One-Way Whiskers

There are $N$ cats living at the vertices of a tree. Cat $i$ lives at vertex $i$ and has ability $A_i$. Each edge has a difficulty.

A cat may traverse an edge if and only if its ability is at least the difficulty of that edge. To visit another cat, it must traverse every edge on the unique path to that cat's vertex.

For two distinct cats $u$ and $v$, call the unordered pair $\{u,v\}$ a one-way acquaintance if exactly one of the following statements is true:

• cat $u$ can visit cat $v$;
• cat $v$ can visit cat $u$.

Count the number of one-way acquaintance pairs.

5
2 7 4 6 1
1 2 3
2 3 5
2 4 6
4 5 2

6