902_B. Coloring a Tree
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 cv. Initially cv = 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 cu = 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, ..., pn (1 ≤ pi < i), where pi means that there is an edge between vertices i and pi.

The third line contains n integers c1, c2, ..., cn (1 ≤ ci ≤ n), where ci 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):

<image>

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

<image>

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

<image>

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

<image>

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

<image>

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

<image>

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

<image>

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

<image>

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

<image>

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

<image>
```python
from queue import *

n=int(input())
parent={}
child={}
for i in range(1,n+1):
    parent[i]=0
    child[i]=[]
l=list(map(int,input().split()))
for i in range(2,n+1):
    parent[i]=l[i-2]
    child[l[i-2]].append(i)
l=list(map(int,input().split()))
color={}
for i in range(1,n+1):
    color[i]=l[i-1]
    
q=Queue()
q.put(1)
ans=0
while(not(q.empty())):
    e=q.get()
    c=0
    if(e==1):
        c=0
    else:
        c=color[parent[e]]
    if(c!=color[e]):
        ans+=1
    for i in child[e]:
        q.put(i)
        
print(ans)


    
    
    
    

```