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:
import java.io.BufferedReader;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;


public class LastHole {

	/**
	 * @param args
	 */
	
	static int x[];
	static int y[];
	
	
	public static void main(String[] args) {
		Parser p = new Parser(System.in);
		PrintWriter pw = new PrintWriter(System.out);
		int n = p.nextInt();
		x = new int[n];
		y = new int[n];
		
		for(int i=0; i<n; ++i){
			x[i] = p.nextInt();
			y[i] = p.nextInt();
		}
		
		double max = -1;
		for(int i=0; i<n; ++i){
			for(int j=i+1; j<n; ++j){
next:			for(int k=j+1; k<n; ++k){
					Point<Double> center = getCenter(x[i], y[i], x[j], y[j], x[k], y[k]);
					double r = getDistance(center.x, center.y, x[i], y[i]);
					boolean found = false;
					if( r <= max )
						continue;
					int triangleType = getTriangleType(x[i], y[i], x[j], y[j], x[k], y[k]);
					if(triangleType == 0){  //Right
						Point<Integer> point = getForth(x[i], y[i], x[j], y[j], x[k], y[k]);
						for(int l=0; l<n; ++l){
							if(l!=i && l!=j && l!= k){
								if(x[l] == (int)point.x && y[l]== (int)point.y){
									found = true;
									continue;
								}
								double d = getDistance(center.x, center.y, x[l], y[l]);
								if(d < r){
									continue next;
								}
							}
						}
					}else if(triangleType == 1){ //Acute
						found = true;
						for(int l=0; l<n; ++l){
							if(l!=i && l!=j && l!= k){
								double d = getDistance(center.x, center.y, x[l], y[l]);
								if(d < r){
									continue next;
								}
							}
						}
						
					}
										
					if(found)
						max = r;
				}
			}
		}
		if(max == -1.0){
			pw.print("-1");
		}else
		pw.print(max);
		
		pw.close();
	}


	
	
	public static double getDistance(double x1, double y1, double x2,
			double y2) {
		double d1 = Math.abs(x1 - x2);
		double d2 = Math.abs(y1 - y2);
		return Math.sqrt(d1*d1 + d2*d2);
	}





	public static Point<Double> getCenter(double x1, double y1, double x2,
			double y2, double x3, double y3) {
			Point<Double> c = new Point<Double>();
			double D = 2*(x1*(y2-y3) + x2*(y3-y1) + x3 * (y1 - y2));
			double Ux = ((x1*x1 + y1*y1)*(y2-y3) + (x2*x2 + y2*y2)*(y3 - y1) + (x3*x3 + y3*y3)*(y1 - y2));
			double Uy = ((x1*x1 + y1*y1)*(x3-x2) + (x2*x2 + y2*y2)*(x1 - x3) + (x3*x3 + y3*y3)*(x2 - x1));
			c.x = Ux/D;
			c.y = Uy/D;
			return c;
	}

	public static Point<Double> getSym(double x1, double y1, double x2,
			double y2) {
		if(x1 == x2 || y1 == y2){
			throw new IllegalArgumentException("segment cant be pararel to axis");
		}
		double xs = (x1+x2)/2;
		double ys = (y1+y2)/2;
		double a = (y2-y1)/(x2-x1);
		double a2 = -1/a;
		double b2 = ys + xs/a;
		Point<Double> sym = new Point<Double>();
		sym.x = a2;
		sym.y = b2;
		return sym;
	}




	public static Point<Integer> getForth(int x1, int y1, int x2, int y2, int x3, int y3) {
		int x[] = {x1, x2, x3};
		int y[] = {y1, y2, y3};
		double maxD = 0;
		int maxI = 0;
		for(int i=0; i<3; ++i){
			int j = (i+1)%3;
			double d = getDistance(x[i], y[i], x[j], y[j]);
			if(d > maxD){
				maxI = (i+2)%3;
				maxD = d;
			}
		}
		int l = (maxI +2)%3;
		int r = (maxI + 1)%3;
		int x4 = x[l]+x[r] - x[maxI];
		int y4 = y[l]+ y[r] - y[maxI];
		Point<Integer> f = new Point<Integer>();
		f.x = x4;
		f.y = y4;
		return f;
	}




