Alyona has a tree with n vertices. The root of the tree is the vertex 1. In each vertex Alyona wrote an positive integer, in the vertex i she wrote ai. Moreover, the girl wrote a positive integer to every edge of the tree (possibly, different integers on different edges).

Let's define dist(v, u) as the sum of the integers written on the edges of the simple path from v to u.

The vertex v controls the vertex u (v ≠ u) if and only if u is in the subtree of v and dist(v, u) ≤ au.

Alyona wants to settle in some vertex. In order to do this, she wants to know for each vertex v what is the number of vertices u such that v controls u.

Input

The first line contains single integer n (1 ≤ n ≤ 2·105).

The second line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 109) — the integers written in the vertices.

The next (n - 1) lines contain two integers each. The i-th of these lines contains integers pi and wi (1 ≤ pi ≤ n, 1 ≤ wi ≤ 109) — the parent of the (i + 1)-th vertex in the tree and the number written on the edge between pi and (i + 1).

It is guaranteed that the given graph is a tree.

Output

Print n integers — the i-th of these numbers should be equal to the number of vertices that the i-th vertex controls.

Examples

Input

5
2 5 1 4 6
1 7
1 1
3 5
3 6


Output

1 0 1 0 0


Input

5
9 7 8 6 5
1 1
2 1
3 1
4 1


Output

4 3 2 1 0

Note

In the example test case the vertex 1 controls the vertex 3, the vertex 3 controls the vertex 5 (note that is doesn't mean the vertex 1 controls the vertex 5).
import java.io.*;
import java.util.ArrayList;
import java.util.List;
import java.util.Scanner;
import java.util.StringTokenizer;

public class Main {

    static int n;
    static Node[] a;
    static long[] sum;
    static int[] path;

    public static void main(String[] args) {
        Reader in = new Reader(new InputStreamReader(System.in));
        PrintWriter out = new PrintWriter(new OutputStreamWriter(System.out));

        n = in.nextInt();
        a = new Node[n + 1];
        sum = new long[n + 2];
        path = new int[n + 2];
        a[0] = new Node();
        for (int i = 1; i <= n; i++) {
            a[i] = new Node();
            a[i].value = in.nextInt();
        }
        for (int i = 2; i <= n; i++) {
            int p = in.nextInt();
            long w = in.nextLong();
            a[p].next.add(new Path(i, w));
        }

        dfs(1, 1);

        for (int i = 1; i <= n; i++) {
            out.print(a[i].ans + " ");
        }

        out.flush();
        out.close();
    }

    private static void dfs(int now, int deep) {
        path[deep] = now;

        int nextDeep = deep + 1;
        int father = path[deep - 1];

        int left = 1;
        int right = deep;
        while (left != right) {
            int mid = (left + right) >> 1;
            long midValue = sum[deep] - sum[mid];
            if (a[now].value > midValue) {
                right = mid;
            } else if (a[now].value < midValue) {
                left = mid + 1;
            } else {
                left = right = mid;
            }
        }
        int aimPos = path[left - 1];
        a[aimPos].ans--;
        a[father].ans++;

        for (Path path : a[now].next) {
            int next = path.p;
            sum[nextDeep] = sum[deep] + path.w;
            dfs(next, nextDeep);
        }

        a[father].ans += a[now].ans;
    }

    static class Node {
        long value;
        int ans = 0;
        List<Path> next = new ArrayList<>();
    }

    static class Path {
        int p;
        long w;

        Path(int p, long w) {
            this.p = p;
            this.w = w;
        }
    }

    static class Reader {
        BufferedReader reader;
        StringTokenizer st;

        public Reader(InputStreamReader stream) {
            reader = new BufferedReader(stream);
            st = null;
        }

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

        public int nextInt() {
            return Integer.parseInt(next());
        }
        public String nextLine() throws IOException{
            return reader.readLine();
        }
        public long nextLong(){
            return Long.parseLong(next());
        }
        public double nextDouble(){
            return Double.parseDouble(next());
        }

    }
}