//#define _GLIBCXX_DEBUG

//#pragma GCC target("avx2")
//#pragma GCC optimize("O3")
//#pragma GCC optimize("unroll-loops")

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


#ifdef LOCAL
#include <debug_print.hpp>
#define OUT(...) debug_print::multi_print(#__VA_ARGS__, __VA_ARGS__)
#else
#define OUT(...) (static_cast<void>(0))
#endif

#define endl '\n'
#define lfs cout<<fixed<<setprecision(15)
#define ALL(a)  (a).begin(),(a).end()
#define ALLR(a)  (a).rbegin(),(a).rend()
#define UNIQUE(a) (a).erase(unique((a).begin(),(a).end()),(a).end())
#define spa << " " <<
#define fi first
#define se second
#define MP make_pair
#define MT make_tuple
#define PB push_back
#define EB emplace_back
#define rep(i,n,m) for(ll i = (n); i < (ll)(m); i++)
#define rrep(i,n,m) for(ll i = (ll)(m) - 1; i >= (ll)(n); i--)
using ll = long long;
using ld = long double;
const ll MOD1 = 1e9+7;
const ll MOD9 = 998244353;
const ll INF = 1e18;
using P = pair<ll, ll>;
template<typename T> using PQ = priority_queue<T>;
template<typename T> using QP = priority_queue<T,vector<T>,greater<T>>;
template<typename T1, typename T2>bool chmin(T1 &a,T2 b){if(a>b){a=b;return true;}else return false;}
template<typename T1, typename T2>bool chmax(T1 &a,T2 b){if(a<b){a=b;return true;}else return false;}
ll median(ll a,ll b, ll c){return a+b+c-max({a,b,c})-min({a,b,c});}
void ans1(bool x){if(x) cout<<"Yes"<<endl;else cout<<"No"<<endl;}
void ans2(bool x){if(x) cout<<"YES"<<endl;else cout<<"NO"<<endl;}
void ans3(bool x){if(x) cout<<"Yay!"<<endl;else cout<<":("<<endl;}
template<typename T1,typename T2>void ans(bool x,T1 y,T2 z){if(x)cout<<y<<endl;else cout<<z<<endl;}  
template<typename T1,typename T2,typename T3>void anss(T1 x,T2 y,T3 z){ans(x!=y,x,z);};  
template<typename T>void debug(const T &v,ll h,ll w,string sv=" "){for(ll i=0;i<h;i++){cout<<v[i][0];for(ll j=1;j<w;j++)cout<<sv<<v[i][j];cout<<endl;}};
template<typename T>void debug(const T &v,ll n,string sv=" "){if(n!=0)cout<<v[0];for(ll i=1;i<n;i++)cout<<sv<<v[i];cout<<endl;};
template<typename T>void debug(const vector<T>&v){debug(v,v.size());}
template<typename T>void debug(const vector<vector<T>>&v){for(auto &vv:v)debug(vv,vv.size());}
template<typename T>void debug(stack<T> st){while(!st.empty()){cout<<st.top()<<" ";st.pop();}cout<<endl;}
template<typename T>void debug(queue<T> st){while(!st.empty()){cout<<st.front()<<" ";st.pop();}cout<<endl;}
template<typename T>void debug(deque<T> st){while(!st.empty()){cout<<st.front()<<" ";st.pop_front();}cout<<endl;}
template<typename T>void debug(PQ<T> st){while(!st.empty()){cout<<st.top()<<" ";st.pop();}cout<<endl;}
template<typename T>void debug(QP<T> st){while(!st.empty()){cout<<st.top()<<" ";st.pop();}cout<<endl;}
template<typename T>void debug(const set<T>&v){for(auto z:v)cout<<z<<" ";cout<<endl;}
template<typename T>void debug(const multiset<T>&v){for(auto z:v)cout<<z<<" ";cout<<endl;}
template<typename T,size_t size>void debug(const array<T, size> &a){for(auto z:a)cout<<z<<" ";cout<<endl;}
template<typename T,typename V>void debug(const map<T,V>&v){for(auto z:v)cout<<"["<<z.first<<"]="<<z.second<<",";cout<<endl;}
template<typename T>vector<vector<T>>vec(ll x, ll y, T w){vector<vector<T>>v(x,vector<T>(y,w));return v;}
vector<ll>dx={1,-1,0,0,1,1,-1,-1};vector<ll>dy={0,0,1,-1,1,-1,1,-1};
template<typename T>vector<T> make_v(size_t a,T b){return vector<T>(a,b);}
template<typename... Ts>auto make_v(size_t a,Ts... ts){return vector<decltype(make_v(ts...))>(a,make_v(ts...));}
template<typename T1, typename T2>ostream &operator<<(ostream &os, const pair<T1, T2>&p){return os << "(" << p.first << "," << p.second << ")";}