	public static int getTriangleType(double x1, double y1, double x2,
			double y2, double x3, double y3) {
		double d1 = getDistance(x1, y1, x2, y2);
		double d2 = getDistance(x1, y1, x3, y3);
		double d3 = getDistance(x2, y2, x3, y3);
		double d[] = {d1, d2, d3};
		int i=0;
		double a = 0,b = 0,c = 0;
		if(!(d1 + d2 > d3 && d1 + d3 > d3 && d2 + d3 > d1)){
			return 2;
		}
		for(i = 0; i<3; ++i){
			c = d[i];
			b =  d[(i+1)%3];
			a = d[(i+2)%3];
			if(c >= a && c >=b){
				break;
			}
		}
		double cos = (-c*c  +a*a + b*b);
		if(Math.abs(cos) < 0.1){
			return 0; //Right
		}else if(cos > 0 ) //Acute
			return 1;
		else
			return 2; //Obuse
	}





	static class Point<T>{
		T x;
		T y;
		
		void swap(Point<T> p){
			T tmp = this.x;
			this.x = p.x;
			p.x = tmp;
			tmp = this.y;
			this.y = p.y;
			p.y = tmp;
		}
		
		boolean equalsOne(Point<T> p){
			return this.x.equals(p.x) || this.y.equals(p.y);
		}
	}









	static class Parser{
		
		StringTokenizer st;
		BufferedReader br;

		public Parser(InputStream is){
			this.br = new BufferedReader( new InputStreamReader(is));
			
		}
		
		public int nextInt(){
			return Integer.parseInt(nextToken());
		}
		
		public double nextDouble(){
			return Double.parseDouble(nextToken());
		}
		
		public String nextString(){
			return nextToken();
		}
		
		public int[] nextIntArray(int s){
			int[] a = new int[s];
			for(int i=0; i<s; ++i){
				a[i] = nextInt();
			}
			return a;
		}
		
		public int[][] nextIntTable(int r, int c){
			int[][] a = new int[r][c];
			for(int i=0; i<r; ++i){
				a[i] = nextIntArray(c);
			}
			return a;
		}
	
		private String nextToken() {
			if( st == null || ! st.hasMoreTokens() ){
				try{
					st = new StringTokenizer( br.readLine());
				}catch( Exception e){
					e.printStackTrace();
				}
			}
			return st.nextToken();
		}
		
	}
}


/*	public static Point<Double> getCenter(double x1, double y1, double x2,
double y2, double x3, double y3) {
Point<Double> p1 = new Point<Double>(), p2= new Point<Double>(), p3= new Point<Double>();
Point<Double> c = new Point<Double>();
p1.x = x1;
p1.y = y1;
p2.x = x2;
p2.y = y2;
p3.y = y3;
p3.x = x3;
if(p1.equalsOne(p2)){
p2.swap(p3);
if(p1.equalsOne(p2)){
	p1.swap(p3);
}
}
Point<Double> sym1 = getSym(p1.x, p1.y, p2.x, p2.y); // always ok
if(p1.equalsOne(p3)){
if(p1.x.equals(p3.x)){
	p1.swap(p2);
}
if(p1.y.equals(p3.y)){
	c.x = (p1.x +p3.x)/2;
	c.y = sym1.x*c.x + sym1.y;
	return c;
}
}
Point<Double> sym2 = getSym(p1.x, p1.y, p3.x, p3.y); //ok

c.x = (sym1.y - sym2.y)/(sym2.x - sym1.x);
c.y = sym1.x*c.x+sym1.y;
return c;
}

*/