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 a_{i}. 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) ≤ a_{u}.

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 ≤ 2·10^5).

The second line contains n integers a_1, a_2, ..., a_{n} (1 ≤ a_{i} ≤ 10^9) — the integers written in the vertices.

The next (n - 1) lines contain two integers each. The i-th of these lines contains integers p_{i} and w_{i} (1 ≤ p_{i} ≤ n, 1 ≤ w_{i} ≤ 10^9) — 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).

Difficulty: competition

Starter code:

Solutions:
import sys
import threading
from bisect import bisect_left

n   = int(input())
a   = list(map(int, input().split()))
e   = {}
g   = [[] for i in range(n)]
d   = [0]*(n+5)
ans = [0]*n
p   = [0]*(n+5)

for i in range(n-1):
        c, w = map(int, input().split())
        c-= 1
        g[c].append(i+1)
        e[i+1] = w

def dfs(i, h):
    nonlocal ans, a, e, g, d, p
    p[h]=0
    for j in g[i]:
        d[h+1] = d[h]+e[j] 
        dfs(j, h+1)
    x = bisect_left(d, d[h]-a[i], 0, h+1)
    #print(x-1, i, h, d[h], d[h], a[i])
    if x>=0:
        p[x-1]-=1
    p[h-1]+=p[h]+1
    ans[i]=p[h]



def solve():  
    nonlocal ans
    dfs(0, 0)
    print(' '.join(map(str, ans)))

max_recur_size = 10**5*2 + 1000
max_stack_size = max_recur_size*500
sys.setrecursionlimit(max_recur_size)
threading.stack_size(max_stack_size)
thread = threading.Thread(target=solve)
thread.start()