Problem:
Score : 200 points

Problem Statement

There is a kangaroo at coordinate 0 on an infinite number line that runs from left to right, at time 0.
During the period between time i-1 and time i, the kangaroo can either stay at his position, or perform a jump of length exactly i to the left or to the right.
That is, if his coordinate at time i-1 is x, he can be at coordinate x-i, x or x+i at time i.
The kangaroo's nest is at coordinate X, and he wants to travel to coordinate X as fast as possible.
Find the earliest possible time to reach coordinate X.

Constraints

X is an integer.

1≤X≤10^9

Input

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

X

Output

Print the earliest possible time for the kangaroo to reach coordinate X.

Sample Input 1

6

Sample Output 1

3

The kangaroo can reach his nest at time 3 by jumping to the right three times, which is the earliest possible time.

Sample Input 2

2

Sample Output 2

2

He can reach his nest at time 2 by staying at his position during the first second, and jumping to the right at the next second.

Sample Input 3

11

Sample Output 3

5

Solution in Perl (v5.18.2) (judge verdict: Wrong Answer)

#!/usr/bin/perl
#= CPAN mocules =====================================================#
require 5.8.8;			# Perl 5.8.8以降
use strict;				# strictモード
use warnings;			# 警告有効
use utf8;				# UTF8モード ON

#= Global values ====================================================#
#= Local routines ===================================================#
sub main(){
	my $input = <>;
	chomp $input;

	my $pos = 0;
	foreach (1..14142){
		$pos += $_;
		if ($pos >= $input){
			printf("%d\n", $_);
			last;
		}
	}
	return 0;
}

#----- 実行 -----#
exit( main() );