively all their descendants) is **monochromatic** (all vertices in the subtree have the same color). **Formal Condition for Valid Root $ r $:** Let $ r \in V $ be a candidate root. For every child $ u $ of $ r $ in the rooted tree $ T_r $, the entire connected component (subtree) rooted at $ u $ must be monochromatic. Equivalently: For every edge $ (r, u) \in E $, the connected component of $ T \setminus \{r\} $ containing $ u $ must be monochromatic. **Note:** The root $ r $ itself is ignored in the monochromaticity check (its color is not part of any subtree). **Output:** - If such an $ r $ exists, output: ``` YES r ``` - Otherwise, output: ``` NO ``` **Mathematical Restatement:** Does there exist a vertex $ r \in V $ such that for every connected component $ C $ of $ T - r $, all vertices in $ C $ have the same color? That is: $$ \exists r \in V \text{ such that } \forall \text{ connected components } C \text{ of } T - r, \quad \exists \, k_C \in \mathbb{N} \text{ such that } \forall v \in C, \, c(v) = k_C $$