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 (Python):
import math

n = int(input())
l = [list(map(int, input().split())) for _ in range(n)]

sum = 0
for i in range(n):
    for j in range(i+1, n):
        sum += math.sqrt((l[i][0]-l[j][0])**2 + (l[i][1]-l[j][1])**2)

ans = sum*2/n

print(ans)

Solution (Python):
n=int(input())
xy=[list(map(int,input().split())) for i in range(n)]
sum = 0
for i in range(n):
    for j in range(n):
        sum += ((xy[i][0]-xy[j][0])**2+(xy[i][1]-xy[j][1])**2)**0.5
print(sum/n)

Solution (Python):
import math

n=int(input())
L=[list(map(int,input().split())) for _ in range(n)]
D=0
for i in range(n-1):
    for j in range(i+1,n):
        D += 2*math.factorial(n-1)*(((L[i][0]-L[j][0])**2 
        + (L[i][1]-L[j][1])**2)**0.5)
print(D/math.factorial(n))

Solution (Python):
import itertools
import math


n =int(input())
xy= [tuple(map(int,input().split())) for i in range(n)]

nfact = math.factorial(n)

sum = 0

perm = list(itertools.permutations(xy))

for i in range(nfact):
    xy_ = perm[i]
    dist = 0
    for j in range(0,n-1):
        x1, y1 = xy_[j]
        x2, y2 = xy_[j+1]
        dist += ( (x1-x2)**2 + (y1-y2)**2 )**0.5
    sum += dist

ans = sum/nfact

print(ans)

Solution (Python):
def main(sample_file = ''):

    """ convenient functions
    
    
    
    
    
    """

    """convenient decorator
    
    
        
        
        
        
        
        
        
        
        
        
    """
    
    
    import sys
    sys.setrecursionlimit(10**7)
    from itertools import accumulate, combinations, permutations, product 
    
    from math import factorial, ceil, floor, sqrt
    def factorize(n):
        """return the factors of the Arg and count of each factor
        
        Args:
            n (long): number to be resolved into factors
        
        Returns:
            list of tuples: factorize(220) returns [(2, 2), (5, 1), (11, 1)]
        """
        fct = []  
        b, e = 2, 0  
        while b * b <= n:
            while n % b == 0:
                n = n // b
                e = e + 1
            if e > 0:
                fct.append((b, e))
            b, e = b + 1, 0
        if n > 1:
            fct.append((n, 1))
        return fct
    def combinations_count(n, r):
        """Return the number of selecting r pieces of items from n kinds of items.
        
        Args:
            n (long): number
            r (long): number
        
        Raises:
            Exception: not defined when n or r is negative
        
        Returns:
            long: number
        """
        
        if n < 0 or r < 0:
            raise Exception('combinations_count(n, r) not defined when n or r is negative')
        if n - r < r: r = n - r
        if r < 0: return 0
        if r == 0: return 1
        if r == 1: return n
        numerator = [n - r + k + 1 for k in range(r)]
        denominator = [k + 1 for k in range(r)]
        for p in range(2,r+1):
            pivot = denominator[p - 1]
            if pivot > 1:
                offset = (n - r) % p
                for k in range(p-1,r,p):
                    numerator[k - offset] /= pivot
                    denominator[k] /= pivot
        result = 1
        for k in range(r):
            if numerator[k] > 1:
                result *= int(numerator[k])
        return result
    def combinations_with_replacement_count(n, r):
        """Return the number of selecting r pieces of items from n kinds of items allowing individual elements to be repeated more than once.
        
