Problem:


Score : 300 points

Problem Statement

You have a pot and N ingredients. Each ingredient has a real number parameter called value, and the value of the i-th ingredient (1 \leq i \leq N) is v_i.

When you put two ingredients in the pot, they will vanish and result in the formation of a new ingredient. The value of the new ingredient will be (x + y) / 2 where x and y are the values of the ingredients consumed, and you can put this ingredient again in the pot.

After you compose ingredients in this way N-1 times, you will end up with one ingredient. Find the maximum possible value of this ingredient.

Constraints

2 \leq N \leq 50

1 \leq v_i \leq 1000

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
v_1 v_2 \ldots v_N

Output

Print a decimal number (or an integer) representing the maximum possible value of the last ingredient remaining.

Your output will be judged correct when its absolute or relative error from the judge's output is at most 10^{-5}.

Sample Input 1

2
3 4

Sample Output 1

3.5

If you start with two ingredients, the only choice is to put both of them in the pot. The value of the ingredient resulting from the ingredients of values 3 and 4 is (3 + 4) / 2 = 3.5.

Printing 3.50001, 3.49999, and so on will also be accepted.

Sample Input 2

3
500 300 200

Sample Output 2

375

You start with three ingredients this time, and you can choose what to use in the first composition. There are three possible choices:

Use the ingredients of values 500 and 300 to produce an ingredient of value (500 + 300) / 2 = 400. The next composition will use this ingredient and the ingredient of value 200, resulting in an ingredient of value (400 + 200) / 2 = 300.

Use the ingredients of values 500 and 200 to produce an ingredient of value (500 + 200) / 2 = 350. The next composition will use this ingredient and the ingredient of value 300, resulting in an ingredient of value (350 + 300) / 2 = 325.

Use the ingredients of values 300 and 200 to produce an ingredient of value (300 + 200) / 2 = 250. The next composition will use this ingredient and the ingredient of value 500, resulting in an ingredient of value (250 + 500) / 2 = 375.

Thus, the maximum possible value of the last ingredient remaining is 375.

Printing 375.0 and so on will also be accepted.

Sample Input 3

5
138 138 138 138 138

Sample Output 3

138



Sample input:
2
3 4


Sample output:
3.5

Submission status: Accepted

Solution code:
N = int(input())
v = list(map(int, input().split()))

v_s = sorted(v)

out = 0
for i in range(N):
  if i == 0:
    out += v_s[i]*((1/2)**(N-1))
  else:
    out += v_s[i]*((1/2)**(N-i))
  
print(out)

Submission status: Accepted

Solution code:
# -*- coding: utf-8 -*-

num = int(input())
val_list = [int(i) for i in input().split()]

val_list.sort()

init_1 = val_list.pop(0)
init_2 = val_list.pop(0)

rtn = (init_1 + init_2)/2

for i in val_list:
  rtn = (rtn + i)/2

print(rtn)

Submission status: Accepted

Solution code:
count = int(input())
numlist = list(map(int, sorted(input().split())))
result = 0

  
for i in range(1,count):
  numlist = sorted(numlist)
  sum = (numlist[1] + numlist[0]) / 2
  del numlist[0:2] #0,1番目の要素を削除
  numlist.append(sum)

  
print(sum)

Submission status: Accepted

Solution code:
N = int(input())
V = list(map(int, input().split()))
V_sorted = sorted(V, reverse = True)

ans = 0
for i in range(N):
    ans += V_sorted[i] /(2 ** (i+1))
ans += V_sorted[N-1]/(2 ** N)
print(ans)

Submission status: Accepted

Solution code:
N = int(input())
arr = input()
guzai = arr.split(" ")
guzai_int = [int(i) for i in guzai]

for i in range(1, N):
  guzai_int.sort()
  x = guzai_int.pop(0)
  y = guzai_int.pop(0)
  guzai_int.append((x+y)/2)

print(guzai_int.pop())

Submission status: Accepted

Solution code:
N = int(input())
v = list(map(int,input().split()))
v.sort()
v.reverse()
for i in range(N-1):
    v[-2] = (v[-1]+v[-2])/2
    del v[-1]
print(v[0])

Submission status: Accepted

Solution code:
import numpy as np
 
N = int(input())
Vi = np.array(list(map(int,input().split())))
for i in range(N):
    if len(Vi)>2:
        Vi = np.sort(Vi)
        Vi = np.concatenate(([Vi[:2].mean()],Vi[2:]))
    else:
        Vi = Vi.mean()
        break
print(Vi)

Submission status: Accepted

Solution code:
n = int(input())
v = list(map(int,input().split()))

c = n*(n-1)/2
ans = []

for i in range(n-1):
	v.sort()
	m1 = v.pop(0)
	m2 = v.pop(0)
	m = (m1+m2)/2
	v.append(m)

print(v[0])

Submission status: Accepted

Solution code:
n=int(input())
v=list(map(int, input().split()))
v.sort()
ans = v[0]
for v2 in v[1:]:
    ans = (ans+v2)/2
print(ans)

