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.Linq;

namespace ABC056C
{
    class Program
    {
        static void Main(string[] args)
        {
            new Solver().Solve();
        }
    }

    class Solver
    {
        int X;

        public void Solve()
        {
            // キャスト前の値以上の整数なら条件を満たす.
            int ans = (int)((-1.0 + Math.Sqrt(1 + 8 * X)) / 2.0);

            // 条件を満たすときtrueを返す.
            Func<int, bool> check = t => t * t + t - 2 * X >= 0;
            if (!check(ans))
            {
                ans++;
            }
            Console.WriteLine(ans);
        }

        public Solver()
        {
            X = ReadInt();
        }

        static String ReadString() { return Console.ReadLine(); }
        static int ReadInt() { return int.Parse(Console.ReadLine()); }
        static long ReadLong() { return long.Parse(Console.ReadLine()); }
        static double ReadDouble() { return double.Parse(Console.ReadLine()); }
        static String[] ReadStringArray() { return Console.ReadLine().Split(' '); }
        static int[] ReadIntArray() { return Console.ReadLine().Split(' ').Select(e => int.Parse(e)).ToArray(); }
        static long[] ReadLongArray() { return Console.ReadLine().Split(' ').Select(e => long.Parse(e)).ToArray(); }
        static double[] ReadDoubleArray() { return Console.ReadLine().Split(' ').Select(e => double.Parse(e)).ToArray(); }
    }

}