template<typename T>ostream &operator<<(ostream &os, const vector<T> &v){os<<"[";for(auto &z:v)os << z << ",";os<<"]"; return os;}
template<typename T>void rearrange(vector<int>&ord, vector<T>&v){
  auto tmp = v;
  for(int i=0;i<tmp.size();i++)v[i] = tmp[ord[i]];
}
template<typename Head, typename... Tail>void rearrange(vector<int>&ord,Head&& head, Tail&&... tail){
  rearrange(ord, head);
  rearrange(ord, tail...);
}
template<typename T> vector<int> ascend(const vector<T>&v){
  vector<int>ord(v.size());iota(ord.begin(),ord.end(),0);
  sort(ord.begin(),ord.end(),[&](int i,int j){return make_pair(v[i],i)<make_pair(v[j],j);});
  return ord;
}
template<typename T> vector<int> descend(const vector<T>&v){
  vector<int>ord(v.size());iota(ord.begin(),ord.end(),0);
  sort(ord.begin(),ord.end(),[&](int i,int j){return make_pair(v[i],-i)>make_pair(v[j],-j);});
  return ord;
}
template<typename T> vector<T> inv_perm(const vector<T>&ord){
  vector<T>inv(ord.size());
  for(int i=0;i<ord.size();i++)inv[ord[i]] = i;
  return inv;
}
ll FLOOR(ll n,ll div){assert(div>0);return n>=0?n/div:(n-div+1)/div;}
ll CEIL(ll n,ll div){assert(div>0);return n>=0?(n+div-1)/div:n/div;}
ll digitsum(ll n){ll ret=0;while(n){ret+=n%10;n/=10;}return ret;}
ll modulo(ll n,ll d){return (n%d+d)%d;};
template<typename T>T min(const vector<T>&v){return *min_element(v.begin(),v.end());}
template<typename T>T max(const vector<T>&v){return *max_element(v.begin(),v.end());}
template<typename T>T acc(const vector<T>&v){return accumulate(v.begin(),v.end(),T(0));};
template<typename T>T reverse(const T &v){return T(v.rbegin(),v.rend());};
//mt19937 mt(chrono::steady_clock::now().time_since_epoch().count());
int popcount(ll x){return __builtin_popcountll(x);};
int poplow(ll x){return __builtin_ctzll(x);};
int pophigh(ll x){return 63 - __builtin_clzll(x);};
template<typename T>T poll(queue<T> &q){auto ret=q.front();q.pop();return ret;};
template<typename T>T poll(priority_queue<T> &q){auto ret=q.top();q.pop();return ret;};
template<typename T>T poll(QP<T> &q){auto ret=q.top();q.pop();return ret;};
template<typename T>T poll(stack<T> &s){auto ret=s.top();s.pop();return ret;};
ll MULT(ll x,ll y){if(LLONG_MAX/x<=y)return LLONG_MAX;return x*y;}
ll POW2(ll x, ll k){ll ret=1,mul=x;while(k){if(mul==LLONG_MAX)return LLONG_MAX;if(k&1)ret=MULT(ret,mul);mul=MULT(mul,mul);k>>=1;}return ret;}
ll POW(ll x, ll k){ll ret=1;for(int i=0;i<k;i++){if(LLONG_MAX/x<=ret)return LLONG_MAX;ret*=x;}return ret;}
std::ostream &operator<<(std::ostream &dest, __int128_t value) {
  std::ostream::sentry s(dest);
  if (s) {
    __uint128_t tmp = value < 0 ? -value : value;
    char buffer[128];
    char *d = std::end(buffer);
    do {
      --d;
      *d = "0123456789"[tmp % 10];
      tmp /= 10;
    } while (tmp != 0);
    if (value < 0) {
      --d;
      *d = '-';
    }
    int len = std::end(buffer) - d;
    if (dest.rdbuf()->sputn(d, len) != len) {
      dest.setstate(std::ios_base::badbit);
    }
  }
  return dest;
}
namespace converter{
  int dict[500];
  const string lower="abcdefghijklmnopqrstuvwxyz";
  const string upper="ABCDEFGHIJKLMNOPQRSTUVWXYZ";
  const string digit="0123456789";
  const string digit1="123456789";
  void regi_str(const string &t){
    for(int i=0;i<t.size();i++){
      dict[t[i]]=i;
    }
  }
  void regi_int(const string &t){
    for(int i=0;i<t.size();i++){
      dict[i]=t[i];
    }
  }
  vector<int>to_int(const string &s,const string &t){
    regi_str(t);
    vector<int>ret(s.size());
    for(int i=0;i<s.size();i++){
      ret[i]=dict[s[i]];
    }
    return ret;
  }
  vector<int>to_int(const string &s){
    auto t=s;
    sort(t.begin(),t.end());
    t.erase(unique(t.begin(),t.end()),t.end());
    return to_int(s,t);
  }
  
