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: Time Limit Exceeded)


import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.NoSuchElementException;
import java.util.concurrent.atomic.AtomicInteger;
import java.util.stream.IntStream;

public class Main {

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

	private void solve() throws IOException {
		try {
			//			solveA();
			//			solveB();
			solveC();
			// solveD();
			// solveE();
			// solveF();
		} finally {
			if (in != null) {
				in.close();
			}
			if (out != null) {
				out.flush();
				out.close();
			}
		}

	}

	private void solveA() {
		String strA = next();
		String strB = next();

		if (strA.equals("H")) {
			System.out.println(strB.equals("H") ? "H" : "D");
		} else {
			System.out.println(strB.equals("H") ? "D" : "H");
		}

	}

	private void solveB() {
		int numW = nextInt();
		int numA = nextInt();
		int numB = nextInt();

		long res = 0;

		if (numA + numW < numB) {
			res = Math.abs(numB - (numA + numW));
		} else if (numB + numW < numA) {
			res = Math.abs(numA - (numB + numW));
		}
		System.out.println(res);
	}

	private void solveC() {
		int numX = nextInt();

		//		int res = 0;
		//
		//		int sum = 0;
		//
		//		int cnt = 0;
		//		int wkTotal = 0;
		//		while (true) {
		//			cnt++;
		//			wkTotal += cnt;
		//			if (wkTotal >= numX) {
		//				res = cnt;
		//				break;
		//			}
		//		}
		//
		//		for (int i = 0;; i++) {
		//			sum += i;
		//			if (sum >= numX) {
		//				res = i;
		//				break;
		//			}
		//		}

		AtomicInteger wkRes = new AtomicInteger(-1);
		IntStream.range(0, 1000000000).reduce(0, (inSum, index) -> {
			int wk = inSum + index;
			if (wk >= numX && wkRes.intValue() == -1) {
				wkRes.set(index);
			}
			return wk;
		});

		//		AtomicInteger wkTotal2 = new AtomicInteger(0);
		//		AtomicInteger wkRes2 = new AtomicInteger(-1);
		//		IntStream.range(0, 200).forEach(index -> {
		//			wkTotal2.addAndGet(index);
		//			if (wkTotal2.intValue() >= numX && wkRes2.intValue() == -1) {
		//				wkRes2.set(index);
		//				return;
		//			}
		//		});

		out.println(wkRes);
	}

	private void solveD() {
		int numN = nextInt();

		out.println("");
	}

	private void solveE() {
		int numN = nextInt();

		out.println("");
	}

	private void solveF() {
		int numN = nextInt();

		out.println("");
	}

	private final PrintWriter out = new PrintWriter(System.out);
	private final InputStream in = System.in;
	private final byte[] buffer = new byte[1024];
	private int ptr = 0;
	private int buflen = 0;

	private boolean hasNextByte() {
		if (ptr < buflen) {
			return true;
		} else {
			ptr = 0;
			try {
				buflen = in.read(buffer);
			} catch (IOException e) {
				e.printStackTrace();
			}
			if (buflen <= 0) {
				return false;
			}
		}
		return true;
	}

	private int readByte() {
		if (hasNextByte())
			return buffer[ptr++];
		else
			return -1;
	}

	private static boolean isPrintableChar(int c) {
		return 33 <= c && c <= 126;
	}

	private void skipUnprintable() {
		while (hasNextByte() && !isPrintableChar(buffer[ptr]))
			ptr++;
	}

	public boolean hasNext() {
		skipUnprintable();
		return hasNextByte();
	}

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

	public String next() {
		if (!hasNext())
			throw new NoSuchElementException();
		StringBuilder sb = new StringBuilder();
		int b = readByte();
		while (isPrintableChar(b)) {
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}

	public long nextLong() {
		if (!hasNext())
			throw new NoSuchElementException();
		long n = 0;
		boolean minus = false;
		int b = readByte();
		if (b == '-') {
			minus = true;
			b = readByte();
		}
		if (b < '0' || '9' < b) {
			throw new NumberFormatException();
		}
		while (true) {
			if ('0' <= b && b <= '9') {
				n *= 10;
				n += b - '0';
			} else if (b == -1 || !isPrintableChar(b)) {
				return minus ? -n : n;
			} else {
				throw new NumberFormatException();
			}
			b = readByte();
		}
	}
}