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 C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;

namespace ARC070
{
    public class Program
    {
        public static void Main(string[] args)
        {
            var X = int.Parse(Console.ReadLine());

            var p1 = 0;
            for (var i = 1;; i++)
            {
                if (X - (p1 + i) < i + 1) break;
                p1 += i;
            }

            var p2 = 0;
            for (var i = 0;; i++)
            {
                p2 += i;
                if (p2 - X >= i + 1) break;
            }

            Console.WriteLine(Math.Min(X - p1, p2 - X));
        }
    }
}