Score : $300$ points

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.

Input

Input is given from Standard Input in the following format:

$N$

$a_1$ $\ldots$ $a_N$

Output

Print the answer.

4
1 3 2 4

2

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

10
5 8 2 2 1 6 7 2 9 10

8