ModSum

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.

Examples

Input

2

Output

1

Input

13

Output

78

Input

1

Output

0

inputFormat

Input

Input is given from Standard Input in the following format:

N

outputFormat

Output

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

Examples

Input

2

Output

1

Input

13

Output

78

Input

1

Output

0

样例

13

78