p02924 AtCoder Beginner Contest 139 - 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
```python
n = int(input())

m = (n-1)*n//2

print(m)
```