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 Scala (2.11.7) (judge verdict: Accepted)

import scala.annotation.tailrec
import scala.io.{StdIn => in}

object Main extends App {

  def calc(num:Int):Int = {
    @tailrec
    def rec(acc:Int, cnt:Int):Int = {
      val fact = acc + cnt
      if(fact >= num) cnt
      else rec(fact, cnt+1)
    }
    rec(0,1)
  }

  val n =in.readInt
  val ans = calc(n)
  println(ans)
}