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 C (GCC 9.2.1) (judge verdict: Accepted)


#pragma warning(disable:4996)

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#define _USE_MATH_DEFINES
#include <math.h>
#include <float.h>

#pragma region 定義
typedef long long  ll;
typedef unsigned long long  ull;


#define _itoa(A,N) sprintf(A, "%d", N);

int i_dsort(const void* a, const void* b);
int i_asort(const void* a, const void* b);

int  _gcd(int a, int b);
int  _swp(int* a, int* b);
int _cknum(char* a, int n);
int _atoi(char* s, int len);

int s_asort(const void* a, const void* b);
int s_dsort(const void* a, const void* b);

//昇順
int s_asort(const void* a, const void* b) {
	return(strcmp((char*)a, (char*)b));
}
int s_dsort(const void* a, const void* b) {
	return(strcmp((char*)b, (char*)a));
}

int i_dsort(const void* a, const void* b) {
	return(*(int*)b - *(int*)a);
}
int i_asort(const void* a, const void* b) {
	return(*(int*)a - *(int*)b);
}

int i_gcd(int a, int b);
int i_gcd(int a, int b) {
	if (!b)return a;
	return i_gcd(b, a % b);
}
int i_lcm(int a, int b);
int i_lcm(int a, int b) {
	return (a * b) / i_gcd(a, b);
}
int ll_gcd(ll a, ll b);
int ll_gcd(ll a, ll b) {
	if (!b)return a;
	return ll_gcd(b, a % b);
}
int ll_lcm(ll a, ll b);
int ll_lcm(ll a, ll b) {
	return (a * b) / ll_gcd(a, b);
}

// puts("Yes\n") puts("No\n")
// scanf("%d.%d") 浮動小数点入力を整数２つで得る


//#define pai  3.1415926535 
//#define  _USE_MATH_DEFINES でM_PIが使える

#define deg_rad(X)  (X*(M_PI/180))


int _swp(int* a, int* b)
{
	int tmp;
	tmp = *b; *b = *a; *a = tmp;
	return 0;
}
#define _abs(x) ((x)>0?(x):-(x))
#define _min(x,y) ((x)<(y)?(x):(y))
#define _max(x,y) ((x)<(y)?(y):(x))

int _cknum(char* a, int n) {
	int i;
	char t = '0';

	for (i = 0; i < n; i++) {
		if (a[i] < '0' || a[i]>'9') return 1;
	}
	return 0;
}


int _atoi(char* s, int len) {
	char tmp[20];
	memcpy(tmp, s, len);
	tmp[len] = 0x00;
	return (atoi(tmp));
}

//素因数分解　pf素数が入る　pc 素数の数
//ll _pfact(ll a);
//static ll pf[100000000];
//static ll pc;
//
//ll _pfact(ll a) {
//	long i, r;
//	if (a % 2 == 0) {
//		pf[pc] = 2; pc++;
//		return(_pfact(a / 2));
//	}
//	r = sqrt(a);
//	for (i = 3; i <= r; i += 2) {
//		if (a % i == 0) {
//			pf[pc] = i; pc++;
//			return(_pfact(a / i));
//		}
//	}
//	if (a != 1) {
//		pf[pc] = a; pc++;
//	}
//	return 0;
//
//}

//同じものの最初の文字をNULLにして降順
int _sort(const void* a, const void* b);
int _sort(const void* a, const void* b) {
	char rc;

	rc = strcmp((char*)b, (char*)a);
	if (rc == 0) {
		*(char*)a = 0x00;
		return(1);
	}
	return(rc);
}
// 立っている ビットの数
int bitcount(unsigned int uc);
int bitcount(unsigned int uc)
{
	int bit;

	for (bit = 0; 0 != uc; uc = (unsigned int)(uc >> 1))
		if (0 != (uc & 1))++bit;

	return bit;
}//bitco

//10進数の桁数の総和
int _sumdig(int n);
int _sumdig(int n) {
	int sum = 0;
	while (n > 0) {	sum += n % 10;n /= 10;}
	return(sum);
}
int combi(int n, int r);
int combi(int n, int r)
{
	if (r == 0 || r == n) return 1;
	return combi(n - 1, r) + combi(n - 1, r - 1);
}


