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