In this problem we consider a very simplified model of Barcelona city.

Barcelona can be represented as a plane with streets of kind x = c and y = c for every integer c (that is, the rectangular grid). However, there is a detail which makes Barcelona different from Manhattan. There is an avenue called Avinguda Diagonal which can be represented as a the set of points (x, y) for which ax + by + c = 0.

One can walk along streets, including the avenue. You are given two integer points A and B somewhere in Barcelona. Find the minimal possible distance one needs to travel to get to B from A.

Input

The first line contains three integers a, b and c (-10^9≤ a, b, c≤ 10^9, at least one of a and b is not zero) representing the Diagonal Avenue.

The next line contains four integers x_1, y_1, x_2 and y_2 (-10^9≤ x_1, y_1, x_2, y_2≤ 10^9) denoting the points A = (x_1, y_1) and B = (x_2, y_2).

Output

Find the minimum possible travel distance between A and B. Your answer is considered correct if its absolute or relative error does not exceed 10^{-6}.

Formally, let your answer be a, and the jury's answer be b. Your answer is accepted if and only if \frac{|a - b|}{max{(1, |b|)}} ≤ 10^{-6}.

Examples

Input


1 1 -3
0 3 3 0


Output


4.2426406871


Input


3 1 -9
0 3 3 -1


Output


6.1622776602

Note

The first example is shown on the left picture while the second example us shown on the right picture below. The avenue is shown with blue, the origin is shown with the black dot.

<image>
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.StringTokenizer;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.InputStream;

/**
 * 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);
        PrintWriter out = new PrintWriter(outputStream);
        TaskD solver = new TaskD();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskD {
        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int a = in.nextInt();
            int b = in.nextInt();
            int c = in.nextInt();
            int x1 = in.nextInt();
            int y1 = in.nextInt();
            int x2 = in.nextInt();
            int y2 = in.nextInt();
            double ans = Math.abs((long) x1 - x2) + Math.abs((long) y1 - y2);
            go[] walk = new go[4];
            walk[0] = new up();
            walk[1] = new down();
            walk[2] = new right();
            walk[3] = new left();
            for (int i = 0; i < 4; i++) {
                for (int j = 0; j < 4; j++) {
                    pos start = new pos();
                    start.x = x1;
                    start.y = y1;
                    pos pStart = walk[i].calc(start, a, b, c);
                    pos finish = new pos();
                    finish.x = x2;
                    finish.y = y2;
                    pos pFinish = walk[j].calc(finish, a, b, c);
                    ans = Math.min(ans, dist(pStart, pFinish));
                }
            }
            out.println(ans);
        }

        double dist(pos start, pos finish) {
            return start.len + finish.len + Math.sqrt(Math.pow(start.x - finish.x, 2) + Math.pow(start.y - finish.y, 2));
        }

    }

    static class InputReader {
        private BufferedReader reader;
        private StringTokenizer stt;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream));
        }

        public String nextLine() {
            try {
                return reader.readLine();
            } catch (IOException e) {
                return null;
            }
        }

        public String next() {
            while (stt == null || !stt.hasMoreTokens()) {
                stt = new StringTokenizer(nextLine());
            }
            return stt.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

    }

    static class pos {
        double len;
        double x;
        double y;

    }

    static class left implements go {
        public pos calc(pos start, int a, int b, int c) {
            pos res = new pos();
            if (a == 0) {
                if (start.y == -c) {
                    res.len = 0;
                    res.x = start.x;
                    res.y = start.y;
                } else {
                    res.len = Double.POSITIVE_INFINITY;
                }
            } else {
                if (start.x > -(b * start.y + c) / a) {
                    res.len = Double.POSITIVE_INFINITY;
                } else {
                    res.len = -((b * start.y + c) / a + start.x);
                    res.x = -(b * start.y + c) / a;
                    res.y = start.y;
                }
            }
            return res;
        }

    }

    static interface go {
        pos calc(pos start, int a, int b, int c);

    }

    static class up implements go {
        public pos calc(pos start, int a, int b, int c) {
            pos res = new pos();
            if (b == 0) {
                if (start.x == -c) {
                    res.len = 0;
                    res.x = start.x;
                    res.y = start.y;
                } else {
                    res.len = Double.POSITIVE_INFINITY;
                }
            } else {
                if (-(a * start.x + c) / b < start.y) {
                    res.len = Double.POSITIVE_INFINITY;
                } else {
                    res.len = -((a * start.x + c) / b + start.y);
                    res.x = start.x;
                    res.y = -(a * start.x + c) / b;
                }
            }
            return res;
        }

    }

    static class down implements go {
        public pos calc(pos start, int a, int b, int c) {
            pos res = new pos();
            if (b == 0) {
                if (start.x == -c) {
                    res.len = 0;
                    res.x = start.x;
                    res.y = start.y;
                } else {
                    res.len = Double.POSITIVE_INFINITY;
                }
            } else {
                if (-(a * start.x + c) / b > start.y) {
                    res.len = Double.POSITIVE_INFINITY;
                } else {
                    res.len = (a * start.x + c) / b + start.y;
                    res.x = start.x;
                    res.y = -(a * start.x + c) / b;
                }
            }
            return res;
        }

    }

    static class right implements go {
        public pos calc(pos start, int a, int b, int c) {
            pos res = new pos();
            if (a == 0) {
                if (start.y == -c) {
                    res.len = 0;
                    res.x = start.x;
                    res.y = start.y;
                } else {
                    res.len = Double.POSITIVE_INFINITY;
                }
            } else {
                if (start.x < -(b * start.y + c) / a) {
                    res.len = Double.POSITIVE_INFINITY;
                } else {
                    res.len = start.x + (b * start.y + c) / a;
                    res.x = -(b * start.y + c) / a;
                    res.y = start.y;
                }
            }
            return res;
        }

    }
}

