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.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;
        MyBufferedReader in = new MyBufferedReader(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, MyBufferedReader in, PrintWriter out) {
            int n = in.getAnInt();
            Point[] pts = new Point[n];
            for (int i = 0; i < n; i++) {
                int[] data = in.getALineOfInts(2);
                pts[i] = new Point(data[0], data[1]);
            }

            double res = Double.MAX_VALUE;
            for (int i = 0; i < pts.length; i++) {
                Point first = pts[i];
                Point mid = pts[(i + 1) % n];
                Point last = pts[(i + 2) % n];

                Line l = new Line(first, last, true, true);
                res = Math.min(res, mid.minDistance(l) / 2.0);
            }

            out.println(res);
        }

    }

    static class MyBufferedReader {
        BufferedReader in;

        public MyBufferedReader(InputStream s) {
            this.in = new BufferedReader(new InputStreamReader(s));
        }

        public int getAnInt() {
            int res = -1;
            try {
                res = Integer.parseInt(new StringTokenizer(in.readLine()).nextToken());
            } catch (IOException e) {
                e.printStackTrace();
            }
            return res;
        }

        public int[] getALineOfInts(int numExpected) {
            if (numExpected == 0) {
                return new int[0];
            }

            int[] res = new int[numExpected];
            StringTokenizer st = null;
            try {
                st = new StringTokenizer(in.readLine());
            } catch (IOException e) {
                e.printStackTrace();
            }
            for (int i = 0; i < numExpected; i++)
                res[i] = Integer.parseInt(st.nextToken());
            return res;
        }

    }

    static class Line {
        final Point a;
        final Point b;
        final Point lineVector;
        final boolean aIsEnd;
        final boolean bIsEnd;

        public Line(Point end1, Point end2, boolean aIsEnd, boolean bIsEnd) {
            this.a = end1;
            this.b = end2;
            this.aIsEnd = aIsEnd;
            this.bIsEnd = bIsEnd;
            if (aIsEnd || !bIsEnd) {
                lineVector = Point.getVector(a, b);
            } else {
                lineVector = Point.getVector(b, a);
            }
        }

        boolean isLine() {
            return !(aIsEnd || bIsEnd);
        }

        public String toString() {
            return "(" + a.toString() + ", " + b.toString() + ")";
        }

    }

    static class Point {
        public static final int X = 0;
        public static final int Y = 1;
        public static final int Z = 2;
        public double[] coordinates;

        public Point(double... coordinates) {
            this.coordinates = coordinates;
        }

        public double x() {
            return coordinates[X];
        }

        public double y() {
            return coordinates[Y];
        }

        public double z() {
            return coordinates[Z];
        }

        public int dim() {
            return coordinates.length;
        }

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

        public double distance(Point o) {
            double res = 0;
            for (int i = 0; i < dim(); i++) {
                double iDiff = coordinates[i] - o.coordinates[i];
                res += iDiff * iDiff;
            }
            return Math.sqrt(res);
        }

        public double magnitude() {
            double res = 0;
            for (int i = 0; i < dim(); i++) {
                res += coordinates[i] * coordinates[i];
            }
            return Math.sqrt(res);
        }

        public static Point crossProduct(Point vector1, Point vector2) {
            double[] newCoords = new double[3];
            if (vector1.dim() == 3) {
                newCoords[X] = vector1.y() * vector2.z() - vector1.z() * vector2.y();
                newCoords[Y] = vector1.z() * vector2.x() - vector1.x() * vector2.z();
            }

            newCoords[Z] = vector1.x() * vector2.y() - vector1.y() * vector2.x();
            return new Point(newCoords);
        }

        public static Point getVector(Point from, Point to) {
            double[] newCoords = new double[from.dim()];
            for (int i = 0; i < from.dim(); i++) {
                newCoords[i] = to.coordinates[i] - from.coordinates[i];
            }
            return new Point(newCoords);
        }

        public static double dotProduct(Point a, Point b) {
            double res = 0;
            for (int i = 0; i < a.dim(); i++) {
                res += a.coordinates[i] * b.coordinates[i];
            }
            return res;
        }

        public double minDistance(Line s) {
            Point ab = getVector(s.a, s.b);
            if (ab.magnitude() < Numbers.EPSILON) {
                return distance(s.a);
            }

            Point ac = getVector(s.a, this);
            Point ba = getVector(s.b, s.a);
            Point bc = getVector(s.b, this);

            if (s.isLine()) {
                return crossProduct(ac, ab).magnitude() / ab.magnitude();
            }

            double aDot = dotProduct(ab, ac);
            double bDot = dotProduct(ba, bc);

            int aDotAnd0 = Numbers.compareDoubles(aDot, 0, Numbers.EPSILON);
            int bDotAnd0 = Numbers.compareDoubles(bDot, 0, Numbers.EPSILON);

            if (aDotAnd0 >= 0 && bDotAnd0 >= 0 || aDotAnd0 < 0 && !s.aIsEnd || bDotAnd0 < 0 && !s
                .bIsEnd) {
                return crossProduct(ac, ab).magnitude() / ab.magnitude();
            }

            if (aDot < 0) {
                return distance(s.a);
            }

            return distance(s.b);
        }

    }

    static class Numbers {
        public static final double EPSILON = 0.000001;

        public static int compareDoubles(double d1, double d2, double eps) {
            if (Math.abs(d1 - d2) <= eps)
                return 0;

            return ((int) Math.signum(d1 - d2));
        }

    }
}