Problem Statement

For an integer $N$, we will choose a permutation $\\{P_1, P_2, ..., P_N\\}$ of $\\{1, 2, ..., N\\}$.

Then, for each $i=1,2,...,N$, let $M_i$ be the remainder when $i$ is divided by $P_i$.

Find the maximum possible value of $M_1 + M_2 + \\cdots + M_N$.

Constraints

• $N$ is an integer satisfying $1 \\leq N \\leq 10^9$.

Input

Input is given from Standard Input in the following format:

$N$

Output

Print the maximum possible value of $M_1 + M_2 + \\cdots + M_N$.

Sample Input 1

2

Sample Output 1

1

When the permutation $\\{P_1, P_2\\} = \\{2, 1\\}$ is chosen, $M_1 + M_2 = 1 + 0 = 1$.

Sample Input 2

13

Sample Output 2

78

Sample Input 3

1

Sample Output 3

0