  vector<vector<int>>to_int(const vector<string>&s,const string &t){
    regi_str(t);
    vector<vector<int>>ret(s.size(),vector<int>(s[0].size()));
    for(int i=0;i<s.size();i++){
      for(int j=0;j<s[0].size();j++){
        ret[i][j]=dict[s[i][j]];
      }
    }
    return ret;
  }
  vector<vector<int>>to_int(const vector<string>&s){
    string t;
    for(int i=0;i<s.size();i++){
      t+=s[i];
    }
    sort(t.begin(),t.end());t.erase(unique(t.begin(),t.end()),t.end());
    return to_int(s,t);
  }
  string to_str(const vector<int>&s,const string &t){
    regi_int(t);
    string ret;
    for(auto z:s)ret+=dict[z];
    return ret;
  }
  vector<string> to_str(const vector<vector<int>>&s,const string &t){
    regi_int(t);
    vector<string>ret(s.size());
    for(int i=0;i<s.size();i++){
      for(auto z:s[i])ret[i]+=dict[z];
    }
    return ret;
  }
}
template< typename T = int >
struct edge {
  int to;
  T cost;
  int id;
  edge():to(-1),id(-1){};
  edge(int to, T cost = 1, int id = -1):to(to), cost(cost), id(id){}
  operator int() const { return to; }
};

template<typename T>
using Graph = vector<vector<edge<T>>>;
template<typename T>
Graph<T>revgraph(const Graph<T> &g){
  Graph<T>ret(g.size());
  for(int i=0;i<g.size();i++){
    for(auto e:g[i]){
      int to = e.to;
      e.to = i;
      ret[to].push_back(e);
    }
  }
  return ret;
}
template<typename T>
Graph<T> readGraph(int n,int m,int indexed=1,bool directed=false,bool weighted=false){
  Graph<T> ret(n);
  for(int es = 0; es < m; es++){
    int u,v;
    T w=1;
    cin>>u>>v;u-=indexed,v-=indexed;
    if(weighted)cin>>w;
    ret[u].emplace_back(v,w,es);
    if(!directed)ret[v].emplace_back(u,w,es);
  }
  return ret;
}
template<typename T>
Graph<T> readParent(int n,int indexed=1,bool directed=true){
  Graph<T>ret(n);
  for(int i=1;i<n;i++){
    int p;cin>>p;
    p-=indexed;
    ret[p].emplace_back(i);
    if(!directed)ret[i].emplace_back(p);
  }
  return ret;
}
/**
 * @brief Slope-Trick
 * @docs docs/slope-trick.md
 * @see https://maspypy.com/slope-trick-1-%E8%A7%A3%E8%AA%AC%E7%B7%A8
 */
template< typename T >
struct SlopeTrick {
 
  const T INF = numeric_limits< T >::max() / 3;
 
  T min_f;
  priority_queue< T, vector< T >, less<> > L;
  priority_queue< T, vector< T >, greater<> > R;
  T add_l, add_r;
 
  void push_R(const T &a) {
    R.push(a - add_r);
  }
 
  T top_R() const {
    if(R.empty()) return INF;
    else return R.top() + add_r;
  }
 
  T pop_R() {
    T val = top_R();
    if(not R.empty()) R.pop();
    return val;
  }
 
  void push_L(const T &a) {
    L.push(a - add_l);
  }
 
  T top_L() const {
    if(L.empty()) return -INF;
    else return L.top() + add_l;
  }
 
