AT_abc482_e [ABC482E] Diameter Endpoint Colors

You are given a tree $ T $ with $ N $ vertices numbered $ 1,2,\dots,N $ . For $ i=1,2,\dots,N-1 $ , the $ i $ -th edge connects vertices $ u_i $ and $ v_i $ . Each vertex is painted in a color; vertex $ v $ is painted in color $ C_v $ . Find the number of integer pairs $ (u,v) $ with $ 1 \leq u < v \leq N $ that satisfy all of the following conditions. - Vertices $ u $ and $ v $ are painted in the same color. - The length of the simple path connecting vertices $ u $ and $ v $ equals the diameter of the tree $ T $ . Here, the length of a path is the number of edges in it, and the diameter of a tree is the maximum length of a simple path in the tree.

The input is given from Standard Input in the following format: > $ N $ $ u_1 $ $ v_1 $ $ u_2 $ $ v_2 $ $ \vdots $ $ u_{N-1} $ $ v_{N-1} $ $ C_1 $ $ C_2 $ $ \dots $ $ C_N $

Print the answer.

### Sample Explanation 1 There is $ 1 $ integer pair that satisfies the conditions: $ (1,5) $ . ### Sample Explanation 2 There are $ 2 $ integer pairs that satisfy the conditions: $ (3,6) $ and $ (4,7) $ . ### Sample Explanation 3 There are $ 2 $ integer pairs that satisfy the conditions: $ (4,5) $ and $ (5,9) $ . ### Constraints - $ 2 \leq N \leq 2 \times 10^5 $ - $ 1 \leq u_i, v_i \leq N $ - The given graph is a tree. - $ 1 \leq C_i \leq N $ - All input values are integers.