Count the Pairs

This code counts pairs of positions:

count = 0
for i in range(n):
    for j in range(i + 1, n):
        count += 1

Implement count_pairs(n) so it returns the final value of count.

n can be huge, so you cannot run the loops. Work the number out from the shape of the loops.

Examples

Example 1

Input:

count_pairs(4)

Output:

6

The pairs are (0,1) (0,2) (0,3) (1,2) (1,3) (2,3).

Example 2

Input:

count_pairs(1)

Output:

0

No pair fits.

Constraints

• 0 <= n <= 10**12
• Your function must answer instantly, even for the largest n.