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:
//package loosery;
import java.io.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.InputMismatchException;

public class HH {
	InputStream is;
	PrintWriter out;
	String INPUT = "";
	
	void solve()
	{
		long a = ni(), b = ni(), c = ni(), d = ni();
		long x1 = a+b, y1 = a-b;
		long x2 = c+d, y2 = c-d;
		
		if(x1*y2-x2*y1 == 0){
			out.printf("%.12f\n", 0.);
			return;
		}
		
		double min = Double.POSITIVE_INFINITY;
		min = Math.min(min, Math.abs((double)(x2*y1-x1*y2)/(x1+x2)));
		min = Math.min(min, Math.abs((double)(y2*x1-y1*x2)/(y1+y2)));
		if(Double.isNaN(min)){
			out.printf("%.12f\n", 0.);
		}else{
			{
				long[] il = interLinesS(x1, y1, x2, y2, 0, 0, 0, 1);
				if(il != null){
					min = Math.min(min, Math.abs((double)il[1]/il[2]));
				}
			}
			{
				long[] il = interLinesS(x1, y1, x2, y2, 0, 0, 1, 0);
				if(il != null){
					min = Math.min(min, Math.abs((double)il[1]/il[2]));
				}
			}
			out.printf("%.12f\n", min/2);
		}
	}

	public static long[] interLinesS(long ax, long ay, long bx, long by, long cx, long cy, long dx, long dy)
	{
		long aa = bx - ax;
		long cc = by - ay;
		long bb = cx - dx;
		long dd = cy - dy;
		long xx = cx - ax;
		long yy = cy - ay;
		long det = aa * dd - bb * cc;
		if(det == 0)return null;
		long tnum = dd*xx-bb*yy;
		long unum = -cc*xx+aa*yy;
		if(det < 0){
			det = -det;
			tnum = -tnum;
			unum = -unum;
		}
//		if(tnum < 0 || tnum > det || unum < 0 || unum > det)return null;
		return new long[]{
				tnum,
				unum,
				det
		};
	}

	
	void run() throws Exception
	{
		is = oj ? System.in : new ByteArrayInputStream(INPUT.getBytes());
		out = new PrintWriter(System.out);
		
		long s = System.currentTimeMillis();
		solve();
		out.flush();
		tr(System.currentTimeMillis()-s+"ms");
	}
	
	public static void main(String[] args) throws Exception { new HH().run(); }
	
	private byte[] inbuf = new byte[1024];
	private int lenbuf = 0, ptrbuf = 0;
	
	private int readByte()
	{
		if(lenbuf == -1)throw new InputMismatchException();
		if(ptrbuf >= lenbuf){
			ptrbuf = 0;
			try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
			if(lenbuf <= 0)return -1;
		}
		return inbuf[ptrbuf++];
	}
	
	private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
	private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }
	
	private double nd() { return Double.parseDouble(ns()); }
	private char nc() { return (char)skip(); }
	
	private String ns()
	{
		int b = skip();
		StringBuilder sb = new StringBuilder();
		while(!(isSpaceChar(b))){ // when nextLine, (isSpaceChar(b) && b != ' ')
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}
	
	private char[] ns(int n)
	{
		char[] buf = new char[n];
		int b = skip(), p = 0;
		while(p < n && !(isSpaceChar(b))){
			buf[p++] = (char)b;
			b = readByte();
		}
		return n == p ? buf : Arrays.copyOf(buf, p);
	}
	
	private char[][] nm(int n, int m)
	{
		char[][] map = new char[n][];
		for(int i = 0;i < n;i++)map[i] = ns(m);
		return map;
	}
	
	private int[] na(int n)
	{
		int[] a = new int[n];
		for(int i = 0;i < n;i++)a[i] = ni();
		return a;
	}
	
	private int ni()
	{
		int num = 0, b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}
		
		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	
	private long nl()
	{
		long num = 0;
		int b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}
		
		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	
	private boolean oj = System.getProperty("ONLINE_JUDGE") != null;
	private void tr(Object... o) { if(!oj)System.out.println(Arrays.deepToString(o)); }
}