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;
using System.Collections.Generic;
using System.Globalization;
using System.IO;
using System.Linq;
using System.Runtime.Remoting.Contexts;
class Simple {
    private int N;
    void Solve() {
        //input
        N = io.Int;
        //cal
        Func <int, int> f = (n) => n * (2 + (n - 1)) / 2;
        for(int i = 1; ; ++i) {
            if(f(i) >= N) {
                //ret
                Console.WriteLine(i);
                return;                
            }
        }
    }
    SimpleIO io = new SimpleIO();
    public static void Main(string[] args) => new Simple().Stream();
    private void Stream() {
        //var exStdIn = new System.IO.StreamReader("stdin.txt");
        //System.Console.SetIn(exStdIn);
        Solve();
        io.Flush();
    }
}
class SimpleIO {
    string[] _nextBuffer;
    int _bufferCnt;
    char[] cs = new char[] {' ', '"', ','};
    StreamWriter sw = new StreamWriter(Console.OpenStandardOutput()) {AutoFlush = false};
    public SimpleIO() {
        _nextBuffer = new string[0];
        _bufferCnt = 0;
        Console.SetOut(sw);
    }
    public string Next() {
        if(_bufferCnt < _nextBuffer.Length) return _nextBuffer[_bufferCnt++];
        var st = Console.ReadLine();
        while(st == "") st = Console.ReadLine();
        if(st != null) _nextBuffer = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
        else st = "";
        _bufferCnt = 0;
        return _nextBuffer[_bufferCnt++];
    }
    public string String => Next();
    public char Char => char.Parse(String);
    public int Int => int.Parse(String);
    public long Long => long.Parse(String);
    public double Double => double.Parse(String);
    public void Flush() { Console.Out.Flush(); }
}
static class NumericEx {
    public static string pad0 <T>(this T v, int n) { return v.ToString().PadLeft(n, '0'); }
    public static double RoundOff(this double v, int n) { return Math.Round(v, n - 1, MidpointRounding.AwayFromZero); }
    public static bool Odd(this int v) { return v % 2 != 0; }
    public static bool Odd(this long v) { return v % 2 != 0; }
    public static void REP(this int v, Action <int> act) {
        for(int i = 0; i < v; ++i) act(i);
    }
    public static void REPR(this int v, Action <int> act) {
        for(int i = v - 1; i >= 0; --i) act(i);
    }
}