Problem: You are given a convex polygon P with n distinct vertices p1, p2, ..., pn. Vertex pi has coordinates (xi, yi) in the 2D plane. These vertices are listed in clockwise order.

You can choose a real number D and move each vertex of the polygon a distance of at most D from their original positions.

Find the maximum value of D such that no matter how you move the vertices, the polygon does not intersect itself and stays convex.

Input

The first line has one integer n (4 ≤ n ≤ 1 000) — the number of vertices.

The next n lines contain the coordinates of the vertices. Line i contains two integers xi and yi ( - 109 ≤ xi, yi ≤ 109) — the coordinates of the i-th vertex. These points are guaranteed to be given in clockwise order, and will form a strictly convex polygon (in particular, no three consecutive points lie on the same straight line).

Output

Print one real number D, which is the maximum real number such that no matter how you move the vertices, the polygon stays convex.

Your answer will be considered correct if its absolute or relative error does not exceed 10 - 6.

Namely, let's assume that your answer is a and the answer of the jury is b. The checker program will consider your answer correct if <image>.

Examples

Input

4
0 0
0 1
1 1
1 0


Output

0.3535533906


Input

6
5 0
10 0
12 -4
10 -8
5 -8
3 -4


Output

1.0000000000

Note

Here is a picture of the first sample

<image>

Here is an example of making the polygon non-convex.

<image>

This is not an optimal solution, since the maximum distance we moved one point is  ≈ 0.4242640687, whereas we can make it non-convex by only moving each point a distance of at most  ≈ 0.3535533906.

Solution (in JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.BufferedWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Rustam Musin (PloadyFree@gmail.com)
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        TaskB solver = new TaskB();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskB {
        private int n;
        private Point[] all;

        public void solve(int testNumber, InputReader in, OutputWriter out) {
            all = new Point[n = in.readInt()];
            for (int i = 0; i < n; i++) {
                all[i] = new Point(in.readInt(), in.readInt());
            }

            double minDist = Double.MAX_VALUE;
            for (int i = 0; i < n; i++) {
                Point a = all[i];
                Point b = all[(i + 1) % n];
                Point c = all[(i + 2) % n];
                minDist = Math.min(minDist, getDist(a, b, c));
            }

            out.printFormat("%.10f", minDist);
        }

        private double getDist(Point a, Point b, Point c) {
            Vector v = new Vector(a, b);

            double l = 0;
            double r = 1;
            for (int i = 0; i < 100; i++) {
                double m1 = l + (r - l) / 3;
                double m2 = r - (r - l) / 3;
                Point toCheck1 = new Point(a.x + v.x * m1, a.y + v.y * m1);
                Point toCheck2 = new Point(a.x + v.x * m2, a.y + v.y * m2);
                double dist1 = getDist(toCheck1, a, b, c);
                double dist2 = getDist(toCheck2, a, b, c);
                if (dist1 < dist2) {
                    r = m2;
                } else {
                    l = m1;
                }
            }

            Point p = new Point(a.x + v.x * l, a.y + v.y * l);
            return getDist(p, a, b, c);
        }

        private double getDist(Point fixed, Point a, Point b, Point c) {
            Vector v = new Vector(b, c);

            double l = 0;
            double r = 1;
            for (int i = 0; i < 100; i++) {
                double m1 = l + (r - l) / 3;
                double m2 = r - (r - l) / 3;
                Point toCheck1 = new Point(b.x + v.x * m1, b.y + v.y * m1);
                Point toCheck2 = new Point(b.x + v.x * m2, b.y + v.y * m2);
                double dist1 = getDist(fixed.line(toCheck1), a, b, c);
                double dist2 = getDist(fixed.line(toCheck2), a, b, c);
                if (dist1 < dist2) {
                    r = m2;
                } else {
                    l = m1;
                }
            }

            Point p = new Point(b.x + v.x * l, b.y + v.y * l);
            return getDist(fixed.line(p), a, b, c);
        }

        private double getDist(Line line, Point a, Point b, Point c) {
            return Math.max(a.distance(line), Math.max(b.distance(line), c.distance(line)));
        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private InputReader.SpaceCharFilter filter;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

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

        public int readInt() {
            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 boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }

    static class GeometryUtils {
        public static double epsilon = 1e-8;

        public static double fastHypot(double x, double y) {
            return Math.sqrt(x * x + y * y);
        }

    }

    static class Point {
        public final double x;
        public final double y;


        public String toString() {
            return "(" + x + ", " + y + ")";
        }

        public Point(double x, double y) {
            this.x = x;
            this.y = y;
        }

        public Line line(Point other) {
            if (equals(other)) {
                return null;
            }
            double a = other.y - y;
            double b = x - other.x;
            double c = -a * x - b * y;
            return new Line(a, b, c);
        }


        public boolean equals(Object o) {
            if (this == o) {
                return true;
            }
            if (o == null || getClass() != o.getClass()) {
                return false;
            }

            Point point = (Point) o;

            return Math.abs(x - point.x) <= GeometryUtils.epsilon && Math.abs(y - point.y) <= GeometryUtils.epsilon;
        }


        public int hashCode() {
            int result;
            long temp;
            temp = x != +0.0d ? Double.doubleToLongBits(x) : 0L;
            result = (int) (temp ^ (temp >>> 32));
            temp = y != +0.0d ? Double.doubleToLongBits(y) : 0L;
            result = 31 * result + (int) (temp ^ (temp >>> 32));
            return result;
        }

        public double distance(Line line) {
            return Math.abs(line.a * x + line.b * y + line.c);
        }

    }

    static class OutputWriter {
        private final PrintWriter writer;

        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }

        public void printFormat(String format, Object... objects) {
            writer.printf(format, objects);
        }

        public void close() {
            writer.close();
        }

    }

    static class Vector {
        public final double x;
        public final double y;
        public final Point point;

        public Vector(double x, double y) {
            this.x = x;
            this.y = y;
            point = new Point(x, y);
        }

        public Vector(Point point) {
            this.x = point.x;
            this.y = point.y;
            this.point = point;
        }

        public Vector(Point from, Point to) {
            this(to.x - from.x, to.y - from.y);
        }

    }

    static class Line {
        public final double a;
        public final double b;
        public final double c;

        public Line(Point p, double angle) {
            a = Math.sin(angle);
            b = -Math.cos(angle);
            c = -p.x * a - p.y * b;
        }

        public Line(double a, double b, double c) {
            double h = GeometryUtils.fastHypot(a, b);
            this.a = a / h;
            this.b = b / h;
            this.c = c / h;
        }

        public boolean parallel(Line other) {
            return Math.abs(a * other.b - b * other.a) < GeometryUtils.epsilon;
        }


        public boolean equals(Object o) {
            if (this == o) {
                return true;
            }
            if (o == null || getClass() != o.getClass()) {
                return false;
            }

            Line line = (Line) o;

            if (!parallel(line)) {
                return false;
            }
            if (Math.abs(a * line.c - c * line.a) > GeometryUtils.epsilon ||
                    Math.abs(b * line.c - c * line.b) > GeometryUtils.epsilon) {
                return false;
            }

            return true;
        }

    }
}