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.Monad
import Data.List

-- [a,b) -> a .. f aがTrueとなる最大のa, f bはFalse
-- aとbは評価しないので、範囲が0..(n-1)のとき、(a,b)=(-1,n)で呼んで良い
bsearch f (a,b)
    | a+1 == b = a
    | f m  = bsearch f (m,b)
    | True = bsearch f (a,m)
    where m = (a + (b-a)`div`2)

f x a = a*(a+1) < x

main=do
    x<-readLn :: IO Int
    print $ (+) 1 $ bsearch (f (x*2)) (-1,x)