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: Wrong Answer)

import Control.Applicative
import Control.Monad
import Data.List

f :: Int -> [Int]
f x = unfoldr g (0, x)
  where
    g (i, 0) = Nothing
    g (i, r)
        | i + 1 == r  = Just (i + 1, (i + 1, 0))
        | i + 2 <= r' = Just (i + 1, (i + 1, r'))
        | otherwise   = Just (0,     (i + 1, r))
      where
        r' = r - (i + 1)

main :: IO ()
main = do
    x <- readLn :: IO Int
    print $ length (f x)