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 Java7 (OpenJDK 1.7.0) (judge verdict: Wrong Answer)

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


public class Main {

	public static void main(String[] args) throws Exception {
		new Main().solve();
	}
	void solve() throws Exception {
		FastScanner in = new FastScanner(System.in);

		long N = in.nextInt();

		long sum = 0;
		for (int i = 0; i < N; i++) {
			sum += i;
			if (sum >= N) {
				System.out.println(i);
				return;
			}
		}

	}

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	class FastScanner {

		private InputStream _stream;
		private byte[] _buf = new byte[1024];
		private int _curChar;
		private int _numChars;
		private StringBuilder _sb = new StringBuilder();

		FastScanner(InputStream stream) {
			this._stream = stream;
		}

		public int read() {
			if (_numChars == -1) throw new InputMismatchException();
			if (_curChar >= _numChars) {
				_curChar = 0;
				try {
					_numChars = _stream.read(_buf);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (_numChars <= 0) return -1;
			}
			return _buf[_curChar++];
		}

		public String next() {
			int c = read();
			while (isWhitespace(c)) {
				c = read();
			}
			_sb.setLength(0);
			do {
				_sb.appendCodePoint(c);
				c = read();
			} while (!isWhitespace(c));
			return _sb.toString();
		}

		public int nextInt() {
			return (int) nextLong();
		}
		public long nextLong() {
			int c = read();
			while (isWhitespace(c)) {
				c = read();
			}
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			long res = 0;
			do {
				if (c < '0' || c > '9') throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			} while (!isWhitespace(c));
			return res * sgn;
		}

		public boolean isWhitespace(int c) {
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}
	}
}
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