Heaps from Trees

You are given a rooted tree with $n$ nodes. The nodes are labeled $1$ to $n$, and node $1$ is the root. Each node $i$ has a value $v_i$.

You would like to turn this tree into a heap. That is, you would like to choose the largest possible subset of nodes that satisfies the following heap property: for every pair of nodes $i, j$ in the subset, if node $i$ is an ancestor of node $j$ in the tree, then $v_i > v_j$.

Equality is not allowed. Find the maximum number of nodes such a subset can contain. The subset does not have to form a subtree.

The input consists of a single test case.

The first line contains a single integer $n$ ($1 \le n \le 2 \times 10^5$), the number of nodes in the tree. The nodes are numbered $1$ to $n$.

Each of the next $n$ lines describes one node, in order of node number. Line $i$ contains two integers $v_i$ and $p_i$, where $v_i$ ($0 \le v_i \le 10^9$) is the value of the node and $p_i$ ($0 \le p_i < i$) is the index of its parent. Every node's index is strictly greater than its parent's index. Only node $1$, the root, has $p_1 = 0$, since it has no parent. For every other node ($i = 2, \ldots, n$), $1 \le p_i < i$.

Print a single integer: the number of nodes in the largest subset that satisfies the heap property.