Problem: The determinant of a matrix 2 × 2 is defined as follows:

<image>

A matrix is called degenerate if its determinant is equal to zero. 

The norm ||A|| of a matrix A is defined as a maximum of absolute values of its elements.

You are given a matrix <image>. Consider any degenerate matrix B such that norm ||A - B|| is minimum possible. Determine ||A - B||.

Input

The first line contains two integers a and b (|a|, |b| ≤ 109), the elements of the first row of matrix A. 

The second line contains two integers c and d (|c|, |d| ≤ 109) the elements of the second row of matrix A.

Output

Output a single real number, the minimum possible value of ||A - B||. Your answer is considered to be correct if its absolute or relative error does not exceed 10 - 9.

Examples

Input

1 2
3 4


Output

0.2000000000


Input

1 0
0 1


Output

0.5000000000

Note

In the first sample matrix B is <image>

In the second sample matrix B is <image>

Solution (in JAVA):

Solution:
import java.io.BufferedWriter;
import java.util.InputMismatchException;
import java.io.InputStream;
import java.util.NoSuchElementException;
import java.io.OutputStreamWriter;
import java.math.BigInteger;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.Writer;
import java.io.IOException;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
	public static void main(String[] args) {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		InputReader in = new InputReader(inputStream);
		OutputWriter out = new OutputWriter(outputStream);
		TaskH solver = new TaskH();
		solver.solve(1, in, out);
		out.close();
	}
}

class TaskH {
    public void solve(int testNumber, InputReader in, OutputWriter out) {
        long a = in.readLong();
        long b = in.readLong();
        long c = in.readLong();
        long d = in.readLong();
        double ans = Double.MAX_VALUE;
        for (int mask = 0; mask < 16; mask++) {
            long A = 0, B = 0, C = a*d - b*c;
            if ((mask & 1) == 0) B += a; else B -= a;
            if ((mask & 2) == 0) B -= b; else B += b;
            if ((mask & 4) == 0) B -= c; else B += c;
            if ((mask & 8) == 0) B += d; else B -= d;
            if (((mask & 1) == 0) ^ ((mask & 8) == 0)) A--; else A++;
            if (((mask & 2) == 0) ^ ((mask & 4) == 0)) A++; else A--;
            if (A == 0) {
                if (B == 0) {
                    if (C == 0) ans = Math.min(ans, 0);
                } else {
                    ans = Math.min(ans, Math.abs((double)C / B));
                }
            } else {
                double D = (double)B*B - 4.0*A*C;
                if (D >= 0) {
                    double x1 = (-B - Math.sqrt(D)) / (2.0 * A);
                    double x2 = (-B + Math.sqrt(D)) / (2.0 * A);
                    ans = Math.min(ans, Math.abs(x1));
                    ans = Math.min(ans, Math.abs(x2));
                }
            }
            }
        out.printFormat("%.15f\n", ans);
    }
}

class InputReader {

	private InputStream stream;
	private byte[] buf = new byte[1024];
	private int curChar;
	private int numChars;
	private SpaceCharFilter filter;

	public InputReader(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 long readLong() {
		int c = read();
		while (isSpaceChar(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 (!isSpaceChar(c));
		return res * sgn;
	}

	public boolean isSpaceChar(int c) {
		if (filter != null)
			return filter.isSpaceChar(c);
		return isWhitespace(c);
	}

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

	public interface SpaceCharFilter {
		public boolean isSpaceChar(int ch);
	}
}

class OutputWriter {
	private final PrintWriter writer;

	public OutputWriter(OutputStream outputStream) {
		writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
	}

	public void printFormat(String format, Object...objects) {
		writer.printf(format, objects);
	}

	public void close() {
		writer.close();
	}

}