        Args:
            n (long): number
            r (long): number
        
        Raises:
            Exception: not defined when n or r is negative
        
        Returns:
            long: number
        """
        if n < 0 or r < 0:
            raise Exception('combinations_with_replacement_count(n, r) not defined when n or r is negative')
        elif n == 0:
            return 1
        else:
            return combinations_count(n + r - 1, r)
    from bisect import bisect_left, bisect_right
    from collections import deque, Counter, defaultdict 
    from heapq import heapify, heappop, heappush, heappushpop, heapreplace,nlargest,nsmallest 
    from copy import deepcopy, copy 
    import operator
    from operator import itemgetter 
    
    
    from functools import reduce, lru_cache
    def chmin(x, y):
        """change minimum
        if x > y, x = y and return (x, True).
        convenient when solving problems of dp[i]
        
        Args:
            x (long): current minimum value
            y (long): potential minimum value
        
        Returns:
            (x, bool): (x, True) when updated, else (x, False)
        """
        if x > y:
            x = y
            return (x, True)
        else:
            return (x, False)
    def chmax(x, y):
        """change maximum
        if x < y, x = y and return (x, True).
        convenient when solving problems of dp[i]
        
        Args:
            x (long): current maximum value
            y (long): potential maximum value
        
        Returns:
            (x, bool): (x, True) when updated, else (x, False)
        """
        if x < y:
            x = y
            return (x, True)
        else:
            return (x, False)

    from fractions import gcd 
    def gcds(numbers):
        return reduce(gcd, numbers)
    def lcm(x, y):
        return (x * y) // gcd(x, y)
    def lcms(numbers):
        return reduce(lcm, numbers, 1)
    def make_divisors(n, reversed=False):
        """create list of divisors
        
        Args:
            number (int): number from which list of divisors is created
            reversed (bool, optional): ascending order if False. Defaults to False.
        
        Returns:
            list: list of divisors
        """
        divisors = set()
        for i in range(1, int(n**0.5)+1):
            if n % i == 0:
                divisors.add(i)
                divisors.add(n//i)
        return sorted(list(divisors),reverse=reversed)
    
    
    
    INF = 10 ** 18
    MOD = 10 ** 9 + 7
    modpow = lambda a, n, p = MOD: pow(a, n, p) 
    def modinv(a, p = MOD):
        
        
        return modpow(a, p-2, p)
    def modinv_list(n, p = MOD):
        if n <= 1:
            return [0,1][:n+1]
        else:
            inv_t = [0,1]
            for i in range(2, n+1):
                inv_t += [inv_t[p % i] * (p - int(p / i)) % p]
            return inv_t
    def modfactorial_list(n, p = MOD):
        if n == 0:
            return [1]
        else:
            l = [0] * (n+1)
            tmp = 1
            for i in range(1, n+1):
                tmp = tmp * i % p
                l[i] = tmp
            return l
    def modcomb(n, k, fac_list = [], p = MOD):
        
        
        from math import factorial
        if n < 0 or k < 0 or n < k: return 0
        if n == 0 or k == 0: return 1
        if len(fac_list) <= n:
            a = factorial(n) % p
            b = factorial(k) % p
            c = factorial(n-k) % p
        else:
            a = fac_list[n]
            b = fac_list[k]
            c = fac_list[n-k]
        return (a * modpow(b, p-2, p) * modpow(c, p-2, p)) % p
    def modadd(a, b, p = MOD):
        return (a + b) % MOD
    def modsub(a, b, p = MOD):
        return (a - b) % p
    def modmul(a, b, p = MOD):
        return ((a % p) * (b % p)) % p
    def moddiv(a, b, p = MOD):
        return modmul(a, modpow(b, p-2, p))

    class UnionFindTree:
        """union find tree class
        TODO: fix this description...
        how to use (example):
        >>  uf = UnionFindTree(N) 
        >>  if uf.find_root(a) == uf.find_root(b):
        >>      do something
        >>  else:
        >>      do something
        >>      uf.unite(a, b)
        """
        def __init__(self, N):
            self.root = [-1] * (N+1)
            self.rank   = [0]  * (N+1)
            self.connected_num = [1] * (N+1)
    
        def find_root(self,x):
            root = self.root
            while root[x] != -1:
                x = root[x]
            return x
    
        def unite(self,x,y):
            root = self.root
            rank = self.rank
            connected_num = self.connected_num
            find_root = self.find_root
    
            rx = find_root(x)
            ry = find_root(y)
            if rx != ry:
                if rank[rx] < rank[ry]:
                    root[rx] = ry
                    rx,ry = ry,rx
                else:
                    if rank[rx] == rank[ry]:
                        rank[rx] += 1
                    root[ry] = rx       
                connected_num[rx] += connected_num[ry]

