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: Accepted)

using System;
using System.Collections.Generic;
using System.Text;

namespace AtTest.C_Challenge
{
    class ABC_056
    {
        static void Main(string[] args)
        {
            Method(args);
            Console.ReadLine();
        }

        static void Method(string[] args)
        {
            long x = long.Parse(Console.ReadLine());
            long min = 0, max = 100000;
            while (max - min != 1)
            {
                long mid = (min + max) / 2;
                long sum = (mid * (mid + 1)) / 2;
                long sum2 = ((mid - 1) * mid) / 2;
                //Console.WriteLine(max);
                //Console.WriteLine(mid);
                //Console.WriteLine(min);
                if (sum2 < x && x <= sum)
                {
                    Console.WriteLine(mid);
                    return;
                }
                else if (x <= sum2)
                {
                    max = mid;
                }
                else if (sum < x)
                {
                    min = mid;
                }
            }
            Console.WriteLine(min);
        }
    }
}