Teemu is an assistant at the course CS-A1150 - Databases. One of the tasks on the course is to create a family database.

A family database consists of $n$ entries numbered $1, 2, 3, \ldots n$ each representing a family member. Each entry $i$ has a single number $p_i$ pointing to the parent of the entry.

As we all know nobody can be their own ancestor. Still many of the students have managed to create databases with cycles. A cycle is a set of $k$ nodes $\{a_1, a_2, \dotsc, a_k\}$ for some $k\ge 2$ such that $a_{i+1}$ is the parent of $a_i$ for all $i = 1, 2, \dotsc, k-1$ and finally $a_1$ is the parent of $a_k$.

As the assistant of the course, Teemu needs your help to count cycles in the students' databases.

Input

The first line contains a single integer, $n$, the number of entries in the database.

The second line contains $n$ integers, $p_1, p_2, \ldots, p_n$. We have $1 \le p_i \le n$ and $p_i \ne i$ for all $i$.

Output

Output a single integer, the number of cycles in the given database.

Limits

• $2 \le n \le 10^6$

Example 1

Input:

16
2 3 4 5 6 1 4 7 7 4 12 11 14 15 13 13

Output:

3

Explanation: Cycles in the input are $\{1, 2, 3, 4, 5, 6\}$, $\{11, 12\}$ and $\{13, 14, 15\}$.