#include<bits/stdc++.h>
using namespace std;
#define fo(i,a,b) for(int i=a;i<=b;++i)
#define fod(i,a,b) for(int i=a;i>=b;--i)
#define ll long long
#define lx edge[x][i]
int T;
int n;
int big[100011],fa[100011],sz[100011];
vector<int>edge[100011];
struct convex{
    multiset<int>L;
    multiset<int>R;
    int x,y;
    void clear(){
        x=0,y=0;
        L.clear();
        R.clear();
    }
    void operator += (const convex &A) {
        vector<int>a;
        a.resize(max((int)A.L.size()+(int)A.R.size()+1,(int)L.size()+(int)R.size()+1));
        fo(i,0,(int)a.size()-1){
            a[i]=0;
        }
        int u=A.x,v=A.y;
        a[u]+=A.y;
        for(auto it=A.L.begin();it!=A.L.end();++it){
            --u;
            v+=*it;
            a[u]+=v;
        }
        u=A.x,v=A.y;
        for(auto it=A.R.begin();it!=A.R.end();++it){
            ++u;
            v+=*it;
            a[u]+=v;
        }

        u=x,v=y;
        a[u]+=y;
        for(auto it=L.begin();it!=L.end();++it){
            --u;
            v+=*it;
            a[u]+=v;
        }
        u=x,v=y;
        for(auto it=R.begin();it!=R.end();++it){
            ++u;
            v+=*it;
            a[u]+=v;
        }
        int len=min((int)A.L.size()+(int)A.R.size()+1,(int)L.size()+(int)R.size()+1);
        while(a.size()>len)a.pop_back();
        u=0,v=1e9;
        fo(i,0,len-1){
            if(v>a[i]){
                v=a[i],u=i;
            }
        }
        clear();
        x=u,y=v;
        fod(i,u-1,0){
            L.insert(a[i]-a[i+1]);
        }
        fo(i,u+1,len-1){
            R.insert(a[i]-a[i-1]);
        }
    }
    void print(){
        vector<int>a;
        a.resize((int)L.size()+(int)R.size()+1);
        int u=x,v=y;
        a[u]+=y;
        for(auto it=L.begin();it!=L.end();++it){
            --u;
            v+=*it;
            a[u]+=v;
        }
        u=x,v=y;
        for(auto it=R.begin();it!=R.end();++it){
            ++u;
            v+=*it;
            a[u]+=v;
        }
        cout<<a.size()<<endl;
        fo(i,0,a.size()-1)cout<<a[i]<<" ";
        cout<<endl;
    }
}c[100011];
char col[100011];
int ans[100011],p[100011];
void solve(){
    scanf("%d",&n);
    scanf("%s",col);
    fo(i,2,n){
        scanf("%d",&fa[i]);
        sz[i]=0;
        edge[i].clear();
    }
    fod(i,n,1){
        ++sz[i];
        if(i>1)edge[fa[i]].push_back(i);
        if(i>1)sz[fa[i]]+=sz[i];
    }
    fo(i,1,p[0])c[i].clear();
    p[0]=0;
    fo(x,1,n){
        if(!p[x])p[x]=++p[0];
        big[x]=0;
        fo(i,0,(int)edge[x].size()-1){
            if(sz[big[x]]<sz[lx])big[x]=lx;
        }
        if(big[x])p[big[x]]=p[x];
    }
    fod(x,n,1){
        int y=p[x];
        if(!edge[x].size()){
            if(col[x-1]=='0'){
                c[y].x=0;
                c[y].y=0;
                c[y].R.insert(1);
            }
            else {
                c[y].x=1;
                c[y].y=0;
                c[y].L.insert(1);
            }
        }
        else{
            fo(i,0,(int)edge[x].size()-1){
                if(lx!=big[x])c[y]+=c[p[lx]];
            }
            if(col[x-1]=='0'){
                c[y].R.insert(1);
            }
            else {
                c[y].x++;
                c[y].L.insert(1);
            }
        }
        ans[x]=c[y].y;
    }
    fo(i,1,n-1){
        printf("%d ",ans[i]);
    }
    printf("%d\n",ans[n]);
}
int main(){
    scanf("%d",&T);
    while(T){
        --T;
        solve();
    }
    return 0;
}