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.util.Scanner;
import java.io.OutputStream;
import java.io.IOException;
import java.io.PrintWriter;
import java.io.InputStream;

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

class TaskH {
    public void solve(int testNumber, Scanner in, PrintWriter out) {
        int a = in.nextInt();
        int b = in.nextInt();
        int c = in.nextInt();
        int d = in.nextInt();
        double result = 1e99;
        for ( int w11 = -1; w11 <= 1; w11 += 2)
            for ( int w12 = -1; w12 <= 1; w12 += 2)
                for ( int w21 = -1; w21 <= 1; w21 += 2)
                    for ( int w22 = -1; w22 <= 1; w22 += 2) {
                        double x1 = w11*w22;
                        double y1= (a*w22+d*w11);
                        double z1 = (double)d*(double)a;
                        double x2 = w12*w21;
                        double y2= (b*w21+c*w12);
                        double z2 = (double)b*(double)c;
                        double A = x1 - x2;
                        double B = y1 - y2;
                        double C = z1 - z2;
                        if ( Math.abs(A) < 1e-9 ) {
                            double alpha = -C/B;
                            if ( alpha >= -1e-9 ) result = Math.min(alpha, result);
                        } else {
                            double disc = B*B-4*A*C;
                            if ( Math.abs(disc) <1e-9 ) disc = 0.0;
                            if ( disc >= -1e-9 ) {
                                double root = Math.sqrt(disc);
                                for ( int i = -1; i <= 1; i += 2) {
                                    double alpha = (-B + i*root)/(2*A);
                                    if (alpha >= -1e-9) result = Math.min(result, alpha);
                                }
                            }

                        }

                    }
        result = Math.max(0.0, result);
        out.printf("%.12f\n", result);
    }
}