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You are given a tree consisting of N nodes You are also given two arrays A and P of size N each where the value Ai denotes the value written on the ith node and the value Pi denotes that there is an$...$

Question

You are given a tree consisting of N nodes

You are also given two arrays A and P of size N each, where the value A$[$i$]$ denotes the value written on the ith node and the value P$[$i$]$ denotes that there is an edge between the node i and P$[$i$].$

We say that an edge is considered good, if after deleting this edge $($this will result in formation of $2$ trees$),$ the values in each of the nodes of the trees are distinct.

Find the total number of good edges present in tree.

Input format:

$1.$ The first line contains an integer, N$,$ denoting the number of elements in A

$2.$ Each line i of the N subsequent lines $($where $0<=$ i N$)$ contains an integer describing A$[$i$].$

$3.$ Each line i of the N subsequent lines $($where $0<=$ i N$)$ contains an integer describing P$[$i$].$

Constraints:

$1<=$ N $<=10^5$

$1<=$ A$[$i$]<=10^5$

$1<=$ P$[$i$]<=10^5$

Sample Test Cases:

Case $1$:

Input :

$2$

$1$

$1$

$0$

$1$

Output:

$1$

Explanation:

Given N $=2,$ A $=[1,1],$ P $=[0,1]$