Score : $400$ points

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 $M_1 + M_2 + \cdots + M_N$.

2

1

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

13

78

1

0