// Source: https://usaco.guide/general/io

#include <algorithm>
#include <bits/stdc++.h>
using namespace std;

vector<vector<int>> g , b;
vector<int> a , ans;
vector<array<int , 2>> c;

int t = 0;

void dfs(int h){
    c[h][0] = t++;
    b[a[h]].push_back(c[h][0]);
    for(int x : g[h])dfs(x);
    c[h][1] = t++;
}

int dfs2(int h){
    ans[h] = 1;
    for(int x : g[h])ans[h] = max(dfs2(x) , ans[h]);
    while(*lower_bound(b[ans[h]].begin() , b[ans[h]].end() , c[h][0]) <= c[h][1])ans[h]++;
    return ans[h];
}

int main() {
	int n; cin >> n;
    g.resize(n);
    b.resize(n+2);
    ans.resize(n);
    c.resize(n);
    for(int i = 0; i < n; i++){
        int y; cin >> y;y--;
        if(y != -1)g[y].push_back(i);
    }
    for(int i = 0; i < n; i++){
        int y; cin >> y;
        a.push_back(y);
    }
    dfs(0);
    for(int i = 0; i < b.size(); i++){
        b[i].push_back(1000000);
    }
    dfs2(0);
    for(int x : ans)cout << x << " ";
}