#include <bits/stdc++.h>

using namespace std;

typedef long long ll;

const int inf = 1e9 + 10;

struct MinDeque {
    deque<pair<int, int>> data;
    deque<pair<int, int>> suf_min;
    void push_back(int val, int pos) {
        auto cur = make_pair(val, -pos);
        while (!suf_min.empty() && suf_min.back() > cur) {
            suf_min.pop_back();
        }
        data.push_back(cur);
        suf_min.push_back(cur);
    }
    void pop_front() {
        if (!data.empty()) {
            if (suf_min.front() == data.front()) {
                suf_min.pop_front();
            }
            data.pop_front();
        }
    }
    int get_min() const {
        if (data.empty()) {
            return inf;
        } else {
            return suf_min.front().first;
        }
    }
    size_t size() const {
        return data.size();
    }
    void clear() {
        data.clear();
        suf_min.clear();
    }
};

void add(int& x, int y) {
    x = min(inf, x + y);
}

MinDeque mdeq;

const int N = 1e5 + 10;
vector<int> g[N];
bool is_black[N];
int ans[N];
vector<int> dp[N];
int reds[N], blacks[N];
int dist_leaf[N];

void init(int n) {
    for (int i = 1; i <= n; i++) {
        g[i].clear();
        dp[i].clear();
        reds[i] = 0;
        blacks[i] = 0;
        dist_leaf[i] = 0;
    }
}

void recalc(vector<int>& cur, int red_cnt, int black_cnt, int max_len) {
    cur.resize(cur.size() + red_cnt, inf);
    mdeq.clear();
    for (int i = 0; i < cur.size(); i++) {
        mdeq.push_back(cur[i] - i, i);
        while (mdeq.size() > red_cnt + 1) {
            mdeq.pop_front();
        }
        cur[i] = mdeq.get_min() + i;
    }
    cur.resize(cur.size() + black_cnt, inf);
    for (int i = int(cur.size()) - 1; i >= 0; i--) {
        if (i >= black_cnt) {
            cur[i] = cur[i - black_cnt];
        } else {
            cur[i] = inf;
        }
    }
    mdeq.clear();
    for (int i = int(cur.size()) - 1; i >= 0; i--) {
        mdeq.push_back(cur[i] + i, -i);
        while (mdeq.size() > black_cnt + 1) {
            mdeq.pop_front();
        }
        cur[i] = mdeq.get_min() - i;
    }
    cur.resize(max_len);
}

void dfs(int v, int p) {
    if (g[v].empty()) {
        ans[v] = 0;
        reds[v] = 0;
        blacks[v] = 0;
        dp[v] = {is_black[v], !is_black[v]};
        dist_leaf[v] = 0;
    } else if (g[v].size() == 1) {
        int to = g[v].front();
        dfs(to, v);
        dist_leaf[v] = dist_leaf[to] + 1;
        ans[v] = ans[to];
        reds[v] = reds[to] + !is_black[v];
        blacks[v] = blacks[to] + is_black[v];
        swap(dp[v], dp[to]);
        dp[to].clear();
    } else {
        dist_leaf[v] = inf;
        for (int to : g[v]) {
            dfs(to, v);
            dist_leaf[v] = min(dist_leaf[v], dist_leaf[to] + 1);
        }

        dp[v].assign(dist_leaf[v] + 2, 0);
        for (int to : g[v]) {
            assert(dp[to].size() + reds[to] + blacks[to] == dist_leaf[to] + 2);

            recalc(dp[to], reds[to], blacks[to], dp[v].size());
            for (int i = 0; i < dp[v].size(); i++) {
                add(dp[v][i], dp[to][i]);
            }
            dp[to].clear();
        }

        if (is_black[v]) {
            for (int i = int(dp[v].size()) - 1; i >= 1; i--) {
                dp[v][i] = dp[v][i - 1];
            }
            dp[v][0] = inf;
            for (int i = 0; i + 1 < dp[v].size(); i++) {
                dp[v][i] = min(dp[v][i], dp[v][i + 1] + 1);
            }
        } else {
            dp[v].back() = inf;
            for (int i = int(dp[v].size()) - 1; i >= 1; i--) {
                dp[v][i] = min(dp[v][i], dp[v][i - 1] + 1);
            }
        }

        reds[v] = 0;
        blacks[v] = 0;
        ans[v] = inf;
        for (int i = 0; i < dp[v].size(); i++) {
            ans[v] = ans[v] = min(ans[v], dp[v][i]);
        }
    }
}

int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);
#ifdef LOCAL
    freopen("input.txt", "r", stdin);
#endif

    int t;
    cin >> t;
    while (t--) {
        int n;
        cin >> n;
        init(n);
        string cols;
        cin >> cols;
        for (int i = 1; i <= n; i++) {
            is_black[i] = cols[i - 1] == '1';
        }
        for (int i = 2; i <= n; i++) {
            int par;
            cin >> par;
            g[par].push_back(i);
        }
        dfs(1, 1);
        for (int i = 1; i <= n; i++) {
            cout << ans[i];
            if (i != n) {
                cout << " ";
            }
        }
        if (t >= 1) {
            cout << "\n";
        }
    }

#ifdef LOCAL
    cout << "\nTime elapsed: " << double(clock()) / CLOCKS_PER_SEC << " s.\n";
#endif
}