Problem: Luyi has n circles on the plane. The i-th circle is centered at (xi, yi). At the time zero circles start to grow simultaneously. In other words, the radius of each circle at time t (t > 0) is equal to t. The circles are drawn as black discs on an infinite white plane. So at each moment the plane consists of several black and white regions. Note that the circles may overlap while growing.

<image>

We define a hole as a closed, connected white region. For instance, the figure contains two holes shown by red border. During growing some holes may be created and it is easy to see that each created hole will disappear eventually. Luyi asks you to find moment of time such that the last hole disappears. In other words, you should find the first moment such that no hole can be seen after that.

Input

The first line of the input contains integer n (1 ≤ n ≤ 100). Each of the next n lines contains two integers xi and yi ( - 104 ≤ xi, yi ≤ 104), indicating the location of i-th circle.

It's guaranteed that no two circles are centered at the same point.

Output

Print the moment where the last hole disappears. If there exists no moment in which we can find holes print -1.

The answer will be considered correct if the absolute or relative error does not exceed 10 - 4.

Examples

Input

3
0 0
1 1
2 2


Output

-1


Input

4
0 0
0 2
2 2
2 0


Output

1.414214


Input

4
0 1
0 -1
-2 0
4 0


Output

2.125000

Solution (in JAVA):

Solution:
//package round168;
import java.awt.geom.Point2D;
import java.io.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.InputMismatchException;


public class C5 {
	InputStream is;
	PrintWriter out;
	String INPUT = "";
//	String INPUT = "3 0 0 1 1 2 2 ";
//	String INPUT = "4 0 0 0 2 2 2 2 0";
//	String INPUT = "4 0 1 0 -1 -2 0 4 0";
//	String INPUT = "4 0 0 4 8 8 0 4 3";
//	String INPUT = "20\r\n" + 
//			"3789 -1964\r\n" + 
//			"7033 -4086\r\n" + 
//			"2379 -7467\r\n" + 
//			"8609 -4677\r\n" + 
//			"-8359 8919\r\n" + 
//			"3391 8515\r\n" + 
//			"1368 2089\r\n" + 
//			"1898 2663\r\n" + 
//			"-9870 2524\r\n" + 
//			"5768 -1414\r\n" + 
//			"-7549 739\r\n" + 
//			"-3691 -1850\r\n" + 
//			"-7118 -3897\r\n" + 
//			"2204 3144\r\n" + 
//			"1191 8585\r\n" + 
//			"-6875 6888\r\n" + 
//			"4309 -5523\r\n" + 
//			"4816 5772\r\n" + 
//			"-9541 -2271\r\n" + 
//			"9337 7795";
	
	void solve()
	{
		int n = ni();
		double[][] co = new double[n][];
		for(int i = 0;i < n;i++){
			co[i] = new double[]{ni(), ni()};
		}
		double[][][][] exs = new double[n][n][n][];
		for(int i = 0;i < n;i++){
			for(int j = 0;j < n;j++){
				for(int k = 0;k < n;k++){
					exs[i][j][k] = excircle2(co[i][0], co[i][1], co[j][0], co[j][1], co[k][0], co[k][1]);
				}
			}
		}
		
		double max = -1;
		for(int i = 0;i < n;i++){
			for(int j = i+1;j < n;j++){
				inner:
				for(int k = j+1;k < n;k++){
					double cross = 
							(co[k][0]-co[i][0])*(co[j][1]-co[i][1])-
							(co[k][1]-co[i][1])*(co[j][0]-co[i][0]);
					if(cross == 0)continue;
					double dot =
							(co[k][0]-co[i][0])*(co[j][0]-co[i][0])+
							(co[k][1]-co[i][1])*(co[j][1]-co[i][1])
							;
					double dot2 =
							(co[k][0]-co[j][0])*(co[i][0]-co[j][0])+
							(co[k][1]-co[j][1])*(co[i][1]-co[j][1])
							;
					double dot3 =
							(co[i][0]-co[k][0])*(co[j][0]-co[k][0])+
							(co[i][1]-co[k][1])*(co[j][1]-co[k][1])
							;
					if(dot <= 0){
						max = Math.max(max, go(i, j, k, co, exs));
					}else if(dot2 <= 0){
						max = Math.max(max, go(j, k, i, co, exs));
					}else if(dot3 <= 0){
						max = Math.max(max, go(k, i, j, co, exs));
					}else{
						double eps = 1E-10;
						for(int l = 0;l < n;l++){
							if(Point2D.distance(exs[i][j][k][0], exs[i][j][k][1], co[l][0], co[l][1]) < exs[i][j][k][2]-eps){
								continue inner;
							}
						}
						max = Math.max(max, exs[i][j][k][2]);
					}
				}
			}
		}
		
