/*
60 + 0 + 100 + 64 = 224.
*/

#include <bits/stdc++.h>
using namespace std;
//#define int long long
#define L(i, j, k) for (int i = (j); i <= (k); i++)
#define R(i, j, k) for (int i = (j); i >= (k); i--)
#define pb push_back
#define pii pair<int, int>
inline int read()
{
	int sum = 0, nega = 1;
	char ch = getchar();
	while (ch > '9'||ch < '0')
	{
	    if (ch == '-') nega = -1;
		ch = getchar();
	}
	while (ch <= '9' && ch >= '0') sum = sum * 10 + ch - '0', ch = getchar();
	return sum * nega;
}
const int N = 1e5 + 9, mod = 998244353;
inline void add(int &x, int y) {x = (x + y) % mod;}
inline void del(int &x, int y) {x = (x - y + mod) % mod;}
int n, col[N], c[N][2], rt[N], ans[N];
vector<int> G[N], T[N], tmp[N];
char s[N];
int mn[N << 2];
inline int lc(int p) {return p << 1;}
inline int rc(int p) {return p << 1 | 1;}
inline void build(int l, int r, int p)
{
	mn[p] = 1e9;
	if(l == r) return ;
	int mid = (l + r) >> 1;
	build(l, mid, lc(p)), build(mid + 1, r, rc(p)); return ;
}
inline void update(int l, int r, int p, int L, int R, int v)
{
	if(L <= l && r <= R) {mn[p] = min(mn[p], v); return ;}
	int mid = (l + r) >> 1;
	if(mid >= L) update(l, mid, lc(p), L, R, v);
	if(mid < R) update(mid + 1, r, rc(p), L, R, v);
}
inline int query(int l, int r, int p, int pos)
{
	if(l == r) return mn[p];
	int mid = (l + r) >> 1, res = mn[p];
	if(mid >= pos) res = min(res, query(l, mid, lc(p), pos));
	else res = min(res, query(mid + 1, r, rc(p), pos)); return res;
}
int f[N], g[N], h[N];
inline void get(int u, int x, int y)
{
	int siz = T[u].size(), t = siz + x + y;
	L(i, 1, siz + x + y) f[i] = g[i] = h[i] = 1e9;
	build(1, t, 1);
	L(i, 1, siz)
	{
		int v = T[u][i - 1];
		update(1, t, 1, i, i + y, v + i + y);
	}
	L(i, 1, siz + x + y) h[i] = min(h[i], query(1, t, 1, i) - i);
	build(1, t, 1);
	L(i, 1, siz)
	{
		int v = T[u][i - 1];
		update(1, t, 1, i + y, i + x + y, v - i - y);
	}
	L(i, 1, siz + x + y) h[i] = min(h[i], query(1, t, 1, i) + i);
	T[u].clear(); T[u].resize(siz + x + y);
	L(i, 1, siz + x + y) T[u][i - 1] = h[i];
	return ;
}
inline void dfs(int u)
{
	if(G[u].size() == 0)
	{
		T[u].pb(0); ans[u] = 0; c[u][col[u]] = 1;
		return ;
	}
	else if(G[u].size() == 1)
	{
		int v = G[u][0];
		dfs(v); swap(rt[u], rt[v]); ans[u] = ans[v];
		L(i, 0, 1) c[u][i] = c[v][i]; c[u][col[u]]++; return ;
	}
	int mn = 1e9;
	for (auto v : G[u])
	{
		dfs(v); get(rt[v], c[v][0], c[v][1]);
		mn = min(mn, (int)T[rt[v]].size());
	}
	T[u].resize(mn);
	L(i, 0, mn - 1) T[u][i] = 0;
	for (auto v : G[u])
		L(j, 0, mn - 1) T[u][j] += T[rt[v]][j];
	ans[u] = 1e9;
	L(i, 0, mn - 1) ans[u] = min(ans[u], T[u][i]);
	c[u][col[u]]++;
	return ;
}
inline void solve()
{
	n = read();
	scanf("%s", s + 1);
	L(i, 1, n) G[i].clear(), rt[i] = i, c[i][0] = c[i][1] = 0, T[i].clear();
	L(i, 1, n) col[i] = s[i] - '0';
	L(i, 2, n)
	{
		int x = read();
		G[x].pb(i);
	}
	dfs(1);
	L(i, 1, n) printf("%d ", ans[i]);
	puts("");
	return ;
}
signed main()
{
	int T = read();
	L(i, 1, T) solve();
	return 0;
}