Problem Statement

You are given a rooted tree with $N$ vertices numbered from $1$ to $N$, rooted at vertex $1$. The parent of vertex $i$ is vertex $p_i$ ($2\leq i\leq N$).

Alice and Bob play a game using this tree as follows.

• Alice goes first, and Bob goes second. They take turns placing a stone, with a white side and a black side, on a vertex of the tree. Alice places the stone with the white side up, and Bob places the stone with the black side up.
• In each turn, a stone can only be placed on a vertex that does not have a stone on itself while all its descendants already have stones on them.
• When placing a stone on a vertex, all the stones on the descendants of that vertex are flipped over (the placed stone itself is not flipped).

The game ends when all vertices have stones. Alice's score is the number of stones with the white side up at this point.

Alice tries to maximize her score, and Bob tries to minimize Alice's score. If both play optimally, what will be Alice's score?

Constraints

• $2 \leq N \leq 2 \times 10^5$
• $1 \leq p_i < i$ $(2\leq i \leq N)$
• All input values are integers.
• The given graph is a tree.

Input

The input is given from Standard Input in the following format:

N
p_2 p_3 \ldots p_N

Output

Print the answer as an integer.