    
    
    
    
    

    def BellmanFord(N, M, ABC, vertex_start, vertex_end, value_if_inf = -1, find_shortest = False):
        """to calculate furthest or shortest length between vertex_start and vertex_end using BellmanFord algorithm
        
        Args:
            N (int): number of vertices
            M (int): number of edges
            ABC (list): [(ai, bi, ci) for _ in range(N)] where i-th edge is directed from vertex ai to vertex bi and the length is ci 
            vertex_start (int): start vertex. usually use 0.
            vertex_end (int): end vertex. usually use N-1.
            value_if_inf (int or string as you like, optional): value you want when the furthest (or shortest) distance is infinite (or -infinite). Defaults to -1.
            find_shortest (bool, optional): choose False to find furthest path. Defaults to False.
        
        Returns:
            int or string: normally int (but can be str if you set value_if_inf to str)
            
        Example:
                N, M, P = R()
                ABC = [R() for _ in range(M)]
                ABC = [(a-1, b-1, c-P) for a, b, c in ABC]
                print(BellmanFord(N, M, ABC, 0, N-1, value_if_inf = 'inf'))

        """

        def make_reachable_list(N, M, ABC, vertex_start, vertex_end):
            reachable_to_direct = defaultdict(list)
            reachable_from_direct = defaultdict(list)
            reachable_from_start = [False] * N
            reachable_to_end = [False] * N
            reachable_from_start[vertex_start] = True
            reachable_to_end[vertex_end] = True
            reachable_from_both_sides = [False] * N
            dfs_from_start = []
            dfs_to_end = []
            for a, b, c in ABC:
                reachable_to_direct[a].append(b)
                reachable_from_direct[b].append(a)
                if a == vertex_start:
                    dfs_from_start.append(b)
                    reachable_from_start[b] = True
                if b == vertex_end:
                    dfs_to_end.append(a)
                    reachable_to_end[a] = True
            while dfs_from_start:
                v = dfs_from_start.pop()
                for i in reachable_to_direct[v]:
                    if not reachable_from_start[i]:
                        reachable_from_start[i] = True
                        dfs_from_start.append(i)
            while dfs_to_end:
                v = dfs_to_end.pop()
                for i in reachable_from_direct[v]:
                    if not reachable_to_end[i]:
                        reachable_to_end[i] = True
                        dfs_to_end.append(i)
            for i in range(N):
                reachable_from_both_sides[i] = reachable_from_start[i] and reachable_to_end[i]
            return reachable_from_both_sides
        
        reachable_from_both_sides = make_reachable_list(N, M, ABC, vertex_start, vertex_end)
        
        if find_shortest:
            dist = [INF for i in range(N)]
        else:
            dist = [-INF for i in range(N)]
        
        dist[vertex_start] = 0
        for i in range(N):
            updated = False
            for a, b, c in ABC:
                if not reachable_from_both_sides[a]:
                    continue
                elif find_shortest:
                    update_condition = dist[a] + c < dist[b]
                else:
                    update_condition = dist[a] + c > dist[b]
                if dist[a] != INF and update_condition:
                    dist[b] = dist[a] + c
                    updated = True
                    if i == N-1:
                        return value_if_inf
            if not updated:
                break
        return dist[vertex_end]

    """ initialize variables and set inputs
    
        
        
    
        
        
        
        
        
        
        
    
        
        
        
        
    
        
        
    """

    
    r = lambda: sys.stdin.readline().strip()
    r_int = lambda: int(r())
    R = lambda: list(map(int, r().split()))
    Rmap = lambda: map(int, r().split())
    Rfloat = lambda: list(map(float, r().split()))
    Rtuple = lambda: tuple(map(int, r().split()))

    """ how to treat input
    
    
    
    
    
    
    
    """

    
    if sample_file:
        sys.stdin = open(sample_file)
        
    
    

