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B. Coloring a Tree

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou are given a rooted tree with *n* vertices. The vertices are numbered from 1 to *n*, the root is the vertex number 1.

Each vertex has a color, let's denote the color of vertex *v* by *c* _{ v}. Initially *c* _{ v} = 0.

You have to color the tree into the given colors using the smallest possible number of steps. On each step you can choose a vertex *v* and a color *x*, and then color all vectices in the subtree of *v* (including *v* itself) in color *x*. In other words, for every vertex *u*, such that the path from root to *u* passes through *v*, set *c* _{ u} = *x*.

It is guaranteed that you have to color each vertex in a color different from 0.

You can learn what a rooted tree is using the link: https://en.wikipedia.org/wiki/Tree_(graph_theory).

Input

The first line contains a single integer *n* (2 ≤ *n* ≤ 10^{4}) — the number of vertices in the tree.

The second line contains *n* - 1 integers *p* _{2}, *p* _{3}, ..., *p* _{ n} (1 ≤ *p* _{ i} < *i*), where *p* _{ i} means that there is an edge between vertices *i* and *p* _{ i}.

The third line contains *n* integers *c* _{1}, *c* _{2}, ..., *c* _{ n} (1 ≤ *c* _{ i} ≤ *n*), where *c* _{ i} is the color you should color the *i*-th vertex into.

It is guaranteed that the given graph is a tree.

Output

Print a single integer — the minimum number of steps you have to perform to color the tree into given colors.

Examples

Input

6

1 2 2 1 5

2 1 1 1 1 1

Output

3

Input

7

1 1 2 3 1 4

3 3 1 1 1 2 3

Output

5

Note

The tree from the first sample is shown on the picture (numbers are vetices' indices):

On first step we color all vertices in the subtree of vertex 1 into color 2 (numbers are colors):

On seond step we color all vertices in the subtree of vertex 5 into color 1:

On third step we color all vertices in the subtree of vertex 2 into color 1:

The tree from the second sample is shown on the picture (numbers are vetices' indices):

On first step we color all vertices in the subtree of vertex 1 into color 3 (numbers are colors):

On second step we color all vertices in the subtree of vertex 3 into color 1:

On third step we color all vertices in the subtree of vertex 6 into color 2:

On fourth step we color all vertices in the subtree of vertex 4 into color 1:

On fith step we color all vertices in the subtree of vertex 7 into color 3:

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