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 Haskell (GHC 7.10.3) (judge verdict: Accepted)

import Control.Applicative ((<$>), (<*>))
import Control.Monad
import Data.List

main :: IO ()
main = do
  solve <$> getl read >>= print

solve :: Int -> Int
solve x = f [a .. b]
  where
    a = ceiling (sqrt (2 * fromIntegral x) - 1)
    b = floor (sqrt (2 * fromIntegral x) + 1)
    f (h:ts)
      | h * (h + 1) `div` 2 >= x = h
      | otherwise = f ts

getl :: (String -> a) -> IO a
getl f = f <$> getLine