  T pop_L() {
    T val = top_L();
    if(not L.empty()) L.pop();
    return val;
  }
 
  size_t size() {
    return L.size() + R.size();
  }
 
  SlopeTrick() : min_f(0), add_l(0), add_r(0) {}
 
  struct Query {
    T lx, rx, min_f;
  };
 
  // return min f(x)
  Query query() const {
    return (Query) {top_L(), top_R(), min_f};
  }
 
  // f(x) += a
  void add_all(const T &a) {
    min_f += a;
  }
 
  // add \_
  // f(x) += max(a - x, 0)
  void add_a_minus_x(const T &a) {
    min_f += max(T(0), a - top_R());
    push_R(a);
    push_L(pop_R());
  }
 
  // add _/
  // f(x) += max(x - a, 0)
  void add_x_minus_a(const T &a) {
    min_f += max(T(0), top_L() - a);
    push_L(a);
    push_R(pop_L());
  }
 
  // add \/
  // f(x) += abs(x - a)
  void add_abs(const T &a) {
    add_a_minus_x(a);
    add_x_minus_a(a);
  }
 
  // \/ -> \_
  // f_{new} (x) = min f(y) (y <= x)
  void clear_right() {
    while(not R.empty()) R.pop();
  }
 
  // \/ -> _/
  // f_{new} (x) = min f(y) (y >= x)
  void clear_left() {
    while(not L.empty()) L.pop();
  }
 
  // \/ -> \_/
  // f_{new} (x) = min f(y) (x-b <= y <= x-a)
  void shift(const T &a, const T &b) {
    assert(a <= b);
    add_l += a;
    add_r += b;
  }
 
  // \/. -> .\/
  // f_{new} (x) = f(x - a)
  void shift(const T &a) {
    shift(a, a);
  }
 
  // L, R を破壊する
  T get(const T &x) {
    T ret = min_f;
    while(not L.empty()) {
      ret += max(T(0), pop_L() - x);
    }
    while(not R.empty()) {
      ret += max(T(0), x - pop_R());
    }
    return ret;
  }
 
  void merge(SlopeTrick &st) {
    if(st.size() > size()) {
      swap(st.L, L);
      swap(st.R, R);
      swap(st.add_l, add_l);
      swap(st.add_r, add_r);
      swap(st.min_f, min_f);
    }
    while(not st.R.empty()) {
      add_x_minus_a(st.pop_R());
    }
    while(not st.L.empty()) {
      add_a_minus_x(st.pop_L());
    }
    min_f += st.min_f;
  }
};
int main(){
  cin.tie(nullptr);
  ios_base::sync_with_stdio(false);
  ll res=0,buf=0;
  bool judge = true;
  ll t;cin>>t;
  while(t--){
    ll n;cin>>n;
    string s;cin>>s;
    auto g=readParent<int>(n);
    vector<ll>mi(n);
    {
      vector<int>sub(n,1e9);
      auto dfs=[&](auto &&f,int v)->SlopeTrick<ll> {
        SlopeTrick<ll>ret;
        for(auto to:g[v]){
          auto tmp=f(f,to);
          ret.merge(tmp);
          chmin(sub[v],(sub[to]+1));
        }
        if(g[v].empty())sub[v]=0;
        //OUT(v,"-----------");
        //OUT(ret.add_l,ret.L,ret.add_r,ret.R,ret.min_f);
        ll cnt=0;
        while(!ret.R.empty()&&ret.top_R()>sub[v]){
          ret.pop_R();
        }
        if(ret.R.empty()&&!ret.L.empty()){
          ll cnt=0,sum=0;
          while(!ret.L.empty()&&ret.top_L()>sub[v]){
            ret.min_f+=ret.pop_L()-sub[v];
            cnt++;
          }
          rep(_,0,cnt)ret.push_L(sub[v]);
        }
        ret.add_a_minus_x(0);
        ret.add_x_minus_a(sub[v]);
        if(s[v]=='0'){
          if(ret.L.size()>=2){
            auto mxr=ret.pop_R();
            ret.add_r+=1;
            ret.push_R(mxr);
          }
        }
        else{
          ret.shift(1);
          if(ret.L.size()>=2){
            auto mxl=ret.pop_L();
            ret.add_l-=1;
            ret.push_L(mxl);
          }
        }
        mi[v]=ret.min_f;
        //OUT(ret.add_l,ret.L,ret.add_r,ret.R,ret.min_f);
        return ret;
      };
      dfs(dfs,0);
    }
    debug(mi);
  }
  return 0;
}