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.IOException;
import java.util.InputMismatchException;

public class DegenerateMatrix {
    public static void main(String[] args) {
        FasterScanner sc = new FasterScanner();
        
        long A = sc.nextInt();
        long B = sc.nextInt();
        long C = sc.nextInt();
        long D = sc.nextInt();
        
        double L = 0;
        double R = 1e18;
        for (int i = 0; i < 1024; i++) {
        	double M = (L + R) / 2;
        	Interval i1 = new Interval();
        	Interval i2 = new Interval();
        	i1.addPoint((A - M) * (D - M));
        	i1.addPoint((A - M) * (D + M));
        	i1.addPoint((A + M) * (D - M));
        	i1.addPoint((A + M) * (D + M));
        	i2.addPoint((B - M) * (C - M));
        	i2.addPoint((B - M) * (C + M));
        	i2.addPoint((B + M) * (C - M));
        	i2.addPoint((B + M) * (C + M));
        	if (i1.intersects(i2)) {
        		R = M;
        	} else {
        		L = M;
        	}
        }
        System.out.format("%.10f\n", L);
    }
    
    public static class Interval {
    	public double left, rite;
    	
    	public Interval() {
    		this.left = Double.MAX_VALUE;
    		this.rite = -Double.MAX_VALUE;
    	}
    	
    	public Interval(double L, double R) {
    		this.left = L;
    		this.rite = R;
    	}
    	
    	public void addPoint(double val) {
    		this.left = Math.min(this.left, val);
    		this.rite = Math.max(this.rite, val);
    	}
    	
    	public boolean intersects(Interval i) {
    		return ((this.left >= i.left && this.left <= i.rite) || (i.left >= this.left && i.left <= this.rite));
    	}
    }
    
	public static class FasterScanner {
		private byte[] buf = new byte[1024];
		private int curChar;
		private int numChars;

		public int read() {
			if (numChars == -1)
				throw new InputMismatchException();
			if (curChar >= numChars) {
				curChar = 0;
				try {
					numChars = System.in.read(buf);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (numChars <= 0)
					return -1;
			}
			return buf[curChar++];
		}

		public String nextLine() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isEndOfLine(c));
			return res.toString();
		}

		public String nextString() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isSpaceChar(c));
			return res.toString();
		}

		public long nextLong() {
			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 int nextInt() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			int 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 int[] nextIntArray(int n) {
	        return nextIntArray(n, 0);
	    }
	    
	    public int[] nextIntArray(int n, int off) {
	    	int[] arr = new int[n + off];
	    	for (int i = 0; i < n; i++) {
	    		arr[i + off] = nextInt();
	    	}
	    	return arr;
	    }
	    
	    public long[] nextLongArray(int n) {
	    	return nextLongArray(n, 0);
	    }
        
		public long[] nextLongArray(int n, int off) {
		    long[] arr = new long[n + off];
		    for (int i = 0; i < n; i++) {
		        arr[i + off] = nextLong();
		    }
		    return arr;
		}

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

		private boolean isEndOfLine(int c) {
			return c == '\n' || c == '\r' || c == -1;
		}
	}
}