Description

There are $n$ people. Some of them are civilians, and some of them are gangsters.

Now the civilians want to find all the gangsters, so each of the $n$ people has accused one person of being a gangster.

If a person is a civilian, they will accuse someone randomly. Otherwise, they will accuse a civilian.

Find the maximum possible number of gangsters.

Input Format

The first line contains an integer $n$.

The next $n$ lines each contain an integer $k$. Line $i$ means that person $i$ accused person $k$.

Output Format

Output a single integer: the maximum possible number of gangsters.

3
2
1
1

2

3
2
3
1

1

7
3
3
4
5
6
4
4

4

Hint

Sample Explanation

Explanation for Sample Input/Output 1

The gangsters can be person $2$ and person $3$.

Explanation for Sample Input/Output 2

The gangsters could be everyone, but then there can only be one gangster among them. If there is one more gangster, a gangster would accuse a gangster, which is not allowed.

Constraints

• For the testdata worth $40$ points, it is guaranteed that $n\le 15$.
• For the testdata worth $80$ points, it is guaranteed that $n\le 2\times 10^4$.
• For the testdata worth $100\%$ of the testdata, it is guaranteed that $1\le n\le 5\times 10^5$, $1\le k\le n$.

Note

The total score of this problem is $120$ points.

This problem is translated from Croatian Open Competition in Informatics 2014/2015 Contest #1 T4 MAFIJA.

Translated by ChatGPT 5