HandsOn

$2$: Nodes Reordering

You are given a tree which consists of $N$ nodes and an array A where $A[U]$ represents the value of node $U.$

You are also given an array $P$ where the parent of node $U$ is given by $.$

We say that the path from $U$ to $V$ is considered good if for each pair of adjacent nodes $i,j,$ the values written on these nodes satisfy the following condition:

$A[i{]}^A[j]$ is smaller than both $A[i]$ and $A[j]($where $^$ is the bitwise xor operator$).$

Find the maximum length of a good path that you can get.

Note:

It is given that $P[1]=0.$

Input Format

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

Each line $i$ of the $N$ subsequent lines $($where

$0P[i]N.1A[i]{10}^{5}0i0i$

Sample Test Cases

Case $1$

Input:

Input:

$5$

$0$

$1$

$2$

$3$

$4$

$1$

$1$

$1$

$1$

$1$

Output:

$5$

Explanation:

The good path consists of nodes $1,2,3,4,5.$ They satisfy the condition as the pair of value of nodes present in good path has a XOR equal to $0,$ which is smaller than the values of the nodes.

Hence, the answer for this case is equal to $5.$

Case $2$

Input:

$5$

$0$

$1$

$2$

$3$

$4$

$2$

$2$

$4$

$6$

$2$

Output:

$3$

Explanation:

Given $,2,4,6,2.$

The good pafs consists of nodes $3,4,5.$ They satisfy the condition as the pair of value of nodes present in good path has a XOR which is maller than the values of the nodes.

Hence, the answer for this case is equal to $3$

Case $3$

Input:

$4$

o

$1$

$1$

$1$

$1$

$1$

$1$

$1000$

Output:

$3$

Explanation:

$]$

$[1,1,1000$

The good path consists of nodes $1,2,3.$ They satisfy the condition as the pair of value of nodes present in good path has a XOR of $$ which is smaller than the values of the nodes.

complete the function $.$public static int get$\_$ans$($int N$,$ List P$,$ List A$)$