Problem:
Score : 300 points

Problem Statement

There are N towns in a coordinate plane. Town i is located at coordinates (x_i, y_i). The distance between Town i and Town j is \sqrt{\left(x_i-x_j\right)^2+\left(y_i-y_j\right)^2}.

There are N! possible paths to visit all of these towns once. Let the length of a path be the distance covered when we start at the first town in the path, visit the second, third, \dots, towns, and arrive at the last town (assume that we travel in a straight line from a town to another). Compute the average length of these N! paths.

Constraints

2 \leq N \leq 8

-1000 \leq x_i \leq 1000

-1000 \leq y_i \leq 1000

\left(x_i, y_i\right) \neq \left(x_j, y_j\right) (if i \neq j)

(Added 21:12 JST) All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
x_1 y_1
:
x_N y_N

Output

Print the average length of the paths.
Your output will be judges as correct when the absolute difference from the judge's output is at most 10^{-6}.

Sample Input 1

3
0 0
1 0
0 1

Sample Output 1

2.2761423749

There are six paths to visit the towns: 1 → 2 → 3, 1 → 3 → 2, 2 → 1 → 3, 2 → 3 → 1, 3 → 1 → 2, and 3 → 2 → 1.

The length of the path 1 → 2 → 3 is \sqrt{\left(0-1\right)^2+\left(0-0\right)^2} + \sqrt{\left(1-0\right)^2+\left(0-1\right)^2} = 1+\sqrt{2}.

By calculating the lengths of the other paths in this way, we see that the average length of all routes is:

\frac{\left(1+\sqrt{2}\right)+\left(1+\sqrt{2}\right)+\left(2\right)+\left(1+\sqrt{2}\right)+\left(2\right)+\left(1+\sqrt{2}\right)}{6} = 2.276142...

Sample Input 2

2
-879 981
-866 890

Sample Output 2

91.9238815543

There are two paths to visit the towns: 1 → 2 and 2 → 1. These paths have the same length.