    N = r_int()
    XY = [R() for i in range(N)]
    cnt = 0
    s = 0
    for i in range(N):
        for j in range(N):
            if i != j:
                s += sqrt((XY[i][0]-XY[j][0])**2+(XY[i][1]-XY[j][1])**2)
                cnt += 1
    print(s/cnt*(N-1))
    
    
    

    """memo: how to use defaultdict of list
    
    Dic = defaultdict(list)
    
    Dic[x].append(y)
    
    for k, v in Dic.items():
    """
    
    """memo: how to solve binary problems
    
    >>> a = 5
    >>> bin_str_a = format(a, '
    >>> print(bin_str_a)
    0b0101 
    """
    
    """memo: how to solve the problem
    creating simple test/answer
    greed
    simple dp
    graph
    """

if __name__ == '__main__':
    main()

Solution (Python):
import itertools
n = int(input())
t = 1
for i in range(1,n+1):
  t *= i
L = []
for i in range(n):
  L.append(list(map(int,input().split())))
seq = []
for i in range(n):
  seq.append(i)
K = list(itertools.permutations(seq))
ans = 0
keiro = []
for i in range(n):
  T = [0 for j in range(n)]
  keiro.append(T)
for i in range(n):
  for j in range(n):
    keiro[i][j] = ((L[i][0]-L[j][0])**2+(L[i][1]-L[j][1])**2)**0.5
for i in range(len(K)):
  cur = 0
  for j in range(len(K[i])-1):
    cur += keiro[K[i][j]][K[i][j+1]]
  ans += cur
print(ans/t)

Solution (Python):
n = int(input())
a = [[int(i) for i in input().split()] for _ in range(n)]
dp = {}
ans = 0
for i in range(n):
    for k in range(i+1,n):
        dp[(i,k)] = (((a[i][0]-a[k][0])**2 + (a[i][1]-a[k][1])**2)**0.5)
        ans += dp[(i,k)]
print(ans*2/n)

Solution (Python):
n = int(input())
xy = [[int(i) for i in input().split()]for j in range(n)]

ans = 0

for i in range(n):
    for j in range(i+1,n):
        ans += ((xy[i][0] - xy[j][0]) ** 2 + (xy[i][1] - xy[j][1]) ** 2) ** 0.5
        
print(ans*4/(n*2))

Solution (Python):
import math


def solve(n, x_list, y_list):
    d_total = 0.0
    for i in range(n - 1):
        for j in range(i + 1, n):
            d_total += math.sqrt((x_list[i] - x_list[j]) ** 2 + (y_list[i] - y_list[j]) ** 2)
    return d_total * 2 / n


def main():
    n = int(input())
    x_list = [0] * n
    y_list = [0] * n
    for i in range(n):
        x, y = map(int, input().split())
        x_list[i] = x
        y_list[i] = y
    res = solve(n, x_list, y_list)
    print(res)


def test():
    assert abs(solve(3, [0, 1, 0], [0, 0, 1]) - 2.2761423749) < 0.000001
    assert abs(solve(2, [-879, -866], [981, 890]) - 91.9238815543) < 0.000001
    assert abs(solve(
        8, [-406, 512, 494, -955, 128, -986, 763, 449], [10, 859, 362, -475, 553, -885, 77, 310]
    ) - 7641.9817824387) < 0.000001


if __name__ == "__main__":
    test()
    main()

Solution (Python):
import math
import itertools

N = int(input())
XY = [list(map(int,input().split())) for _ in range(N)]

t = 2*math.factorial(N-1)

ans = 0
for p1,p2 in itertools.combinations(XY,2):
    x1,y1 = p1
    x2,y2 = p2
    l = ((x1-x2)**2+(y1-y2)**2)**.5
    ans += l*t
ans /= math.factorial(N)
print(ans)

Solution (Python):
import sys
input = sys.stdin.readline

import itertools
import math

def main():
    N = int(input())
    X =[]
    Y =[]
    for _ in range(N):
        x, y = [int(x) for x in input().split()]
        X.append(x)
        Y.append(y)

    jun = list(itertools.permutations(range(N)))
    to = 0
    for i in jun:
        for j in range(N - 1):
            to += math.sqrt((X[i[j + 1]] - X[i[j]]) ** 2 + (Y[i[j + 1]] - Y[i[j]]) ** 2)

    print(to / (len(jun)))







if __name__ == '__main__':
    main()

