Paternity Testing

You have a tree consisting of $n$ nodes labeled from $1$ to $n$. The tree is rooted at node $1$. A function $cnt(v, l, r)$ is defined as the number of nodes in a subtree of node $v$, that have indices from $l$ to $r$ inclusive. You are required to answer $q$ queries. The query is represented by a pair $(l\_i, r\_i)$. The answer to the query is a sum $\sum\_{l \le i \le r} cnt(i, l, r)$.

First line contains an integer $n$ --- the number of nodes in the tree.

Next $n - 1$ lines indicate ancestors of the nodes in the tree. Each $i$-th line of those $n - 1$ lines contains the ancestor's index for the $i + 1$-th node in the tree.

The following line contains a single integer $q$ --- the number of queries to be answered.

Each of the next $q$ lines contains two numbers $u\_i$ and $v\_i$ --- encoded queries.

Print $q$ lines. The $i$-th line should contain the answer to the query $(l\_i, r\_i)$.

• $1 \le n \le 50000$
• $1 \le q \le 50000$
• $0 \le u\_i, v\_i \le 10^9$

Let $ans\_i$ be the answer to the $i$-th query ($ans\_0 = 0$). Then, the parameters of the  $i$-th query are:

• $x\_i = 1 + ((u\_i \oplus ans\_{i-1}) \mod n)$
• $y\_i = 1 + ((v\_i \oplus ans\_{i-1}) \mod n)$
• $l\_i = min(x\_i, y\_i)$
• $r\_i = max(x\_i, y\_i)$