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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.*;

/**
 * @author andrey
 */
public class D {

    private static class Pair implements Comparable {

        long dist;
        int node;

        Pair(long dist, int node) {
            this.dist = dist;
            this.node = node;
        }


        @Override
        public int compareTo(Object o) {
            final Pair other = (Pair) o;

            if (dist > other.dist) {
                return 1;
            } else {
                if (dist < other.dist) {
                    return -1;
                }
                return 0;
            }
        }
    }

    private static long[] nodeNums;
    private static List<Integer>[] children;
    private static long[] parentWeight;
    private static int[] parent;
    private static int[] dominates;

    private static void dfs(int curNode, long fromRoot, TreeSet<Pair> path) {
        path.add(new Pair(fromRoot, curNode));

        Pair res = path.ceiling(new Pair(fromRoot - nodeNums[curNode], 0));
        //System.out.println("" + curNode + " | " + res.dist + " " + res.node);
        dominates[parent[res.node]]--;
        dominates[parent[curNode]]++;

        if (!children[curNode].isEmpty()) {
            for (Integer child : children[curNode]) {
                dfs(child, fromRoot + parentWeight[child], path);
                dominates[curNode] += dominates[child];
            }
        }

        path.remove(new Pair(fromRoot, curNode));
    }

    private static StringTokenizer tok;
    private static BufferedReader reader;

    private static String nextToken() throws IOException {
        while (tok == null || !tok.hasMoreTokens()) {
            tok = new StringTokenizer(reader.readLine());
        }
        return tok.nextToken();
    }

    private static int nextInteger() throws IOException {
        return Integer.parseInt(nextToken());
    }

    private static long nextLong() throws IOException {
        return Integer.parseInt(nextToken());
    }

    public static void main(String[] args) throws IOException {
        reader = new BufferedReader(new InputStreamReader(System.in));

        final int n = nextInteger();
        nodeNums = new long[n];
        parentWeight = new long[n];
        children = new List[n];
        dominates = new int[n + 1];
        parent = new int[n];

        for (int i = 0; i < n; i++) {
            nodeNums[i] = nextInteger();
            children[i] = new ArrayList<>();
        }

        parent[0] = n;
        for (int i = 1; i < n; i++) {
            int p = nextInteger();
            long w = nextLong();
            parentWeight[i] = w;
            children[p - 1].add(i);
            parent[i] = p - 1;
        }

        dfs(0, 0, new TreeSet<>());

        for(int i = 0; i < n; i++) {
            System.out.print((i == 0 ? "" : " ") + dominates[i]);
        }
    }

}
