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;
using System.Collections.Generic;
using System.Diagnostics;
using System.IO;
using System.Linq;

namespace Codeforces
{
	internal class Template
	{
		private void Solve()
		{
			var x = cin.NextLong();
			var queue = new Queue<Tuple<int, int>>();
			queue.Enqueue(Tuple.Create(0, 0));
			while (queue.Any())
			{
				var front = queue.Dequeue();
				if (front.Item1 == x)
				{
					Console.WriteLine(front.Item2);
					return;
				}
				queue.Enqueue(Tuple.Create(front.Item1 - front.Item2 - 1, front.Item2 + 1));
				queue.Enqueue(Tuple.Create(front.Item1 + front.Item2 + 1, front.Item2 + 1));
			}
		}

		private static readonly Scanner cin = new Scanner();

		private static void Main()
		{
#if DEBUG
			var inputText = File.ReadAllText(@"..\..\input.txt");
			var testCases = inputText.Split(new[] { "input" }, StringSplitOptions.RemoveEmptyEntries);
			var consoleOut = Console.Out;
			for (var i = 0; i < testCases.Length; i++)
			{
				var parts = testCases[i].Split(new[] { "output" }, StringSplitOptions.RemoveEmptyEntries);
				Console.SetIn(new StringReader(parts[0].Trim()));
				var stringWriter = new StringWriter();
				Console.SetOut(stringWriter);
				var sw = Stopwatch.StartNew();
				new Template().Solve();
				sw.Stop();
				var output = stringWriter.ToString();

				Console.SetOut(consoleOut);
				var color = ConsoleColor.Green;
				var status = "Passed";
				if (parts[1].Trim() != output.Trim())
				{
					color = ConsoleColor.Red;
					status = "Failed";
				}
				Console.ForegroundColor = color;
				Console.WriteLine("Test {0} {1} in {2}ms", i + 1, status, sw.ElapsedMilliseconds);
			}
			Console.ReadLine();
			Console.ReadKey();
#else
			new Template().Solve();
			Console.ReadLine();
#endif
		}
	}

	internal class Scanner
	{
		private string[] s = new string[0];
		private int i;
		private readonly char[] cs = { ' ' };

		public string NextString()
		{
			if (i < s.Length) return s[i++];
			var line = Console.ReadLine() ?? string.Empty;
			s = line.Split(cs, StringSplitOptions.RemoveEmptyEntries);
			i = 1;
			return s.First();
		}

		public double NextDouble()
		{
			return double.Parse(NextString());
		}

		public int NextInt()
		{
			return int.Parse(NextString());
		}

		public long NextLong()
		{
			return long.Parse(NextString());
		}
	}
}