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 Java8 (OpenJDK 1.8.0) (judge verdict: Memory Limit Exceeded)

import java.util.*;

public class Main {

    static long X;

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        X = sc.nextLong();
        System.out.println(findMinTimeToGoHome(0, 0));
    }

    static long findMinTimeToGoHome(long currentTime, long currentPosition) {
        if(currentPosition == X) return currentTime;
        if(currentPosition > X) return Long.MAX_VALUE;
        if(currentTime > X) return Long.MAX_VALUE;
        long candidateTime1 = findMinTimeToGoHome(currentTime + 1, currentPosition);
        long candidateTime2 = findMinTimeToGoHome(currentTime + 1, currentPosition + (currentTime + 1));
        long candidateTime3 = findMinTimeToGoHome(currentTime + 1, currentPosition - (currentTime - 1));
        return Math.min(Math.min(candidateTime1, candidateTime2), candidateTime3);
    }
}