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.InputMismatchException;
import java.io.IOException;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Jaswant Singh[joney_000][jaswantsinghyadav007@gmail.com][jaswant.singh@practo.com]
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        FastReader in = new FastReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskD solver = new TaskD();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskD {
        FastReader in;
        PrintWriter out;

        void set(FastReader in, PrintWriter out) {
            this.in = in;
            this.out = out;
        }

        public void solve(int testNumber, FastReader in, PrintWriter out) {
            set(in, out);
            int n = i(); //int m = i();
            double ans = 1e12;
//            out.write("HERE\n");
//            out.flush();
            Point[] p = new Point[n + 1];

            for (int i = 1; i <= n; i++) p[i] = new Point(d(), d());


            for (int i = 1; i <= n; i++) {
                // out.write("i = "+i+" "+p[i]+"\n");
                // out.flush();
                Point a = p[i];
                Point b, c;

                if (i == n - 1) {
                    b = p[n];
                    c = p[1];
                } else if (i == n) {
                    b = p[1];
                    c = p[2];
                } else {
                    b = p[(i + 1)];
                    c = p[(i + 2)];
                }

                ans = Math.min(ans, linePointDist(a, c, b, false));
            }
            out.write("" + (ans / 2.0) + "");

        }

        double dot(Point A, Point B, Point C) {
            double AB[] = new double[2];//0=>x , 1=>y
            double BC[] = new double[2];
            AB[0] = B.x - A.x;            // AB is vector : A vector defines (direction + Magnitude/Length) But not the start point or end point
            AB[1] = B.y - A.y;
            BC[0] = C.x - B.x;
            BC[1] = C.y - B.y;
            double dot = AB[0] * BC[0] + AB[1] * BC[1];
            return dot;
        }

        double cross(Point A, Point B, Point C) {
            double AB[] = new double[2];//0=>x , 1=>y
            double AC[] = new double[2];
            AB[0] = B.x - A.x;
            AB[1] = B.y - A.y;
            AC[0] = C.x - A.x;
            AC[1] = C.y - A.y;
            double cross = AB[0] * AC[1] - AB[1] * AC[0];
            return cross;
        }

        double distance(Point A, Point B) {
            double d1 = A.x - B.x;
            double d2 = A.y - B.y;
            return Math.sqrt(d1 * d1 + d2 * d2);
        }

        double linePointDist(Point A, Point B, Point C, boolean isSegment) {
            double dist = cross(A, B, C) / distance(A, B);
            if (isSegment) {
                double dot1 = dot(A, B, C);
                if (dot1 > 0) return distance(B, C);
                double dot2 = dot(B, A, C);
                if (dot2 > 0) return distance(A, C);
            }
            return dist;
        }

        int i() {
            //return Integer.parseInt(br.readLine().trim());
            return in.nextInt();
        }

        double d() {
            return in.nextDouble();
        }

    }

    static class Point implements Comparable<Point> {
        public double x;
        public double y;

        public Point() {
            this.x = 0;
            this.y = 0;
        }

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

        public int compareTo(Point p) {
            if (this.x < p.x) return -1;
            else if (this.x > p.x) return 1;
            else {
                if (this.y < p.y) return -1;
                else if (this.y > p.y) return 1;
                else return 0;

            }
        }

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

    }

    static class FastReader {
        private InputStream stream;
        private byte[] buf = new byte[2 * 1024];
        private int curChar;
        private int numChars;
        private FastReader.SpaceCharFilter filter;

        public FastReader(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 nextInt() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c == ',') {
                    c = read();
                }
                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 double nextDouble() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            double res = 0;
            while (!isSpaceChar(c) && c != '.') {
                if (c == 'e' || c == 'E') {
                    return res * Math.pow(10, nextInt());
                }
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            }
            if (c == '.') {
                c = read();
                double m = 1;
                while (!isSpaceChar(c)) {
                    if (c == 'e' || c == 'E') {
                        return res * Math.pow(10, nextInt());
                    }
                    if (c < '0' || c > '9') {
                        throw new InputMismatchException();
                    }
                    m /= 10;
                    res += (c - '0') * m;
                    c = read();
                }
            }
            return res * sgn;
        }

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

        }

    }
}