#include <bits/stdc++.h>
#define ll long long
#define P 998244353
using namespace std;
const int N=500005;
int n,m,k,s,t,fa[N],b[N],tt;
ll a[N],mx=-1,ans[N];
vector<int> e[N];
struct node{//Trie 
	int a[N*60][2],b[N*60],tot=1;
	void clear(){
		memset(a,0,sizeof(a));
		memset(b,0,sizeof(b));
		tot=1;
	}
	void insert(ll k,int id){
		int p=1;
		for (int i=59;i>=0;--i){
			int o=((k>>i)&1);
			if (!a[p][o]) a[p][o]=++tot;
			p=a[p][o];
		}
		b[p]=id;
	}
	void find(ll k,int id){
		int p=1;ll x=0;
		for (int i=59;i>=0;--i){
			int o=((k>>i)&1); 
			if (a[p][o^1]) p=a[p][o^1],x=(x<<1)+1;
			else p=a[p][o],x<<=1;
		}
		if (b[p] && x>mx){
			mx=x;s=b[p];t=id;
		}
	}
}T;
void dfs(int u,int o){//遍历以u为根的子树，但不去o 
	T.find(a[u],u);
	T.insert(a[u],u);
	for (int &v:e[u]) if (v!=fa[u] && v!=o){
		dfs(v,o);
	}
}
void calc(int s){
	tt=0;
	for (;;s=fa[s]){
		b[++tt]=s;
		if (s==1) break;
	}
	T.clear();
	mx=0;
	for (int i=tt;i>=1;--i){
		ans[b[i]]=mx;
		if (i!=1) dfs(b[i],b[i-1]);
	}
}
int main() {
	//freopen("in.txt","r",stdin);
	//freopen("out.txt","w",stdout);
	cin>>n;
	for (int i=2;i<=n;++i){
		cin>>s;fa[i]=s;
		e[s].push_back(i);
	}
	for (int i=1;i<=n;++i) {
		cin>>a[i];//权值 
		T.find(a[i],i);
		T.insert(a[i],i);
	}
	for (int i=1;i<=n;++i) ans[i]=mx;
	int _t=t;
	calc(s);
	calc(_t);
	for (int i=1;i<=n;++i) cout<<ans[i]<<'\n';
}