Description

Input

The first line contains a single integer $n$ ($2 \le n \le 10^5$) — the number of heart-shaped cards.

The second line contains $n - 1$ integers $p_2, p_3, \dots, p_n$ ($1 \le p_i < i$) describing which card that each card hangs onto.

Output

Print a single integer — the maximum length of the longest non-decreasing subsequence of $s$ at the end if Pak Chanek does all the steps optimally.

6
1 2 1 4 2

4

2
1

2

Note

The following is the structure of the cards in the first example.

Pak Chanek can choose the permutation $a = [1, 5, 4, 3, 2, 6]$.

Let $w_i$ be the number written on card $i$. Initially, $w_i = a_i$. Pak Chanek can do the following operations in order:

1. Select card $5$. Append $w_5 = 2$ to the end of $s$. As $w_4 > w_5$, the value of $w_4$ becomes $2$. Remove card $5$. After this operation, $s = [2]$.
2. Select card $6$. Append $w_6 = 6$ to the end of $s$. As $w_2 \leq w_6$, the value of $w_2$ is left unchanged. Remove card $6$. After this operation, $s = [2, 6]$.
3. Select card $4$. Append $w_4 = 2$ to the end of $s$. As $w_1 \leq w_4$, the value of $w_1$ is left unchanged. Remove card $4$. After this operation, $s = [2, 6, 2]$.
4. Select card $3$. Append $w_3 = 4$ to the end of $s$. As $w_2 > w_3$, the value of $w_2$ becomes $4$. Remove card $3$. After this operation, $s = [2, 6, 2, 4]$.
5. Select card $2$. Append $w_2 = 4$ to the end of $s$. As $w_1 \leq w_2$, the value of $w_1$ is left unchanged. Remove card $2$. After this operation, $s = [2, 6, 2, 4, 4]$.
6. Select card $1$. Append $w_1 = 1$ to the end of $s$. Remove card $1$. After this operation, $s = [2, 6, 2, 4, 4, 1]$.

One of the longest non-decreasing subsequences of $s = [2, 6, 2, 4, 4, 1]$ is $[2, 2, 4, 4]$. Thus, the length of the longest non-decreasing subsequence of $s$ is $4$. It can be proven that this is indeed the maximum possible length.