//221.2.86.180:9009

#include <bits/stdc++.h>

#define fir first
#define sec second
#ifdef LOCAL
#define dbg(x) cerr << "In Line " << __LINE__ << " the " << #x << " = " << x << '\n';
#define dpi(x, y) cerr << "In Line " << __LINE__ << " the " << #x << " = " << x << " ; " << "the " << #y << " = " << y << '\n';
#define dbgf(fmt, args...) fprintf(stderr, fmt, ##args);
#else
#define dbg(x) void();
#define dpi(x, y) void();
#define dbgf(fmt, args...) void();
#endif

using namespace std;

using ll = long long;
using ull = unsigned long long;
using i128 = __int128_t;
using pii = pair<int, int>;
using pil = pair<int, ll>;
using pli = pair<ll, int>;
using vi = vector<int>;
using vpii = vector<pii>;

bool Mbe;
constexpr int MOD = 998244353;
template<typename T> T add(T a, T b, T p = MOD) { return (a + b >= p) ? (a + b - p) : (a + b); }
template<typename T> T del(T a, T b, T p = MOD) { return (a - b < 0) ? (a - b + p) : (a - b); }
template<typename T> T mul(T a, T b, T p = MOD) { return 1ll * a * b % p; }
template<typename T> T cadd(T &a, T b, T p = MOD) { return a = add(a, b, p); }
template<typename T> T cdel(T &a, T b, T p = MOD) { return a = del(a, b, p); }
template<typename T> T cmul(T &a, T b, T p = MOD) { return a = mul(a, b, p); }
template<typename T> T cmax(T &a, T b) { return a = max(a, b); }
template<typename T> T cmin(T &a, T b) { return a = min(a, b); }

namespace FastIO {
	constexpr int LEN = 1 << 20;
	char in[LEN + 1], out[LEN + 1];
	char *pin = in, *pout = out, *ein = in, *eout = out + LEN;

	char gc() { return pin == ein && (ein = (pin = in) + fread(in, 1, LEN, stdin), ein == in) ? EOF : *pin ++; }
	void pc(char c) { pout == eout && (fwrite(out, 1, LEN, stdout), pout = out); (*pout ++) = c; return; }
	void Flush() { fwrite(out, 1, pout - out, stdout); pout = out; }

	template<typename T> T Read() {
		T x = 0; int f = 1; char ch = gc();
		while (ch < '0' || ch > '9') f = (ch == '-' ? (~f + 1) : f), ch = gc();
		while (ch >= '0' && ch <= '9') x = (x << 1) + (x << 3) + (ch ^ 48), ch = gc();
		return x * f;
	}
	template<typename T> void Write(T x, char c) {
		static char stk[40]; int tp = 0;
		if (x < 0) pc('-'), x = ~x + 1;
		do stk[tp++] = x % 10 + 48, x /= 10; while (x);
		while (tp --) pc(stk[tp]); pc(c); return;
	}
	void Read(char *s) {
		char ch = gc();
		while (!((ch >= 'a' && ch <= 'z') || (ch >= 'A' && ch <= 'Z') ||
			(ch >= '0' && ch <= '9'))) ch = gc();
		while ((ch != EOF) && ((ch >= 'a' && ch <= 'z') || (ch >= 'A' && ch <= 'Z') ||
			(ch >= '0' && ch <= '9'))) *s = ch, s ++, ch = gc();
		*s = '\0'; return;
	}
	void Write(char *s) {
		while (*s != '\0') pc(*s), s ++; return;
	}
	void Puts(char *s) {
		Write(s), pc('\n'); return;
	}
}

#define getchar FastIO::gc
#define putchar FastIO::pc
#define Flush FastIO::Flush
#define Read FastIO::Read
#define Write FastIO::Write
#define Puts FastIO::Puts

constexpr int MAXN = 1e5 + 5;
int n, ans[MAXN], g[MAXN], mx[MAXN];
char s[MAXN];
vector<int> G[MAXN];
priority_queue<int> f[MAXN];

void dp(int u) {
	for (auto v : G[u]) {
		dp(v);
		if (v == G[u].front()) {
			swap(f[u], f[v]);
			mx[u] = mx[v], ans[u] = ans[v];
			continue;
		}
		int sz = min(f[u].size(), f[v].size());
		for (int i = 0; i < sz; i ++)
			g[i] = f[u].top() + f[v].top(),
			f[u].pop(), f[v].pop();
		ans[u] = (mx[u] += mx[v]);
		while (f[u].size()) f[u].pop();
		for (int i = 0; i < sz; i ++)
			f[u].emplace(g[i]), cmin(ans[u], ans[u] - g[i]);
	}
	if (s[u] == '0') f[u].emplace(-1);
	else f[u].emplace(1), mx[u] ++;
	return;
}

void slv() {
	n = Read<int>(), Read(s + 1);
	for (int i = 2; i <= n; i ++)
		G[Read<int>()].emplace_back(i);
	dp(1);
	for (int i = 1; i <= n; i ++)
		Write(ans[i], ' ');
	Puts("");
	return;
}
void clr() {
	for (int i = 1; i <= n; i ++) {
		mx[i] = ans[i] = 0, G[i].clear();
		while (f[i].size()) f[i].pop();
	}
	return;
}

bool Med;
int main() {
#ifdef LOCAL
	freopen("!in.in", "r", stdin);
	freopen("!out.out", "w", stdout);
	fprintf(stderr, "%.3lf Mb\n", fabs((&Mbe - &Med) / 1048576.0));
#endif
//	int T = 1; 
	int T = Read<int>();
	while (T --) slv(), clr();
	Flush();
#ifdef LOCAL
	fprintf(stderr, "%d ms\n", (int)clock());
#endif
	return 0;
}