Polycarpus got hold of a family relationship tree. The tree describes family relationships of n people, numbered 1 through n. Each person in the tree has no more than one parent.
Let's call person a a 1-ancestor of person b, if a is the parent of b.
Let's call person a a k-ancestor (k>1) of person b, if person b has a 1-ancestor, and a is a (k-1)-ancestor of b's 1-ancestor.
Family relationships don't form cycles in the found tree. In other words, there is no person who is his own ancestor, directly or indirectly (that is, who is an x-ancestor for himself, for some x, x>0).
Let's call two people x and y (x≠y) p-th cousins (p>0), if there is person z, who is a p-ancestor of x and a p-ancestor of y.
Polycarpus wonders how many counsins and what kinds of them everybody has. He took a piece of paper and wrote m pairs of integers vi, pi. Help him to calculate the number of pi-th cousins that person vi has, for each pair vi, pi.
The first input line contains a single integer n (1≤n≤105) − the number of people in the tree. The next line contains n space-separated integers r1,r2,...,rn, where ri (1≤ri≤n) is the number of person i's parent or 0, if person i has no parent. It is guaranteed that family relationships don't form cycles.
The third line contains a single number m (1≤m≤105) − the number of family relationship queries Polycarus has. Next m lines contain pairs of space-separated integers. The i-th line contains numbers vi, pi (1≤vi,pi≤n).
Print m space-separated integers − the answers to Polycarpus' queries. Print the answers to the queries in the order, in which the queries occur in the input.
6
0 1 1 0 4 4
7
1 1
1 2
2 1
2 2
4 1
5 1
6 1
0 0 1 0 0 1 1