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 $M_1 + M_2 + \cdots + M_N$.

Input

Input is given from Standard Input in the following format:
N

Output

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

Constraints

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

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

见题面 Input 部分

见题面 Output 部分