Degenerate Matrix

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

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 . 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 

In the second sample matrix B is 

Solution:

#include <bits/stdc++.h>

using namespace std;

void solve(long double a, long double b, long double c, long double d, long double &from, long double &to) {
vector <long double> z;
z.push_back(a * c);
z.push_back(a * d);
z.push_back(b * c);
z.push_back(b * d);
sort(z.begin(), z.end());
from = z[0];
to = z[3];
}

int main() {
long long a, b, c, d;
cin >> a >> b;
cin >> c >> d;
long double low = 0, high = 1e10;
for (int it = 0; it < 200; it++) {
    long double x = 0.5 * (low + high);
    long double h1, h2;
    solve(a - x, a + x, d - x, d + x, h1, h2);
    long double v1, v2;
    solve(b - x, b + x, c - x, c + x, v1, v2);
    if (v1 > h2 || h1 > v2) {
low = x;
} else {
high = x;
}
}
printf("%.17f\n", (double) (0.5 * (low + high)));
return 0;
}