Solution (Python):
N = int(input())
place = []
for _ in range(N):
    place.append(tuple(map(int, input().split())))

length = 0
for i in range(N):
    for j in range(i):
        length += ((place[i][0] - place[j][0]) ** 2 + (place[i][1] - place[j][1]) ** 2) ** (1 / 2)

print(length * 2 / N)

Solution (Python):
def d(x,y):
    return ((x[0]-y[0])**2+(x[1]-y[1])**2)**(1/2)

import itertools
ans=0
k=1
n= int(input())
xy=[list(map(int,input().split())) for i in range(n)]
l=[i for i in range(n)]
for v in itertools.permutations(l, n):
    for i in range(n-1):
        ans+=d(xy[v[i]],xy[v[i+1]])
for i in range(1,n+1):
    k*=i
print(ans/k)

Solution (Python):
import sys
sys.setrecursionlimit(10000000)
import itertools


def calc_distance(cord1, cord2):
    x1, y1 = cord1
    x2, y2 = cord2

    return ((x1 - x2) ** 2 + (y1 - y2) ** 2) ** 0.5


def main():
    N = int(input())
    cords = []
    for _ in range(N):
        x, y = map(int,input().split())
        cords.append((x, y))
    
    n_lists = [i for i in range(N)]
    sum_distance = 0
    num = 0
    for order in itertools.permutations(n_lists):
        distance = 0
        for i in range(1, N):
            from_, to_ = order[i - 1], order[i]
            distance += calc_distance(cords[from_], cords[to_])
        sum_distance += distance
        num += 1
    
    sum_distance /= num
    print(sum_distance)

    




if __name__ == '__main__':
    main()

Solution (Python):
N = int(input())
city = []

for i in range(N):
    city.append(list(map(int, input().split())))

sum = 0

for i in range(N):
    for j in range(N):
        if i > j:
            sum += ((city[i][0]-city[j][0])**2 + (city[i][1]-city[j][1])**2) ** (1/2)

ave = 2 * sum / N
print(ave)

Solution (Python):

from itertools import permutations
import numpy as np
n = int(input())
machis = []
for _ in range(n):
    x, y = list(map(int, input().split()))
    machis.append((x, y))
kumi = permutations(machis)

nagasa = []
for k in list(kumi):
    kwa = 0
    for i in range(len(k)-1):
        x, y = k[i]
        nx, ny = k[i+1]
        kwa += np.sqrt((x-nx)**2 + (y-ny)**2)
    nagasa.append(kwa)
print(np.mean(nagasa))

Solution (Python):
import itertools
import math

def makelist(n, m):
    return [[0 for _ in range(m)] for _ in range(n)]


N = int(input())
hoge = [0]*N
for i in range(N):
    x, y = list(map(int, input().split()))
    hoge[i] = (x, y)

lsts = list(itertools.permutations(range(N)))

ans = 0
b = len(lsts)

for lst in lsts:
    lst = list(lst)

    for i in range(N-1):
        (x1, y1) = hoge[lst[i]]
        (x2, y2) = hoge[lst[i+1]]
        s = math.pow(x1-x2, 2)
        t = math.pow(y1-y2, 2)

        ans += math.sqrt(s + t)

ans /= b

print(ans)

Solution (Python):
import math

N = int(input())
T = [tuple(map(int, input().split())) for i in range(N)]

S = 0
for i in range(N - 1):
    for j in range(i, N):
        S += math.sqrt((T[i][0] - T[j][0]) ** 2 + (T[i][1] - T[j][1]) ** 2)
print(S * 2 / N)

