import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.StringTokenizer;
import java.io.BufferedReader;
import java.util.Collections;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskH solver = new TaskH();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskH {
        static final long INF = (long) 1e18;
        int n;
        int[] parent;
        int[] a;
        long[][] best;
        int[][] k;
        ArrayList<Integer> order;
        ArrayList<Integer>[] g;

        public void solve(int testNumber, InputReader in, PrintWriter out) {
            n = in.nextInt();
            g = new ArrayList[n];
            for (int i = 0; i < n; ++i)
                g[i] = new ArrayList<>();
            a = new int[n];
            for (int i = 0; i < n; ++i) {
                a[i] = in.nextInt();
            }
            parent = new int[n];
            parent[0] = -1;
            for (int i = 1; i < n; ++i) {
                parent[i] = in.nextInt() - 1;
                g[parent[i]].add(i);
            }
            best = new long[n][n];
            k = new int[n][n];
            for (int i = 0; i < n; ++i) {
                Arrays.fill(best[i], INF);
                Arrays.fill(k[i], -1);
                best[i][i] = a[i];
                k[i][i] = i;
            }

            order = new ArrayList<>();
            dfs(0);

            int[] prevKid = new int[n];
            Arrays.fill(prevKid, -1);
            int[] brother = new int[n];
            Arrays.fill(brother, -1);
            int[] depth = new int[n];
            for (int i : order) {
                if (i == 0) continue;
                brother[i] = prevKid[parent[i]];
                prevKid[parent[i]] = i;
                depth[i] = depth[parent[i]] + 1;
            }

            for (int i : order) {
                if (i == 0) continue;
                // p[i] -> i

                long sum = a[i];

                int x = parent[i];
                int prevX = i;
                while (x != -1) {
                    sum += a[x];
                    // d[x][i]
                    // k[x][i - 1] <= k[x][i] <= k[x - 1][i]

                    int l = k[x][parent[i]];
                    int r = parent[x] == -1 ? i : k[prevX][i];
                    prevX = x;
                    if (brother[i] != -1) {
                        int brotherL = k[x][brother[i]];
                        if (brotherL == brother[i]) {
                            l = i;
                        } else {
                            if (brotherL != -1 && depth[brotherL] > depth[l])
                                l = brotherL;
                        }
                    }

                    int y = r;
                    while (y != x) {
                        long cur = sum + best[x][parent[y]] + best[y][i];
                        if (cur < best[x][i]) {
                            best[x][i] = cur;
                            k[x][i] = y;
                        }
                        if (y == l) break;
                        y = parent[y];
                    }

                    x = parent[x];
                }
            }

            for (int i = 0; i < n; ++i) {
                out.println(best[0][i]);
            }
        }

        private void dfs(int x) {
            order.add(x);
            ArrayList<Pair> kids = new ArrayList<>();
            for (int y : g[x]) {
                kids.add(new Pair(a[y], y));
            }
            Collections.sort(kids);
            for (Pair kid : kids)
                dfs(kid.second);
        }

        static class Pair implements Comparable<Pair> {
            int first;
            int second;

            public Pair(int first, int second) {
                this.first = first;
                this.second = second;
            }


            public int compareTo(Pair o) {
                if (first != o.first)
                    return Integer.compare(first, o.first);
                return Integer.compare(second, o.second);
            }

        }

    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

    }
}