Problem Statement

Snuke has a rooted tree with $N$ vertices, numbered $1$ through $N$. Vertex $1$ is the root of the tree, and the parent of Vertex $i$ ( $2\leq i \leq N$ ) is Vertex $P_i$ ( $P_i < i$ ). There is a number, $0$ or $1$, written on each vertex. The number written on Vertex $i$ is $V_i$.

Snuke would like to arrange the vertices of this tree in a horizontal row. Here, for every vertex, there should be no ancestor of that vertex to the right of that vertex.

After arranging the vertices, let $X$ be the sequence obtained by reading the numbers written on the vertices from left to right in the arrangement. Snuke would like to minimize the inversion number of $X$. Find the minimum possible inversion number of $X$.

Note

The inversion number of a sequence $Z$ whose length $N$ is the number of pairs of integers $i$ and $j$ ( $1 \leq i < j \leq N$ ) such that $Z_i > Z_j$.

Constraints

• $1 \leq N \leq 2 \times 10^5$
• $1 \leq P_i < i$ ( $2 \leq i \leq N$ )
• $0 \leq V_i \leq 1$ ( $1 \leq i \leq N$ )
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
P_2 P_3 ... P_N
V_1 V_2 ... V_N

Output

Print the minimum possible inversion number of $X$.