#include<bits/stdc++.h>
#define MAXN 500010
#define INF 1000000010
#define MOD 998244353
#define LL long long
#define LLL __int128_t
#define For(i,a,b) for(int i=(a);i<=(b);i++)
#define Rof(i,a,b) for(int i=(a);i>=(b);i--)
using namespace std;
int v[MAXN];
vector<int> link[MAXN];
int dep[MAXN];
vector<int> dp[MAXN];
int ans[MAXN];
void dfs(int p){
	dep[p]=INF;
	for (int q:link[p]){
		dfs(q);
		dep[p]=min(dep[p],dep[q]+1);
	}
	if (dep[p]==INF) dep[p]=1;
	dp[p].resize(dep[p]+1);
	for (int q:link[p]){
		For(i,0,dep[p]-1){
			dp[p][i]+=dp[q][i];
		}
	}
	if (v[p]==1){
		Rof(i,dep[p],1) dp[p][i]=dp[p][i-1];
		dp[p][0]=INF;
		For(i,0,dep[p]-1) dp[p][i]=min(dp[p][i],dp[p][i+1]+1);
	}else{
		dp[p][dep[p]]=INF;
		Rof(i,dep[p],1) dp[p][i]=min(dp[p][i],dp[p][i-1]+1);
	}
	ans[p]=INF;
	For(i,0,dep[p]) ans[p]=min(ans[p],dp[p][i]);
}
void Main(){
	int n;cin>>n;
	For(i,1,n){
		link[i].clear();
		dp[i].clear();
	}
	string s;cin>>s;
	For(i,0,s.size()-1) v[i+1]=s[i]-'0';
	For(i,2,n){
		int x;cin>>x;
		link[x].push_back(i);
	}
	dfs(1);
	For(i,1,n) cout<<ans[i]<<" ";
	cout<<"\n";
}
int main(){
	std::ios::sync_with_stdio(0);
	cin.tie(0);cout.tie(0);
	int T=1;cin>>T;
	while (T--) Main();
}
/*
2
9
101011110
1 1 3 3 3 6 2 2
4
1011
1 1 3
*/