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.*;
import java.util.*;

public class Main {

	static Point[] pts;

	public static void main(String[] args) throws IOException {
		Scanner sc = new Scanner();
		PrintWriter out = new PrintWriter(System.out);
		int n = sc.nextInt();
		pts = new Point[n];
		double ans = Double.MAX_VALUE;
		for (int i = 0; i < n; i++) {
			pts[i] = new Point(sc.nextInt(), sc.nextInt());

		}
		for (int i = 0; i < n; i++) {
			int a = i, b = i + 1, c = i + 2;
			ans = Math.min(solve(a, b % n, c % n), ans);
		}
		out.println(ans);
		out.close();

	}

	static double solve(int a, int b, int c) {
		Point p1 = pts[a], p2 = pts[b], p3 = pts[c];
		double dist = Point.distToLine(p2, p1, p3);
		return dist / 2;
	}

	static class Point {
		double x, y;

		static double dot(Point a, Point b) {
			return (a.x * b.x + a.y * b.y);
		}

		static double norm_sq(Point v) {
			return v.x * v.x + v.y * v.y;
		}

		static Point toVec(Point a, Point b) {
			return new Point(b.x - a.x, b.y - a.y);
		}

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

		// returns the distance from p to the line defined by
		// two points a and b (a and b must be different)
		static double distToLine(Point p, Point a, Point b) {
			// formula: c = a + u * ab
			Point ap = toVec(a, p), ab = toVec(a, b);
			double u = dot(ap, ab) / norm_sq(ab);
			Point c = a.translate(ab.scale(u)); // translate a to c
			return dist(p, c);
		}

		private Point scale(double u) {
			return new Point(u * x, y * u);
		}

		Point translate(Point p) {
			return new Point(x + p.x, y + p.y);
		}

		static double dist(Point a, Point b) {
			double dx = a.x - b.x, dy = a.y - b.y;
			return Math.sqrt(dx * dx + dy * dy);
		}
	}

	static class Scanner {
		BufferedReader br;
		StringTokenizer st;

		Scanner() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}

		Scanner(String fileName) throws FileNotFoundException {
			br = new BufferedReader(new FileReader(fileName));
		}

		String next() throws IOException {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}

		String nextLine() throws IOException {
			return br.readLine();
		}

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

		long nextLong() throws NumberFormatException, IOException {
			return Long.parseLong(next());
		}

		double nextDouble() throws NumberFormatException, IOException {
			return Double.parseDouble(next());
		}

		boolean ready() throws IOException {
			return br.ready();
		}

	}

	static void sort(int[] a) {
		shuffle(a);
		Arrays.sort(a);
	}

	static void shuffle(int[] a) {
		int n = a.length;
		Random rand = new Random();
		for (int i = 0; i < n; i++) {
			int tmpIdx = rand.nextInt(n);
			int tmp = a[i];
			a[i] = a[tmpIdx];
			a[tmpIdx] = tmp;
		}
	}

}