问题 D: Tree

Given a tree of $n$ vertices and $n-1$ edges. Each vertex $i$ has a color ��ci = 'a' or 'b' or 'c'.

Please count the number of simple path between $i$ and $j$ satisfy :

• $1\le i\le j\le n$
  
• The number of vertices with three different colors is equal on the path.
  

The first line contains one integer $n$ （n≤105）.

The second line contains a string S with length of $n$ . (Si represents the color of $i$-th vertex，Si= ′a′ or ′b′ or ′c′)

Each of the next $n-1$ lines contains a pair of vertex indices ui and vi （1≤ui,vi≤n）— endpoints of the corresponding edge.