You are given a rooted tree with $n$ nodes. The nodes are labeled
$1$ to $n$, and node $1$ is the root. Each node 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
satisfy this Heap Property: For every node pair $i$,$j$ in the subset, if node
$i$ is an ancestor of node
$j$ in the tree, then
$v_ i > v_ j$. Note
that equality is not allowed.
Figure out the maximum number of nodes you can choose to
form such a subset. The subset does not have to form a
subtree.
Input
Each input will consist of a single test case. Note that
your program may be run multiple times on different inputs. The
first line of input will contain a single integer $n$ ($1
\le n \le 2 \cdot 10^5$), which is the number of nodes
in the tree. The nodes are numbered $1$ to $n$.
Each of the next $n$
lines will describe the nodes, in order from $i=1$ to $n$. They will each contain two
integers $v_ i$ and
$p_ i$, where $v_ i$ ($0 \le v_ i \le 10^9$) is the value in
the node, and $p_ i$
($0 \le p_ i < i$) is
the index of its parent. Every node’s index will be strictly
greater than its parent node’s index. Only node 1, the root,
will have $p_1=0$, since
it has no parent. For all other nodes ($i=2, 3, \ldots , n$), $1 \le p_ i < i$.
Output
Output a single integer representing the number of nodes in
the largest subset satisfying the Heap Property.
Sample Input 1 
Sample Output 1 
5
3 0
3 1
3 2
3 3
3 4

1

Sample Input 2 
Sample Output 2 
5
4 0
3 1
2 2
1 3
0 4

5

Sample Input 3 
Sample Output 3 
6
3 0
1 1
2 1
3 1
4 1
5 1

5

Sample Input 4 
Sample Output 4 
11
7 0
8 1
5 1
5 2
4 2
3 2
6 3
6 3
10 4
9 4
11 4

7
