#include <iostream>
#include <vector>
using namespace std;

int n, mex = 1;
vector <int> p(3e5, 0);
vector <int> a(3e5, 0);
vector <vector <int>> g(3e5);
vector <int> sz(3e5, 1);
vector <int> cnt(3e5, 0);
vector <int> ans(3e5, 0);

void dfs(int x) {
	for (int i = 0; i < g[x].size();i++) {
		int& y = g[x][i];
		dfs(y);
		sz[x] += sz[y];
		if (sz[y] > sz[g[x][0]]) swap(g[x][0], y);
	}
}

void dfs_del(int x) {
	cnt[a[x]]--;
	for (int i : g[x]) dfs_del(i);
}

void del(int x) {
	mex = 1;
	dfs_del(x);
}

void add(int x) {
	cnt[a[x]]++;
	while (cnt[mex]) mex++;
}

void dfs_add(int x) {
	add(x);
	for (int i : g[x]) dfs_add(i);
}

void solve(int x) {
	for (int i = 1; i < g[x].size(); i++) {
		int& y = g[x][i];
		solve(y);
		del(y);
	}
	if (g[x].size()) solve(g[x][0]);
	for (int i = 1; i < g[x].size(); i++) {
		int& y = g[x][i];
		dfs_add(y);
	}
	add(x);
	ans[x] = mex;
}

int main() {
	ios_base::sync_with_stdio(false);
	cin.tie(NULL);
	cin >> n;
	for (int i = 1; i <= n; i++) {
		cin >> p[i];
		g[p[i]].push_back(i);
	}
	for (int i = 1; i <= n; i++) cin >> a[i];
	dfs(1);
	solve(1);
	for (int i = 1; i <= n; i++) cout << ans[i] << " ";
}