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: Accepted)

import java.io.*;
import java.util.*;

public class Main {
    public static PrintWriter out;
    public static FastScanner in;

    private void solve(){
        List<Long> list = new ArrayList<>();

        long cb = 0;
        for(int i=0;cb<=1e9;i++){
            cb = ((long)i*(i+1))/2;
            list.add(cb);
        }

        long b = in.nextLong();
        for(int i=0;i<list.size();i++){
            if(list.get(i) >= b){
                out.print(i);
                return;
            }
        }
    }

    private void runIO() {
        in = new FastScanner();
        out = new PrintWriter(new BufferedOutputStream(System.out));
        solve();
        out.close();
    }
    private static class FastScanner {
        BufferedReader bufferedReader;
        StringTokenizer stringTokenizer;

        private FastScanner() {
            bufferedReader = new BufferedReader(new InputStreamReader(System.in));
        }

        private String next() {
            if (stringTokenizer == null || !stringTokenizer.hasMoreElements()) {
                try {
                    stringTokenizer = new StringTokenizer(bufferedReader.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return stringTokenizer.nextToken();
        }

        private int nextInt() {
            return Integer.parseInt(next());
        }

        private long nextLong() {
            return Long.parseLong(next());
        }

        private String nextLine() {
            String ret = "";
            try {
                ret = bufferedReader.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return ret;
        }
    }

    public static void main(String[] args) {
        new Main().runIO();
    }
}