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 javafx.util.Pair;

import java.io.*;
import java.util.StringTokenizer;

/**
 * @author Aydar Gizatullin a.k.a. lightning95, aydar.gizatullin@gmail.com
 *         Created on 16.04.17.
 */
public class ProbB {

    private void solve() {
        int n = rw.nextInt();
        Pair<Integer, Integer>[] a = new Pair[n];
        for (int i = 0; i < n; ++i) {
            a[i] = new Pair<>(rw.nextInt(), rw.nextInt());
        }
        double ans = Double.MAX_VALUE;
        for (int i = 0; i < n; ++i) {

            int x1 = a[i].getKey();
            int y1 = a[i].getValue();

            int x0 = a[(i + 1) % n].getKey();
            int y0 = a[(i + 1) % n].getValue();

            int x2 = a[(i + 2) % n].getKey();
            int y2 = a[(i + 2) % n].getValue();



            double A = x0 - x1;
            double B = y0 - y1;
            double C = x2 - x1;
            double D = y2 - y1;

            double dot = A * C + B * D;
            double len_sq = C * C + D * D;
            double param = -1;
            if (len_sq != 0) //in case of 0 length line
                param = dot / len_sq;

            double xx, yy;

            if (param < 0) {
                xx = x1;
                yy = y1;
            }
            else if (param > 1) {
                xx = x2;
                yy = y2;
            }
            else {
                xx = x1 + param * C;
                yy = y1 + param * D;
            }

            double dx = x0 - xx;
            double dy = y0 - yy;
            double d = Math.sqrt(dx * dx + dy * dy);
            ans = Math.min(ans, d / 2);
        }

        rw.out.printf("%.10f", ans);
    }

    long gcd(long a, long b) {
        while (a > 0 && b > 0) {
            if (a > b)
                a %= b;
            else b %= a;
        }
        return a + b;
    }

    private RW rw;
    private String FILE_NAME = "file";

    public static void main(String[] args) {
        new ProbB().run();
    }

    private void run() {
        rw = new RW(FILE_NAME + ".in", FILE_NAME + ".out");
        solve();
        rw.close();
    }

    private class RW {
        private StringTokenizer st;
        private PrintWriter out;
        private BufferedReader br;
        private boolean eof;

        RW(String inputFile, String outputFile) {
            br = new BufferedReader(new InputStreamReader(System.in));
            out = new PrintWriter(new OutputStreamWriter(System.out));

            File f = new File(inputFile);
            if (f.exists() && f.canRead()) {
                try {
                    br = new BufferedReader(new FileReader(inputFile));
                    out = new PrintWriter(new FileWriter(outputFile));
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
        }

        private String nextLine() {
            String s = "";
            try {
                s = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return s;
        }

        private String next() {
            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    eof = true;
                    return "-1";
                }
            }
            return st.nextToken();
        }

        private long nextLong() {
            return Long.parseLong(next());
        }

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

        private void println() {
            out.println();
        }

        private void println(Object o) {
            out.println(o);
        }

        private void print(Object o) {
            out.print(o);
        }

        private void close() {
            try {
                br.close();
            } catch (IOException e) {
                e.printStackTrace();
            }
            out.close();
        }
    }
}