Problem:
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.

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

Solution in C (GCC 5.4.1) (judge verdict: Runtime Error)

#include <stdio.h>
#include <stdlib.h>
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
typedef long long ll;

int main(void)
{
    ll ans = 0;
    int n;
    int *p;

    scanf("%d", &n);
    if (n == 2)
    {
        puts("1");
        return 0;
    }

    p = (int *)malloc(sizeof(int) * n);

    rep(i, n)
    {
        if (i == 0)
            p[i] = 1;
        else if (0 < i && i < n - 1)
            p[i] = i + 2;
        else
            p[i] = 2;
    }

    rep(i, n)
        ans += (i + 1) % p[i];

    printf("%lld\n", ans);

    free(p);
    return 0;
}