Score : $1700$ points

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 $X$.

Notes

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 $X$.

6
1 1 2 3 3
0 1 1 0 0 0

4

When the vertices are arranged in the order $1, 3, 5, 6, 2, 4$, $X$ will be $(0, 1, 0, 0, 1, 0)$, whose inversion number is $4$. It is impossible to have fewer inversions, so the answer is $4$.

1

0

0

$X = (0)$, whose inversion number is $0$.

15
1 2 3 2 5 6 2 2 9 10 1 12 13 12
1 1 1 0 1 1 0 0 1 0 0 1 1 0 0

31