Problem Statement

You are given a permutation $P=(P_1,P_2,\dots,P_N)$ of $(1,2,\dots,N)$ and a length-$N$ sequence of positive integers $A=(A_1,A_2,\dots,A_N)$.

For a rooted tree $T$ with $N$ vertices numbered $1$ through $N$, define $f(T)$ as follows.

Among the permutations $Q=(Q_1,Q_2,\dots,Q_N)$ of $(1,2,\dots,N)$, call one that satisfies the following condition a good permutation.

• For every vertex $v$ other than the root, letting $u$ be its parent, $u$ appears before $v$ in $Q$.

Let $f(T)$ be the lexicographically smallest good permutation.

Also, define the cost of a rooted tree $T$ with $N$ vertices as $\sum_{i=1}^{N} A_i c_i^2$, where $c_i$ is the number of children of vertex $i$ in $T$.

Find the minimum cost of a rooted tree $T$ with $N$ vertices satisfying $f(T) = P$.

Constraints

• $1 \le N \le 2 \times 10^5$
• $P$ is a permutation of $(1,2,\dots,N)$.
• $1 \le A_i \le 10^6$
• All input values are integers.

Input

The input is given from Standard Input in the following format:

N
P_1\ P_2\ \dots\ P_N
A_1\ A_2\ \dots\ A_N

Output

Output the answer.