Problem Statement

You are given a sequence of N numbers: $A=(A_1,A_2,\ldots,A_N).$ Here, each $A_i (1\leq i\leq N) satisfies 1\leq A_i \leq N$.
Takahashi and Aoki will play N rounds of a game. For each $i=1,2,\ldots,N$, the i-th game will be played as follows.

• Aoki specifies a positive integer K_i.
• After knowing K_i Aoki has specified, Takahashi chooses an integer S_i between 1 and N, inclusive, and writes it on a blackboard.

• Repeat the following K_i times.

• Replace the integer x written on the blackboard with A_x.

If i is written on the blackboard after the K_i iterations, Takahashi wins the i-th round; otherwise, Aoki wins.
Here, K_i and S_i can be chosen independently for each $i=1,2,\ldots,N$.
Find the number of rounds Takahashi wins if both players play optimally to win.

Input

The input is given from Standard Input in the following format:
N
$A_1 A_2 \ldots A_N$

Output

Find the number of rounds Takahashi wins if both players play optimally to win.

Constraints

• $1\leq N\leq 2\times 10^5$
• $1\leq A_i\leq N$
• All values in the input are integers.

Sample Input 1

3
2 2 3

Sample Output 1

2

In the first round, if Aoki specifies K_1=2, Takahashi cannot win whichever option he chooses for S_1: 1, 2, or 3.
For example, if Takahashi writes S_1=1 on the initial blackboard, the two operations will change this number as follows: $1\to$ $2(=A_1), 2\to$ 2(=A_2). The final number on the blackboard will be $2(\neq 1)$, so Aoki wins.
On the other hand, in the second and third rounds, Takahashi can win by writing 2 and 3, respectively, on the initial blackboard, whatever value Aoki specifies as K_i.
Therefore, if both players play optimally to win, Takashi wins two rounds: the second and the third. Thus, you should print 2.

Sample Input 2

2
2 1

Sample Output 2

2

In the first round, Takahashi can win by writing 2 on the initial blackboard if K_1 specified by Aoki is odd, and 1 if it is even.
Similarly, there is a way for Takahashi to win the second round. Thus, Takahashi can win both rounds: the answer is 2.

见题面 Input 部分

见题面 Output 部分