#include <bits/stdc++.h>
// iostream is too mainstream
#include <cstdio>
// bitch please
#include <iostream>
#include <algorithm>
#include <cstdlib>
#include <vector>
#include <set>
#include <map>
#include <queue>
#include <stack>
#include <list>
#include <cmath>
#include <iomanip>
#include <time.h>
#define dibs reserve
#define OVER9000 1234567890
#define ALL_THE(CAKE,LIE) for(auto LIE =CAKE.begin(); LIE != CAKE.end(); LIE++)
#define tisic 47
#define soclose 1e-8
#define chocolate win
// so much chocolate
#define patkan 9
#define ff first
#define ss second
#define abs(x) ((x < 0)?-(x):x)
#define uint unsigned int
#define dbl long double
#define pi 3.14159265358979323846
using namespace std;
// mylittledoge

#ifdef DONLINE_JUDGE
	// palindromic tree is better than splay tree!
	#define lld I64d
#endif

int N, Pp =0;
vector<int> P,path,S;

struct fin {
	vector<int> T;
	fin() {}
	fin(int N) {T.resize(N+10,0);}

	int lastone(int x) {return x&(x^(x-1));}

	void put(int pos) {
		for(int i =pos+1; i < (int)T.size(); i +=lastone(i)) T[i]++;}

	int get(int pos) {
		int ret =0;
		for(int i =pos+1; i > 0; i -=lastone(i)) ret +=T[i];
		return ret;}
	};

vector<fin> Fp;
vector< map<int,int> > Sp;

void prep(int R, vector< vector<int> > &son) {
	int topson =-1;
	ALL_THE(son[R],it) {
		prep(*it,son);
		S[R] +=S[*it];
		if(topson == -1 || S[*it] > S[topson]) topson =*it;
		}
	if(topson == -1) {
		path[R] =Pp;
		Pp++;}
	else path[R] =path[topson];
	ALL_THE(son[R],it) if(*it != topson) 
		ALL_THE(Sp[path[*it]],jt) Sp[path[R]][jt->ff] =0;
	Sp[path[R]][P[R]] =0;}

int count_brute(int R, vector< vector<int> > &son, int val, vector<int> &listP) {
	int ans =0;
	ALL_THE(son[R],it) 
		ans +=count_brute(*it,son,val,listP);
	listP.push_back(P[R]);
	if(P[R] > val) ans++;
	return ans;}

vector<int> ans;

void count(int R, vector< vector<int> > &son) {
	vector<int> listP;
	ALL_THE(son[R],it) {
		count(*it,son);
		if(path[*it] != path[R]) ans[R] +=count_brute(*it,son,P[R],listP);
		else ans[R] +=S[*it]-Fp[path[R]].get(Sp[path[R]][P[R]]);}
	ALL_THE(listP,it) Fp[path[R]].put(Sp[path[R]][*it]);
	Fp[path[R]].put(Sp[path[R]][P[R]]);}

int main() {
	cin.sync_with_stdio(0);
	cin.tie(0);
	cout << fixed << setprecision(10);
#ifndef LOCAL
	freopen("promote.in","r",stdin);
	freopen("promote.out","w",stdout);
#endif
	int N;
	cin >> N;
	P.resize(N);
	Fp.resize(N);
	Sp.resize(N);
	for(int i =0; i < N; i++) cin >> P[i];
	path.resize(N,-1);
	S.resize(N,1);
	vector< vector<int> > son(N);
	for(int i =1; i < N; i++) {
		int p;
		cin >> p;
		son[p-1].push_back(i);}
	prep(0,son);
	for(int i =0; i < Pp; i++) {
		int x =0;
		ALL_THE(Sp[i],it) it->ss =x++;
		Fp[i] =fin(x);}
	ans.resize(N,0);
	count(0,son);
	for(int i =0; i < N; i++) cout << ans[i] << "\n";
	return 0;}

// look at my code
// my code is amazing