Problem Statement

There is a directed graph with N vertices numbered 1 to N and N edges.
The out-degree of every vertex is 1, and the edge from vertex i points to vertex a_i.
Count the number of pairs of vertices (u, v) such that vertex v is reachable from vertex u.
Here, vertex v is reachable from vertex u if there exists a sequence of vertices $w_0, w_1, \dots, w_K$ of length K+1 that satisfies the following conditions. In particular, if u = v, it is always reachable.

• w_0 = u.
• w_K = v.
• For every $0 \leq i \lt K,$ there is an edge from vertex w_i to vertex w_{i+1}.

Input

The input is given from Standard Input in the following format:
N
$a_1 a_2 \dots a_N$

Output

Print the number of pairs of vertices (u, v) such that vertex v is reachable from vertex u.

Constraints

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

Sample Input 1

4
2 1 1 4

Sample Output 1

8

The vertices reachable from vertex 1 are vertices 1, 2.
The vertices reachable from vertex 2 are vertices 1, 2.
The vertices reachable from vertex 3 are vertices 1, 2, 3.
The vertex reachable from vertex 4 is vertex 4.
Therefore, the number of pairs of vertices (u, v) such that vertex v is reachable from vertex u is 8.
Note that the edge from vertex 4 is a self-loop, that is, it points to vertex 4 itself.

Sample Input 2

5
2 4 3 1 2

Sample Output 2

14

Sample Input 3

10
6 10 4 1 5 9 8 6 5 1

Sample Output 3

41

见题面 Input 部分

见题面 Output 部分