Problem H. How many iterations? ≡

Statement

Young programmer Vasya is learning the beginnings of the algorithm complexity theory. For starters, he wants to be able to quickly estimate the number of iterations of nested loops. As a first example, he wrote the following code:

long long f(int n)
{
   long long ans = 0;
   for (int i = 1; i <= n; i++) 
      for (int j = i+1; j <= n; j++)
         for (int k = j+1; k <= n; k++)
            ans++;
   return ans;
}

function f(n: integer): int64;
var i, j, k: integer;
begin
   result := 0;
   for i := 1 to n do 
      for j := i+1 to n do 
         for k := j+1 to n do
            inc(result);
end;

Using your knowledge of the subject, help Vasya calculate f(n) for given n.

Input file format

Input file contains an integer n.

Output file format

Output file must contain a single integer — f(n).

Constraints

1 ≤ n ≤ 10⁶

Sample tests

1

0

1000

166167000