Solution (Python):
N = int(input())
xy = [list(map(int, input().split())) for _ in range(N)]

import math

dist = [[0] * N for _ in range(N)]
for i in range(N - 1):
    xi, yi = xy[i]
    for j in range(i + 1, N):
        xj, yj = xy[j]
        dist[i][j] = math.sqrt((xi - xj) ** 2 + (yi - yj) ** 2)
        dist[j][i] = dist[i][j]

import itertools

ans = 0
cases = list(itertools.permutations(range(N)))
for case in cases:
    for idx in range(N - 1):
        ans += dist[case[idx]][case[idx + 1]]
ans /= len(cases)

print(ans)

Solution (Python):
def d(a,b,c,d):
    return ((a-b)**2+(c-d)**2)**(1/2)

n = int(input())
s = []
for i in range(n):
    s.append([int(x) for x in input().split()])
f = 0
for dis in s:
    for ris in s:
        f += d(dis[0], ris[0], dis[1], ris[1])

print(str(f/n))

Solution (Python):

import sys, itertools, math


def solve(N: int, x: "List[int]", y: "List[int]"):
    f = 1
    for i in range(2, N+1):
        f *= i
    sm = 0
    for (s, t) in itertools.combinations(range(N), 2):
        sm += math.sqrt((x[s] - x[t])**2 + (y[s] - y[t])**2) * f / N * 2
    print(sm / f)
    return



def main():
    def iterate_tokens():
        for line in sys.stdin:
            for word in line.split():
                yield word
    tokens = iterate_tokens()
    N = int(next(tokens))  
    x = [int()] * (N)  
    y = [int()] * (N)  
    for i in range(N):
        x[i] = int(next(tokens))
        y[i] = int(next(tokens))
    solve(N, x, y)

if __name__ == '__main__':
    main()

Solution (Python):
import itertools
import math

n = int(input())

x = []
y = []
for i in range(n):
    xi, yi = map(int, input().split())
    x.append(xi)
    y.append(yi)

def calcdist(x0, y0, x1, y1):
    return math.sqrt((x0 - x1)**2 + (y0 - y1)**2)

dist_sum = 0
for order in itertools.permutations(range(n), n):
    for i in range(n-1):
        dist_sum += calcdist(x[order[i]], y[order[i]], x[order[i+1]], y[order[i+1]])

print(dist_sum / math.factorial(n))

Solution (Python):
import itertools


def average_distance(N, points):
    order = list(itertools.permutations(points))
    distance = []
    for ord in order:
        d = 0
        for i in range(len(ord) - 1):
            d += ((ord[i][0] - ord[i + 1][0]) ** 2 + (ord[i][1] - ord[i + 1][1]) ** 2) ** (1 / 2)
        distance.append(d)
    return sum(distance) / len(distance)


N = int(input())
town = []
for i in range(N):
    town.append(list(map(int, input().split())))
res = average_distance(N, town)
print(res)

Solution (Python):
import itertools
import math

n = int(input())
m = []
items = []
for i in range(n):
    m.append([int(x) for x in input().split(' ')])
    items.append(i)



total = 0
count = 0
for perms in itertools.permutations(items):
    
    d = 0
    for i in range(n - 1):
        dx = m[perms[i]][0] - m[perms[i + 1]][0]
        dy = m[perms[i]][1] - m[perms[i + 1]][1]
        d += math.sqrt(dx * dx + dy * dy)
    
    total += d
    count += 1

print(total / count)

Solution (Python):
import itertools
n=int(input())
xy=[[int(i) for i in input().split()] for _ in range(n)]
l=list(itertools.permutations(range(n)))
sum = 0
for lis in l:
    for i in range(n-1):
        sum += ((xy[lis[i]][0] - xy[lis[i+1]][0])**2 + (xy[lis[i]][1] - xy[lis[i+1]][1])**2)**(1/2)
print(sum/len(l))

Solution (Python):
import math
N = int(input())
sum = math.factorial(N)
X = [0] * N
Y = [0] * N
ans = 0
for i in range(N):
    X[i], Y[i] = map(int,input().split())
for i in range(N):
    x1 = X[i]
    y1 = Y[i]
    for j in range(i+1,N):
        x2 = X[j]
        y2 = Y[j]
        ans += (((x1-x2)**2+(y1-y2)**2)**(1/2)) * (sum//N) * 2
print(ans/sum)

