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: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.Linq;

public class Program {
	public static void Main() {
		new Calc().calc();
	}
	public class Calc {
		public Calc() { }
		public void calc() {
			int X = int.Parse(Console.ReadLine());
			var list = new List<node>();
			list.Add(new node(0, 0));
			int homeTime = 0;
			bool t = true;
			while (t) {
				var tmp = new List<node>();
				foreach (var item in list) {
					var check = item.makeChildren();
					if (check.FindIndex(_=>_.Node==X)!=-1) { t = false;break; }
					tmp.AddRange(check);
				}
				homeTime++;
				list = tmp;
			}
			Console.WriteLine(homeTime);
		}
		public class node {
			public int Node { get; set; }
			public int Time { get; set; }
			public node(int time,int node) {
				Node = node;Time = time;
			}
			public List<node> makeChildren() {
				var rt = new List<node>();
				rt.Add(new node(Time + 1, Node - (Time+1)));
				rt.Add(new node(Time + 1, Node + (Time+1)));
				rt.Add(new node(Time + 1, Node));
				return rt;
			}
		}
	}
}