Problem:
Score : 100 points

Problem Statement

There are N children in AtCoder Kindergarten. Mr. Evi will arrange the children in a line, then give 1 candy to the first child in the line, 2 candies to the second child, ..., N candies to the N-th child. How many candies will be necessary in total?

Constraints

1≦N≦100

Input

The input is given from Standard Input in the following format:

N

Output

Print the necessary number of candies in total.

Sample Input 1

3

Sample Output 1

6

The answer is 1+2+3=6.

Sample Input 2

10

Sample Output 2

55

The sum of the integers from 1 to 10 is 55.

Sample Input 3

1

Sample Output 3

1

Only one child. The answer is 1 in this case.

Solution in PHP7 (7.0.15) (judge verdict: Wrong Answer)

<?php
    
    function fact($a) {
        if ($a > 1) {
            return $a*fact($a-1);
        } else {
            return 1;
        }
        
    }
    
    function pattern($a, $b) {
        return fact($a+$b)/fact($a)/fact($b);
    }
    
    fscanf(STDIN, "%d %d %d %d", $h, $w, $a, $b);
    
    $all = pattern($h-1, $w-1);
    $unable = 0;
    
    for ($i = 0; $i < $b; $i++) {
        $unable += pattern($a-1, $w-1-$i)*pattern($h-$a-1, $i);
    }
    
    
    echo $all - $unable%(10**9+7);

    
?>