#include <bits/stdc++.h>

#define ll long long
#define F first
#define S second
#define all(x) x.begin(), x.end()
#define pb push_back
#define FIO ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0)

using namespace std;

typedef pair <ll, ll> pii;

const int N = 1e5 + 7, inf = 1e9;

int n, cnt;
vector <int> adj[N];
int col[N], res[N], wh[N], nu[N], siz[N];

queue <int> q;
deque <int> dq;
void Push(int x) {
	q.push(x);
	while (!dq.empty() && dq.back() > x) dq.pop_back();
	dq.pb(x);
}
void Pop() {
	int x = q.front(); q.pop();
	if (dq.front() == x) dq.pop_front();
}
int Min() {return dq.front();}
void Clear() {
	while (!q.empty()) q.pop();
	dq.clear();
}

vector <int> dfs(int x, int y) {
	wh[x] = y;
	nu[y] += col[x];
	siz[y]++;
	if (adj[x].size() == 1) return dfs(adj[x][0], y);
	if (adj[x].empty()) {
		vector <int> ret;
		for (int i = 0; i <= siz[y]; i++) ret.pb(abs(i-nu[y]));
		return ret;
	}
	vector <vector <int> > v;
	int mn = inf;
	for (auto z : adj[x]) {
		v.pb(dfs(z, ++cnt));
		mn = min(mn, (int)v.back().size());
	}
	vector <int> ssum(mn, 0);
	res[y] = inf;
	for (int i = 0; i < mn; i++) {
		for (int j = 0; j < v.size(); j++) {
			ssum[i] += v[j][i];
		}
		res[y] = min(res[y], ssum[i]);
	}
	vector <int> sum;
	for (int i = 0; i < nu[y]; i++) sum.pb(inf);
	for (int i = 0; i < mn; i++) sum.pb(ssum[i]);
	for (int i = 0; i < siz[y]-nu[y]; i++) sum.pb(inf);
	Clear();
	int si = mn + siz[y];
	vector <int> mini(si);
	for (int i = 0; i < si; i++) {
		if (i > siz[y]-nu[y]) Pop();
		Push(sum[i]-i);
		mini[i] = Min() + max(nu[y], i);
	}
	Clear();
	for (int i = si-1, j = 0; i >= 0; i--, j++) {
		if (j > nu[y]) Pop();
		Push(sum[i]-j);
		mini[i] = min(mini[i], Min() + max(siz[y]-nu[y], j));
	}
	return mini;
}

void task() {
	cnt = 1;
	cin >> n;
	for (int i = 1; i <= n; i++) {
		adj[i].clear();
		col[i] = res[i] = wh[i] = nu[i] = siz[i] = 0;
	}
	for (int i = 1; i <= n; i++) {
		char cc; cin >> cc;
		col[i] = cc-'0';
	}
	for (int i = 2; i <= n; i++) {
		int p; cin >> p;
		adj[p].pb(i);
	}
	dfs(1, 1);
	for (int i = 1; i <= n; i++) cout << res[wh[i]] << " ";
	cout << "\n";
}

int main () {
	FIO;
	int tt; cin >> tt;
	while (tt--) task();

	return 0;
}