You are given a rooted tree having n nodes, rooted at node 1. Every node i has two values associated with itself , $A[i]$ and $B[i]$. In this tree you have to count total pairs of nodes which are beautiful. A pair of nodes i , j is beautiful if i is ancestor of node j and $A[i] \lt A[j]$ and $B[i] < B[j]$.
Node i is called an ancestor of some node j, if node i is the parent of node j, or it is the ancestor of parent of node j. The root of a tree has no ancestors.
Input
First line contains a number n as input. Next $n - 1$ lines contain two integers u , v denoting that there is an edge between the nodes u and v. Next line contains n space separated integers that denote the $A[i]$ value for each node. Similarly next line contains n space separated integers that denote the $B[i]$ value for each node.

Output
In the output you have to print total good pairs in the tree.

Constraints
$1 \le N \le 10^5$
$1 \le A[i] \le 10^9$
$1 \le B[i] \le 10^9$