Given a tree of size n(\leq 10^5) with each vertex colored either black or white. Find the number of paths with alternating colors.
Input: First line will have n, the number of vertices of the tree and then n-1 lines will follow of the form u v which denote an edge between the vertex u and v. Finally, the next line will contain the space separated color(either W for white or B for Black) of each vertex.
Output: Single number denoting the number of paths with alternating colors.
W B B