The cows have once again tried to form a startup company, failing to remember from past experience t
hat cows make terrible managers!The cows, conveniently numbered 1…N1…N (1≤N≤100,000), organize t
he company as a tree, with cow 1 as the president (the root of the tree). Each cow except the presid
ent has a single manager (its "parent" in the tree). Each cow ii has a distinct proficiency rating,
p(i), which describes how good she is at her job. If cow ii is an ancestor (e.g., a manager of a man
ager of a manager) of cow jj, then we say jj is a subordinate of ii.
Unfortunately, the cows find that it is often the case that a manager has less proficiency than seve
ral of her subordinates, in which case the manager should consider promoting some of her subordinate
s. Your task is to help the cows figure out when this is happening. For each cow ii in the company,
please count the number of subordinates jj where p(j)>p(i).
The first line of input contains N
The next N lines of input contain the proficiency ratings p(1)…p(N)
for the cows. Each is a distinct integer in the range 1…1,000,000,000
The next N-1 lines describe the manager (parent) for cows 2…N
Recall that cow 1 has no manager, being the president.
Please print N lines of output. The ith line of output should tell the number of
subordinates of cow ii with higher proficiency than cow i.