Sample Input 3

8
-406 10
512 859
494 362
-955 -475
128 553
-986 -885
763 77
449 310

Sample Output 3

7641.9817824387

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.IOException;
import java.io.InputStream;
import java.util.Arrays;
import java.util.NoSuchElementException;
import java.util.Scanner;
class FastScanner {private final InputStream in = System.in;
	private final byte[] buffer = new byte[1024];
	private int ptr = 0;
	private int buflen = 0;
	private boolean hasNextByte() {
        if (ptr < buflen) {
            return true;
        }else{
            ptr = 0;
            try {
                buflen = in.read(buffer);
            } catch (IOException e) {
                e.printStackTrace();
            }
            if (buflen <= 0) {
                return false;
            }
        }
        return true;
    }
	private int readByte() { if (hasNextByte()) return buffer[ptr++]; else return -1;}	
	private static boolean isPrintableChar(int c) { return 33 <= c && c <= 126;}
	public boolean hasNext() { while(hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++; return hasNextByte();}
	public String next() {
        if (!hasNext()) throw new NoSuchElementException();
        StringBuilder sb = new StringBuilder();
        int b = readByte();
        while(isPrintableChar(b)) {
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }
	public long nextLong() {
        if (!hasNext()) throw new NoSuchElementException();
        long n = 0;
        boolean minus = false;
        int b = readByte();
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        if (b < '0' || '9' < b) {
            throw new NumberFormatException();
        }
        while(true){
            if ('0' <= b && b <= '9') {
                n *= 10;
                n += b - '0';
            }else if(b == -1 || !isPrintableChar(b)){
                return minus ? -n : n;
            }else{
                throw new NumberFormatException();
            }
            b = readByte();
        }
    }
	public int nextInt() {
        long nl = nextLong();
        if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE) throw new NumberFormatException();
        return (int) nl;
    }
    public double nextDouble() { return Double.parseDouble(next());}
}
public class Main {
    static FastScanner scan=new FastScanner();
    static Scanner scanner=new Scanner(System.in);
    static long gcd (long a, long b) {return b>0?gcd(b,a%b):a;}
    static long lcm (long a, long b) {return a*b/gcd(a,b);}
    static int max(int a,int b) {return a>b?a:b;}
    static int min(int a,int b) {return a<b?a:b;}
    static long factorial(int i) {return i==1?1:i*factorial(i-1);}
    static int lower_bound(int a[],int key) {
        int low=0,high=a.length;
        while(low<high) {
            int mid=((high-low)/2)+low;
            if(a[mid]<=key)low=mid+1;
            else high=mid;
        }
        return high;
        }
    static int upper_bound(int a[],int key) {
        int low=0,high=a.length;
        while(low<high) {
            int mid=((high-low)/2)+low;
            if(a[mid]<key)low=mid+1;
            else high=mid;
        }
        return high;
        }
    static boolean isPrime (long n) {
        if (n==2) return true;
        if (n<2 || n%2==0) return false;
        double d = Math.sqrt(n);
        for (int i=3; i<=d; i+=2)if(n%i==0){return false;}
        return true;
    }
    static int upper_division(int a,int b) {//切り上げ(int)
        if(a%b==0) {
            return a/b;
        }
        else {
            return a/b+1;
        }
    }
    static long lupper_division(long a,long b) {//切り上げ(long)
        if(a%b==0) {
            return a/b;
        }
        else {
            return a/b+1;
        }
    }
    static long lmax(long a,long b) {return Math.max(a, b);}
    static long lmin(long a,long b) {return Math.min(a, b);}
	static int[] setArray(int a) {//配列を作る
        int b[]=new int[a];
        for(int i=0;i<a;i++) {
            b[i]=scan.nextInt();
        }
        return b;
    }
    static String reverce(String str) {//文字列を逆にする
        String strr="";
        for(int i=str.length()-1;i>=0;i--) {
            strr+=str.charAt(i);
        }
        return strr;
    }
    public static void printArray(boolean[] visited2) {//配列の空白付き出力
        for(int i=0;i<visited2.length-1;i++) {
        System.out.print(visited2[i]+" ");
        }
        System.out.println(visited2[visited2.length-1]);
    }
    public static int[][] doublesort(int[][]a) {//二次元配列のソート
        Arrays.sort(a,(x,y)->Integer.compare(x[0],y[0]));
        return a;
    }
    static long modpow(long x,long n,long mo) {//x^n%mo
        long sum=1;
        while(n>0) {
            if((n&1)==1) {
                sum=sum*x%mo;
            }
            x=x*x%mo;
            n>>=1;
        }
        return sum;
    }
    public char[] revch(char ch[]) {//char[]を逆にする
		char ret[]=new char[ch.length];
		for(int i=ch.length-1,j=0;i>=0;i--,j++) {
			ret[j]=ch[i];
		}
		return ret;
	}
    public int[] revint(int ch[]) {//int[]を逆にする
		int ret[]=new int[ch.length];
		for(int i=ch.length-1,j=0;i>=0;i--,j++) {
			ret[j]=ch[i];
		}
		return ret;
	}
    static int a=scan.nextInt();
	static double cost=0;
	static int b[][]=new int[a][2];
	public static void main(String[] args) {
		for(int i=0;i<a;i++) {
			b[i][0]=scan.nextInt();
			b[i][1]=scan.nextInt();
		}
		long uo=factorial(a)/a;
		for(int i=0;i<a;i++) {
			for(int j=0;j<a;j++) {
				if(i==j)continue;
				long z=(b[i][0]-b[j][0])*(b[i][0]-b[j][0])+(b[i][1]-b[j][1])*(b[i][1]-b[j][1]);
				cost+=Math.sqrt(z)*uo;
			}
		}
		System.out.println(cost/factorial(a));
	}
}