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Contest: Task: Related: TaskB TaskD

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.

Sample Input 1

4
1 3 2 4

Sample Output 1

2

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

Sample Input 2

10
5 8 2 2 1 6 7 2 9 10

Sample Output 2

8