You 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 ≤ 10⁴) — the number of vertices in the tree.

The second line contains n - 1 integers p₂, p₃, ..., 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 c₁, c₂, ..., 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.

Note

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

$\text{[math]}$

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

$\text{[math]}$

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

$\text{[math]}$

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

$\text{[math]}$

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

$\text{[math]}$

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

$\text{[math]}$

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

$\text{[math]}$

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

$\text{[math]}$

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

$\text{[math]}$

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

$\text{[math]}$

Coloring a Tree

Examples