#define _rnd(a,b)    ((a+b-1)/b) //　A/Bの余りを繰り上げる
#define _abs(x) ((x)<0 ? -(x) : (x))
#define _MAX 200000
#pragma endregion

// ABC145 C - Average Length
//int main(void) {
//	int n,i, x[9],y[9],cnt=0;
//	double  sum=0;
//
//	scanf("%d", &n);
//	for (i = 0; i < n; i++) 
//		scanf("%d %d", &x[i], &y[i]);
//
//		for(i=0;i<n-1;i++)
//			for (int j = i + 1; j < n; j++) {
//				sum += hypot(x[i] - x[j], y[i] - y[j]);
//				cnt++;
//				printf("%d %lf\n", cnt, sum);
//			}
//	printf("%lf\n",sum/cnt);
//	return 0;
//}

// C - Sugar Water
//int main(void) {
//	int a, b, c, d, e, f;
//	int mn, mx;
//	scanf("%d%d%d%d%d%d", &a, &b, &c, &d, &e, &f);
//	
//	int tmp,i;
//	for (i = 1;; i++) {
//		tmp = i * 100 + i * e;
//		if (tmp > f) break;
//		if (i % a && i % b)continue;
//		if (i % c && i % d)continue;
//		break;
//	}
//
//	printf("%d %d", i * 100, tmp);
//	return 0;
//}

//D - Road to Millionaire
//static ll  a[81];
//int main(void) {
//	int n,i;
//	ll  c=1000,ans=1000,tmp,cnt=0;
//
//	scanf("%d", &n);
//
//	for(i=0;i<n;i++)
//	    scanf("%lld", &a[i]);
//  
//	tmp = 210;
//	for (i = 0; i < n; i++) {
//		if (tmp == a[i]) continue;
//
//		if (tmp < a[i]) {//売り
//			if (a[i] < a[i + 1])continue;
//			c += cnt * a[i]; 
//			tmp = a[i];
//			ans = _max(c, ans);
//			printf("<S＞i:%d a[i]:%lld ans:%lld \n",i, a[i], ans);
//		}
//		else {            //買い
//3			if (a[i] > a[i + 1])continue;
//			cnt = c / a[i];
//			c = c % a[i];
//			tmp = a[i];
//			printf("<B>i:%d a[i]:%lld  %lld\n", i,a[i],c);
//
//		}
//	}
//	printf("%lld\n",ans);
//	return 0;
//}
//

//
////AGC 011 A-Airport Bus
//double d_asort(const void* a, const void* b);
//double d_asort(const void* a, const void* b) {
//	return(*(double*)a - *(double*)b);
//}
//double t[100001];
//int main(void) {
//	int n,c,k;
//	
//	scanf("%d%d%d", &n,&c,&k);
//	for (int i = 0; i < n; i++) 
//		scanf("%lf", &t[i]);
//	
//	qsort(t, n, sizeof(double), d_asort);
//	
//	int cnt = 0;
//	double  f;
//	for (int i = 0; i < n; i++) {
//	
//
//
//		ans += (a[i] - tmp) * (a[i] - tmp);
//		
//	printf("%d\n", ans);
//}

//C - Average Length
static double x[9], y[9];

int main(void) {
	int i,n;
	double ans=0;

	scanf("%d",&n);
	for (i = 0; i < n; i++) 
	     scanf("%lf%lf", &x[i],&y[i]);
	x[n] = x[0]; y[n] = y[0];

	double tmp=0;
	int j, cnt = 0;
	for (i = 0; i < n - 1; i++) {
		for (j = i + 1; j < n; j++) {
			ans += sqrt(pow(x[i] - x[j], 2) + pow(y[i] - y[j], 2));
			cnt++;
		}
	}

	printf("%.7lf \n",ans/cnt*(n-1));
	
	return 0;
}