DFS——CodeForces740DAlyona and a tree

Posted 2020-10-01 GGBeng

一、题目回顾

题目链接：Alyona and a tree

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 thatv controls u.

 

Input

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

The second line contains n integers a₁,?a₂,?...,?a_n (1?≤?a_i?≤?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?≤?p_i?≤?n, 1?≤?w_i?≤?10⁹) — the parent of the (i?+?1)-th vertex in the tree and the number written on the edge between p_i 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).

题意：对于两个点，如果dis(u,v)<=val(v)且v是u的子孙，则称u掌控v，现在求每个结点掌控点的个数。

二、解题思路