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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.BufferedWriter;
import java.util.InputMismatchException;
import java.util.HashMap;
import java.io.IOException;
import java.util.ArrayList;
import java.util.List;
import java.util.Map;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.io.InputStream;

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

    static class TaskD {
        private int n;
        private long[] a;
        private List<IntLongPair>[] g;
        private int[] ans2;
        private Map<Integer, Integer> counter = new HashMap<>();
        private FenwickTree tree;
        private int[] ans;

        public void solve(int testNumber, InputReader in, OutputWriter out) {
            input(in);

            ans = new int[n];
            tree = new FenwickTree(n + 5);
            dfs(0, 0);
//        out.print(ans);

            ans2 = new int[n];
            dfs2(0, 0);
            out.print(ans2);
        }

        private int dfs2(int v, int depth) {
            int cnt = 0;
            for (IntLongPair e : g[v]) {
                cnt += dfs2(e.first, depth + 1);
            }
            ans2[v] = cnt;
            if (ans[v] != 0) {
                counter.merge(depth - ans[v], 1, Integer::sum);
                cnt++;
            }
            if (counter.containsKey(depth)) {
                cnt -= counter.remove(depth);
            }
            return cnt;
        }

        private void dfs(int v, int depth) {
            int l = 0;
            int r = depth + 1;
            while (r - l > 1) {
                int m = (r + l) / 2;
                long sum = tree.get(depth - m + 1, depth);
                if (sum > a[v]) {
                    r = m;
                } else {
                    l = m;
                }
            }
            ans[v] = l;
            for (IntLongPair e : g[v]) {
                depth++;
                tree.add(depth, e.second);
                dfs(e.first, depth);
                tree.add(depth, -e.second);
                depth--;
            }
        }

        private void input(InputReader in) {
            n = in.readInt();
            a = IOUtils.readLongArray(in, n);
            g = new List[n];
            for (int i = 0; i < n; i++) {
                g[i] = new ArrayList<>();
            }
            for (int i = 1; i < n; i++) {
                int p = in.readInt() - 1;
                long w = in.readLong();
                g[p].add(IntLongPair.makePair(i, w));
            }
        }

    }

    static class FenwickTree {
        private final long[] value;

        public FenwickTree(int size) {
            value = new long[size];
        }

        public long get(int from, int to) {
            return get(to) - get(from - 1);
        }

        private long get(int to) {
            to = Math.min(to, value.length - 1);
            long result = 0;
            while (to >= 0) {
                result += value[to];
                to = (to & (to + 1)) - 1;
            }
            return result;
        }

        public void add(int at, long value) {
            while (at < this.value.length) {
                this.value[at] += value;
                at = at | (at + 1);
            }
        }

    }

    static class IOUtils {
        public static long[] readLongArray(InputReader in, int size) {
            long[] array = new long[size];
            for (int i = 0; i < size; i++) {
                array[i] = in.readLong();
            }
            return array;
        }

    }

    static class IntLongPair implements Comparable<IntLongPair> {
        public final int first;
        public final long second;

        public static IntLongPair makePair(int first, long second) {
            return new IntLongPair(first, second);
        }

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


        public boolean equals(Object o) {
            if (this == o) {
                return true;
            }
            if (o == null || getClass() != o.getClass()) {
                return false;
            }

            IntLongPair pair = (IntLongPair) o;

            return first == pair.first && second == pair.second;
        }


        public int hashCode() {
            int result = Integer.hashCode(first);
            result = 31 * result + Long.hashCode(second);
            return result;
        }


        public String toString() {
            return "(" + first + "," + second + ")";
        }

        @SuppressWarnings({"unchecked"})
        public int compareTo(IntLongPair o) {
            int value = Integer.compare(first, o.first);
            if (value != 0) {
                return value;
            }
            return Long.compare(second, o.second);
        }

    }

    static class OutputWriter {
        private final PrintWriter writer;

        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }

        public void print(int[] array) {
            for (int i = 0; i < array.length; i++) {
                if (i != 0) {
                    writer.print(' ');
                }
                writer.print(array[i]);
            }
        }

        public void close() {
            writer.close();
        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private InputReader.SpaceCharFilter filter;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (numChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

        public int readInt() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public long readLong() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }
}

