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: Time Limit Exceeded)

{-# LANGUAGE ViewPatterns #-}

import Control.Monad
import Data.List
import qualified Data.Sequence as SQ
import Data.Sequence ((|>), ViewL(..))

main=do
    x<-readLn :: IO Int
    print $ f x $ SQ.singleton (0,0)

f x (SQ.viewl -> (a,i) :< seq)
    | x == a = i
    | True = f x $ n seq (i+1) [a-(i+1), a, a+i+1]

n seq i [] = seq
n seq i (a:as)= n (seq|>(a,i)) i as