Solution (Python):
N = int(input())
L = [tuple(map(int, input().split())) for n in range(N)]
Roads = []
for n in range(N):
    for m in range(n + 1, N):
        distance = ((L[n][0] - L[m][0]) ** 2 + (L[n][1] - L[m][1]) ** 2) ** 0.5
        Roads.append(distance)
mean = sum(Roads) / len(Roads)
print(mean * (N - 1))

Solution (Python):
n = int(input())
xy = [list(map(int, input().split())) for _ in range(n)]
import math

ans = 0
for a in xy:
  t = 0
  for b in xy:
    if a == b:
      continue
    t += math.sqrt((b[1] - a[1])**2 + (b[0] - a[0]) **2)
  ans += t  
print(ans/n)

Solution (Python):
import itertools
n = int(input())
p = [list(map(int,input().split())) for _ in range(n)]
order = list(itertools.permutations(range(n)))
length = 0

for o_list in order:
  start_x,start_y = p[o_list[0]]
  for o in o_list[1:]:
    x,y = p[o]
    length += ((start_x-x)**2+(start_y-y)**2)**(1/2)
    start_x,start_y = x,y
print(length/len(order))

Solution (Python):

from collections import defaultdict,deque
from heapq import heappush, heappop
from bisect import bisect_left, bisect_right
import sys, random, itertools, math
sys.setrecursionlimit(10**5)
input = sys.stdin.readline
sqrt = math.sqrt
def LI(): return list(map(int, input().split()))
def LF(): return list(map(float, input().split()))
def LI_(): return list(map(lambda x: int(x)-1, input().split()))
def II(): return int(input())
def IF(): return float(input())
def LS(): return list(map(list, input().split()))
def S(): return list(input().rstrip())
def IR(n): return [II() for _ in range(n)]
def LIR(n): return [LI() for _ in range(n)]
def FR(n): return [IF() for _ in range(n)]
def LFR(n): return [LI() for _ in range(n)]
def LIR_(n): return [LI_() for _ in range(n)]
def SR(n): return [S() for _ in range(n)]
def LSR(n): return [LS() for _ in range(n)]
mod = 1000000007
inf = float('INF')


def solve():
    n = II()
    xy = LIR(n)
    full = itertools.permutations(range(n), n)
    tmp = 0
    ans = 0
    for fu in full:
        i = 0
        bx, by = 0, 0
        for f in fu:
            if i == 0:
                bx, by = xy[f][0], xy[f][1]
                i = 1
                continue
            x, y = xy[f][0], xy[f][1]
            ans += sqrt((bx - x) ** 2 + (by - y) ** 2)
        tmp += 1
    print(ans/tmp)

    return



if __name__ == '__main__':
    solve()

Solution (Python):
n=int(input())
x=[0]*n
y=[0]*n
for i in range(n):
  x[i],y[i]=map(int,input().split())
count=0
for i in range(n):
  for j in range(i+1,n):
    count+=((x[i]-x[j])**2+(y[i]-y[j])**2)**0.5
print(count*2/n)

Solution (Python):
from math import sqrt

n = int(input())

points = [list(map(int, input().split())) for _ in range(n)]


sum_r = 0
for i in range(n):
    for j in range(i+1, n):
        a = points[i]
        b = points[j]
        sum_r += sqrt(pow(a[0]-b[0], 2) + pow(a[1] - b[1], 2))

print(sum_r*2/n)

Solution (Python):

from itertools import permutations
from math import sqrt, factorial


def main():
    n = int(input())

    points = [tuple(map(float, input().split())) for _ in range(n)]

    total_distance = 0.0
    for sample in permutations(range(n), n):
        total_distance += sum(sqrt((points[sample[i]][0] - points[sample[i + 1]][0])**2 + (points[sample[i]][1] - points[sample[i + 1]][1])**2) for i in range(n - 1))

    print(total_distance / factorial(n))


if __name__ == '__main__':
    main()

