Gastronomic Event

The SWERC organizers want to hold a gastronomic event.

The event takes place in a building with $n$ rooms connected by $n - 1$ corridors, where each corridor joins two rooms and it is possible to go from any room to any other room.

In each room, you must set up a tasting of a typical Italian dish. There are $n$ dishes, rated from $1$ to $n$ by quality, where $n$ is the best rating. The $n$ dishes have distinct ratings.

Assign the $n$ dishes to the $n$ rooms so that the number of pleasing tours is maximal. A pleasing tour is a nonempty sequence of rooms such that:

• Each room in the sequence is connected to the next room in the sequence by a corridor.
• The dish ratings along the sequence are increasing.

If you assign the dishes optimally, what is the maximum number of pleasing tours?

The first line contains an integer $n$ ($2 \le n \le 1000000$), the number of rooms.

The second line contains $n - 1$ integers $p_2, p_3, \cdots, p_n$ ($1 \le p_i < i$). Each $p_i$ means there is a corridor between room $i$ and room $p_i$. It is guaranteed that the building lets you go from any room to any other room.

Print the maximum number of pleasing tours.