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.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.*;

/*
                   _ooOoo_
                  o8888888o
                  88" . "88
                  (| -_- |)
                  O\  =  /O
               ____/`---'\____
             .'  \\|     |//  `.
            /  \\|||  :  |||//  \
           /  _||||| -:- |||||-  \
           |   | \\\  -  /// |   |
           | \_|  ''\---/''  |   |
           \  .-\__  `-`  ___/-. /
         ___`. .'  /--.--\  `. . __
      ."" '<  `.___\_<|>_/___.'  >'"".
     | | :  `- \`.;`\ _ /`;.`/ - ` : | |
     \  \ `-.   \_ __\ /__ _/   .-` /  /
======`-.____`-.___\_____/___.-`____.-'======
                   `=---='
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
            pass System Test!
*/

public class D {
  private static class Task {
    class Edge {
      int to;
      long cost;
      Edge(int to, long cost) {
        this.to = to;
        this.cost = cost;
      }
    }

    ArrayList<Edge>[] graph;
    long[] a;
    FenwickTree bit;
    long[] ans;
    long[] imos;

    int dfs(int v, int d) {
      int x = 0;
      for (Edge edge : graph[v]) {
        int next = d + 1;
        bit.set(d, edge.cost);

        int ok = next;
        int ng = -1;
        while (ok - ng > 1) {
          int m = (ok + ng) / 2;
          long sum = bit.sum(m, next);//[m, next]
          if (sum <= a[edge.to]) {
            ok = m;
          } else {
            ng = m;
          }
        }
        int n = next - ok;
        int target = next - n;
        if (target <= next) imos[target]++;
        int y = dfs(edge.to, next);
        y -= imos[next];
        x += y;
        imos[next] = 0;
      }
      ans[v] = x;
      return x + 1;
    }

    void solve(FastScanner in, PrintWriter out) throws Exception {
      int N = in.nextInt();
      a = new long[N];
      for (int i = 0; i < N; i++) {
        a[i] = in.nextInt();
      }

      graph = new ArrayList[N];
      for (int i = 0; i < N; i++) {
        graph[i] = new ArrayList<>();
      }
      for (int i = 0; i < N - 1; i++) {
        int p = in.nextInt() - 1;
        int to = i + 1;
        long w = in.nextInt();
        graph[p].add(new Edge(to, w));
      }
      bit = new FenwickTree(N + 10);
      ans = new long[N];
      imos = new long[N + 10];
      dfs(0, 0);
      for (long a : ans) out.print(a + " ");
      out.println();
    }

    class FenwickTree {
      int N;
      long[] data;

      FenwickTree(int N) {
        this.N = N + 1;
        data = new long[N + 1];
      }

      void add(int k, long val) {
        for (int x = k; x < N; x |= x + 1) {
          data[x] += val;
        }
      }

      void set(int k, long val) {
        long now = get(k);
        long dv = val - now;
        add(k, dv);
      }

      // [0, k)
      long sum(int k) {
        if (k >= N) k = N - 1;
        long ret = 0;
        for (int x = k - 1; x >= 0; x = (x & (x + 1)) - 1) {
          ret += data[x];
        }
        return ret;
      }

      // [l, r)
      long sum(int l, int r) {
        if (l >= r) return 0;
        return sum(r) - sum(l);
      }

      long get(int k) {
        assert (0 <= k && k < N);
        return sum(k + 1) - sum(k);
      }

      int getAsSetOf(int w) {
        w++;
        if (w <= 0) return -1;
        int x = 0;
        int k = 1;
        while (k * 2 <= N) k *= 2;
        for (; k > 0; k /= 2) {
          if (x + k <= N && data[x + k - 1] < w) {
            w -= data[x + k - 1];
            x += k;
          }
        }
        return x;
      }
    }
  }

  /**
   * ここから下はテンプレートです。
   */
  public static void main(String[] args) throws Exception {
    OutputStream outputStream = System.out;
    FastScanner in = new FastScanner();
    PrintWriter out = new PrintWriter(outputStream);
    Task solver = new Task();
    solver.solve(in, out);
    out.close();
  }
  private static class FastScanner {
    private final InputStream in = System.in;
    private final byte[] buffer = new byte[1024];
    private int ptr = 0;
    private int bufferLength = 0;

    private boolean hasNextByte() {
      if (ptr < bufferLength) {
        return true;
      } else {
        ptr = 0;
        try {
          bufferLength = in.read(buffer);
        } catch (IOException e) {
          e.printStackTrace();
        }
        if (bufferLength <= 0) {
          return false;
        }
      }
      return true;
    }

    private int readByte() {
      if (hasNextByte()) return buffer[ptr++];
      else return -1;
    }

    private static boolean isPrintableChar(int c) {
      return 33 <= c && c <= 126;
    }

    private void skipUnprintable() {
      while (hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++;
    }

    boolean hasNext() {
      skipUnprintable();
      return hasNextByte();
    }

    public String next() {
      if (!hasNext()) throw new NoSuchElementException();
      StringBuilder sb = new StringBuilder();
      int b = readByte();
      while (isPrintableChar(b)) {
        sb.appendCodePoint(b);
        b = readByte();
      }
      return sb.toString();
    }

    long nextLong() {
      if (!hasNext()) throw new NoSuchElementException();
      long n = 0;
      boolean minus = false;
      int b = readByte();
      if (b == '-') {
        minus = true;
        b = readByte();
      }
      if (b < '0' || '9' < b) {
        throw new NumberFormatException();
      }
      while (true) {
        if ('0' <= b && b <= '9') {
          n *= 10;
          n += b - '0';
        } else if (b == -1 || !isPrintableChar(b)) {
          return minus ? -n : n;
        } else {
          throw new NumberFormatException();
        }
        b = readByte();
      }
    }

    double nextDouble() {
      return Double.parseDouble(next());
    }

    double[] nextDoubleArray(int n) {
      double[] array = new double[n];
      for (int i = 0; i < n; i++) {
        array[i] = nextDouble();
      }
      return array;
    }

    double[][] nextDoubleMap(int n, int m) {
      double[][] map = new double[n][];
      for (int i = 0; i < n; i++) {
        map[i] = nextDoubleArray(m);
      }
      return map;
    }

    public int nextInt() {
      return (int) nextLong();
    }

    public int[] nextIntArray(int n) {
      int[] array = new int[n];
      for (int i = 0; i < n; i++) array[i] = nextInt();
      return array;
    }

    public long[] nextLongArray(int n) {
      long[] array = new long[n];
      for (int i = 0; i < n; i++) array[i] = nextLong();
      return array;
    }

    public String[] nextStringArray(int n) {
      String[] array = new String[n];
      for (int i = 0; i < n; i++) array[i] = next();
      return array;
    }

    public char[][] nextCharMap(int n) {
      char[][] array = new char[n][];
      for (int i = 0; i < n; i++) array[i] = next().toCharArray();
      return array;
    }

    public int[][] nextIntMap(int n, int m) {
      int[][] map = new int[n][];
      for (int i = 0; i < n; i++) {
        map[i] = nextIntArray(m);
      }
      return map;
    }
  }
}