[ABC262C] Min Max Pair

Problem Statement

You are given a sequence $a = (a_1, \dots, a_N)$ of length $N$ consisting of integers between $1$ and $N$.

Find the number of pairs of integers $i, j$ that satisfy all of the following conditions:

• $1 \leq i \lt j \leq N$
• $\min(a_i, a_j) = i$
• $\max(a_i, a_j) = j$

Constraints

• $2 \leq N \leq 5 \times 10^5$
• $1 \leq a_i \leq N \, (1 \leq i \leq N)$
• All values in input are integers.

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Input

Input is given from Standard Input in the following format:

$N$
$a_1$ $\ldots$ $a_N$

Output

Print the answer.

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Sample Input 1

4
1 3 2 4

Sample Output 1

2

$(i, j) = (1, 4), (2, 3)$ satisfy the conditions.

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Sample Input 2

10
5 8 2 2 1 6 7 2 9 10

其实对于合法的数对可以分成两种：$$a_i=i,a_j=j,i<j$$ $$a_i=j,a_j=i,i>j$$

对于第一种，统计有多少个 \(a_i=i\) ，设有 \(cnt\) 个，则答案为 \(\frac{cnt*(cnt-1)}{2}\)

对于第二种，如果\(a_{a_i}=i\)，答案增加1.

#include<cstdio>
const int N=5e5+5;
int n,a[N],cnt;
long long ans;
int main()
{
	scanf("%d",&n);
	for(int i=1;i<=n;i++)
	{
		scanf("%d",a+i);

		if(a[i]==i)
		{
			ans+=cnt;
			cnt++;
		}
		else if(a[a[i]]==i)
			++ans;
	}
	printf("%lld",ans);
}