Handshake Count

Source: Phước Hưng OJ

Version: Phuoc Hung OJ Extended

Problem Statement

Given $n$ people, every unordered pair of distinct people shakes hands exactly once. Count the total handshakes.

Input

One line containing integer $n$.

Output

Print the number of unordered pairs of distinct people.

Subtask

• Subtask 1 — 100 points: $0\le n\le10^9$.

Example

Input

4

Output

6

Explanation

For $n=4$, each of the six unordered pairs shakes hands once. The formula $4(4-1)/2=6$ gives the output 6.