Solution (Python):
import math
n=int(input())
xy=[]

for i in range(n):
  xy.append(list(map(int,input().split())))

sum=0
count=0
for i in range(len(xy)):
  for j in range(len(xy)):
    if i==j:
      continue
    sum+=math.sqrt((xy[i][0]-xy[j][0])**2+(xy[i][1]-xy[j][1])**2)
  count+=1
print(sum/count)

Solution (Python):
import sys
input = sys.stdin.readline
n=int(input())
XY=[]
for i in range(n):
  x,y=map(int,input().split())
  XY.append((x,y))
ans=0

def dist(a,b):
  ax,ay=a
  bx,by=b
  return ((ax-bx)**2+(ay-by)**2)**0.5

import itertools
for c in itertools.combinations(range(n),2):
  ans+=dist(XY[c[0]],XY[c[1]])
ans=ans*2/n
print(ans)

Solution (Python):
n = int(input())
l = [[0, 0] for _ in range(n)]

for i in range(n):
  x, y = map(float, input().split())
  l[i][0] = x
  l[i][1] = y


import itertools
import math
seq = range(0, n)
seqs = list(itertools.permutations(seq))
ans = 0
for c in seqs:
  t = 0
  for i in range(len(c)-1):
    z1 = c[i]
    z2 = c[i+1]
    t += math.sqrt((l[z1][0] - l[z2][0])**2+(l[z1][1] - l[z2][1])**2)
  ans += t

print(ans/len(seqs))

Solution (Python):
def two_int():
    N, K = map(int, input().split())
    return N,K

def one_int():
    return int(input())

def one_str():
    return input()

def many_int():
    return list(map(int, input().split()))

import itertools as it

N=one_int()

zahyous = [ two_int() for i in range(N)]

all_sums = 0
t = list(it.permutations(zahyous,N))
for i in t:
    sums=0
    for j in range(len(i)-1):
        sums += ( (i[j][0]-i[j+1][0])**2 +(i[j][1]-i[j+1][1])**2 ) ** (1/2)
    all_sums += sums/len(t)

print(all_sums)

Solution (Python):
import sys
import math
sys.setrecursionlimit(10**9)
INF=10**18
def input():
    return sys.stdin.readline().rstrip()

def main():
    N=int(input())
    x=[0]*N
    y=[0]*N
    for i in range(N):
        x[i],y[i]=map(int,input().split())
    kaijou=1
    for i in range(1,N+1):
        kaijou*=i
    ans=0
    for i in range(N):
        for j in range(i+1,N):
            ans+=math.sqrt((x[i]-x[j])**2+(y[i]-y[j])**2)
    print(ans*2/N)
    

if __name__ == '__main__':
    main()

Solution (Python):
n = int(input())
town = []
for _ in range(n):
    xy = list(map(float, input().split()))
    town.append(xy)
    
from itertools import permutations
from math import sqrt
orders = list(permutations(range(n)))
dist_sum = 0
for order in orders:
    for i in range(n-1):
        a = town[order[i]]
        b = town[order[i+1]]
        dist = sqrt((a[0]-b[0])*(a[0]-b[0]) + (a[1]-b[1])*(a[1]-b[1]))
        dist_sum += dist
print(dist_sum/len(orders))

Solution (Python):
def dist(x1, y1, x2, y2):
    return ((x1 - x2) ** 2 + (y1 - y2) ** 2) ** 0.5

n = int(input())
x = []
y = []
for i in range(n):
    seg = input().split()
    x.append(float(seg[0]))
    y.append(float(seg[1]))

edges = n * (n - 1) / 2
frac = 1
for i in range(1, n + 1):
    frac *= i
mul = frac * (n - 1) / edges

ans = 0
for i in range(n):
    for j in range(i + 1, n):
        ans += dist(x[i], y[i], x[j], y[j])

print(ans * mul / frac)

Solution (Python):
import itertools
import math

N = int(input())
x =[]
y = []
for i in range(N):
    a, b = map(int,input().split())
    x.append(a)
    y.append(b)

dist = 0

for i in range(N):
    for j in range(N):
        dist += ((x[i]-x[j])**2+(y[i]-y[j])**2)**0.5 

dist = dist/N

print(dist)