Score : $500$ points

Problem Statement

We have a rooted tree with $N$ vertices, numbered $1, 2, \dots, N$.

Vertex $1$ is the root, and the parent of Vertex $i \, (2 \leq i \leq N)$ is Vertex $P_i$.

You are given $Q$ queries. In the $i$-th query $(1 \leq i \leq Q)$, given integers $U_i$ and $D_i$, find the number of vertices $u$ that satisfy all of the following conditions:

• Vertex $U_i$ is in the shortest path from $u$ to the root (including the endpoints).
• There are exactly $D_i$ edges in the shortest path from $u$ to the root.

Constraints

• $2 \leq N \leq 2 \times 10^5$
• $1 \leq P_i < i$
• $1 \leq Q \leq 2 \times 10^5$
• $1 \leq U_i \leq N$
• $0 \leq D_i \leq N - 1$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$

$P_2$ $P_3$ $\ldots$ $P_N$

$Q$

$U_1$ $D_1$

$U_2$ $D_2$

$\vdots$

$U_Q$ $D_Q$

Output

Print $Q$ lines. The $i$-th line should contain the response to the $i$-th query.

7
1 1 2 2 4 2
4
1 2
7 2
4 1
5 5

3
1
0
0

In the $1$-st query, Vertices $4$, $5$, and $7$ satisfy the conditions. In the $2$-nd query, only Vertices $7$ satisfies the conditions. In the $3$-rd and $4$-th queries, no vertice satisfies the conditions.