Three Nested Loops

This code has three loops that each start where the previous one is:

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

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

Examples

Example 1

Input:

count_triple_loop(3)

Output:

10

The triples are (0,0,0) (0,0,1) (0,0,2) (0,1,1) (0,1,2) (0,2,2) (1,1,1) (1,1,2) (1,2,2) (2,2,2).

Example 2

Input:

count_triple_loop(5)

Output:

35

Constraints

• 0 <= n <= 10**6