		if(max == -1){
			out.println(-1);
		}else{
			out.printf("%.12f\n", max);
		}
	}
	
	boolean inon(double[] t, double[] a, double[] b, double[] c)
	{
		int s = 0;
		s += ccw(a[0], a[1], b[0], b[1], t[0], t[1]);
		s += ccw(b[0], b[1], c[0], c[1], t[0], t[1]);
		s += ccw(c[0], c[1], a[0], a[1], t[0], t[1]);
//		return s >= 3 || s <= -3;
		return s >= 2 || s <= -2;
	}
	
	double go(int k, int i, int j, double[][] co, double[][][][] exs)
	{
		int n = co.length;
//		if(n == 60)return -1;
		double dot = 
				(co[i][0]-co[k][0])*(co[j][0]-co[k][0])+
				(co[i][1]-co[k][1])*(co[j][1]-co[k][1]);
		if(dot != 0)return -1;
		double cross = 
				(co[k][0]-co[i][0])*(co[j][1]-co[i][1])-
				(co[k][1]-co[i][1])*(co[j][0]-co[i][0]);
		double[] ex = exs[i][j][k];
		double r = ex[2];
		double eps = 1E-9;
		boolean found = false;
		for(int l = 0;l < n;l++){
			if(l != i & l != j && l != k){
				double cross2 = 
						(co[l][0]-co[i][0])*(co[j][1]-co[i][1])-
						(co[l][1]-co[i][1])*(co[j][0]-co[i][0]);
				if(cross2 * cross < 0){
					double dot2 = 
							(co[i][0]-co[l][0])*(co[j][0]-co[l][0])+
							(co[i][1]-co[l][1])*(co[j][1]-co[l][1]);
					if(dot2 == 0){
						found = true;
					}
				}
			}
		}
		if(!found)return -1;
		for(int l = 0;l < n;l++){
			if(Point2D.distance(ex[0], ex[1], co[l][0], co[l][1]) < r-eps){
				return -1;
			}
		}
		return r;
	}
	
	public static int ccw(double ax, double ay, double bx, double by, double tx, double ty){
		return (int)Math.signum((tx-ax)*(by-ay)-(bx-ax)*(ty-ay));
	}
	
	public static double[] excircle2(double ax, double ay, double bx, double by, double cx, double cy)
	{
		double A = (bx-cx)*(bx-cx)+(by-cy)*(by-cy);
		double B = (cx-ax)*(cx-ax)+(cy-ay)*(cy-ay);
		double C = (ax-bx)*(ax-bx)+(ay-by)*(ay-by);
		double D = A*(-A+B+C)+B*(A-B+C)+C*(A+B-C);
		double X = (A*(-A+B+C)*ax + B*(A-B+C)*bx + C*(A+B-C)*cx) / D;
		double Y = (A*(-A+B+C)*ay + B*(A-B+C)*by + C*(A+B-C)*cy) / D;
		double R = Math.sqrt((X-ax)*(X-ax)+(Y-ay)*(Y-ay));
//		double R = A*B*C/Math.sqrt((A+B+C)*(-A+B+C)*(A-B+C)*(A+B-C));
		return new double[]{X, Y, R};
	}
	
	void run() throws Exception
	{
		is = oj ? System.in : new ByteArrayInputStream(INPUT.getBytes());
		out = new PrintWriter(System.out);
		
		long s = System.currentTimeMillis();
		solve();
		out.flush();
		tr(System.currentTimeMillis()-s+"ms");
	}
	
	public static void main(String[] args) throws Exception { new C5().run(); }
	
	private byte[] inbuf = new byte[1024];
	private int lenbuf = 0, ptrbuf = 0;
	
	private int readByte()
	{
		if(lenbuf == -1)throw new InputMismatchException();
		if(ptrbuf >= lenbuf){
			ptrbuf = 0;
			try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
			if(lenbuf <= 0)return -1;
		}
		return inbuf[ptrbuf++];
	}
	
	private int ni()
	{
		int num = 0, b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}
		
		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	
	private boolean oj = System.getProperty("ONLINE_JUDGE") != null;
	private void tr(Object... o) { if(!oj)System.out.println(Arrays.deepToString(o)); }
}