Submission status: Accepted

Solution code:
N = int(input())
V = [int(v) for v in input().split()]
V.sort()
ans = (V[0] + V[1]) / 2
for i in range(2,N):
  ans = (ans + V[i]) / 2
print(ans)

Submission status: Accepted

Solution code:
N = int(input())
V = list(map(int, input().split()))

V.sort()
for i in range(N-1):
    new = (V[0] + V[1])/2
    del V[0:2]
    V.append(new)
    V.sort()

print(V[0])

Submission status: Accepted

Solution code:
from heapq import heapify, heappop, heappush

N = int(input())
V = list(map(int, input().split()))

heapify(V)

while len(V)>1:
    x = heappop(V)
    y = heappop(V)
    heappush(V, (x+y)/2.0)

print(heappop(V))

Submission status: Accepted

Solution code:
a=int(input())
b=list(sorted(list(map(int,input().split()))))
c=0
for i in range(a-1):
    c=(b[i]+b[i+1])/2
    b[i+1]=c
print(c)

Submission status: Accepted

Solution code:
N = int(input())
v_n = sorted(map(int, input().split()))

s = v_n[0]
for i in range(1, len(v_n)):
    s = (s + v_n[i]) / 2

print(s)

Submission status: Accepted

Solution code:
N = int(input())
list = list(map(int, input().split()))

list.sort()
num = list[0]
for i in range(0, N):
    num = (num + list[i]) / 2
print(num)

Submission status: Accepted

Solution code:
n = int(input())
v = list(map(int, input().split()))

for i in range(n-1):
    a=min(v)
    v.remove(a)
    b=min(v)
    v.remove(b)
    v.append((a+b)/2)
print(v[0])

Submission status: Accepted

Solution code:
maxi = int(input())
li = list(map(int,input().split()))
li.sort()
for i,num in enumerate(li):
    if i == 0:
        cur = num
    else:
        cur = (num+cur)/2
print(cur)

Submission status: Accepted

Solution code:
n = int(input());
v = input().split(" ");
for i in range(n) :
	v[i] = int(v[i]);

v.sort(reverse=True);

ans = 0;
for i in range(n-1) :
	ans += v[i] / (2**(i+1));

ans += v[n-1] / (2**(n-1));
print(ans);

Submission status: Accepted

Solution code:
n = int(input())

num_list = list(map(int, input().split()))
num_list.sort()

for i in range(n-1):
  num_list[i + 1] = (num_list[i] + num_list[i + 1]) / 2

print(num_list[n-1])

Submission status: Accepted

Solution code:
n = int(input())
value = sorted(list(map(int,input().split())))

ans = value[0]

for i in value[1:] :
    ans = (i + ans) /2

print(ans)

Submission status: Accepted

Solution code:
N = int(input())
L = list(map(int, input().split()))
L.sort()
for a in range(N):
    if a == 0:
        c = L[0]
    else:
        c = (c + L[a])/2
print(c)

Submission status: Accepted

Solution code:
N = int(input())
L = list(map(int, input().split()))
L.sort()
c = 0
for a in range(N):
	
	if a == 0:
		c = c + int(L[0]) / pow(2, N - 1)# (2**(N-1))
	else:
		c = c + int(L[a]) / pow(2, N - a)#(2**(N-a))
print(c)

Submission status: Accepted

Solution code:
N = int(input())
values = sorted(list(map(int, input().split())), reverse=True)
max_value = values[N-1] / (2**N)
for i in range(N):
    max_value += values[i]/(2**(i+1))

print(max_value)

Submission status: Accepted

Solution code:
N = int(input())
v = [int(i) for i in input().split()]

for i in range(N-1):
    v.sort()
    dp = (v[0] + v[1]) / 2
    v.append(dp)
    v = v[2:]

print(v[0])

Submission status: Accepted

Solution code:
N = int(input())
v_list = list(map(int, input().split()))
v_list.sort()
ans = v_list[0]
for i in range(1, N):
    ans = (ans + v_list[i])/2 
print(ans)

Submission status: Accepted

Solution code:
def slove():
    import sys
    input = sys.stdin.readline
    n = int(input().rstrip('\n'))
    v = list(map(int, input().rstrip('\n').split()))
    v.sort()
    t = v[0]
    for i in range(1, n):
        t = (t + v[i]) / 2
    print(t)


if __name__ == '__main__':
    slove()

Submission status: Accepted

Solution code:
N = int(input())
v = list(map(int,input().split()))

v.sort()
ans = 0
for i in range(len(v)):
    if i == 0:
        ans += v[i]/2**(N-1)
    else:
        ans += v[i]/2**(N-i)
print(ans)

Submission status: Accepted

Solution code:
N=int(input())
A=sorted(list(map(int, input().split())))
for i in range(N-1):
    b=(A[0]+A[1])/2
    A.pop(0)
    A.pop(0)
    A.append(b)
    A=sorted(A)
a=A[0]
print(a)

Submission status: Accepted

Solution code:
N = int(input())
v = [float(i) for i in input().split()]
v.sort()
for i in range(N-2):
  b = [(v[0]+v[1])/2]
  v = b + v[2:]
print((v[0]+v[1])/2)

Submission status: Accepted

Solution code:
n = int(input())
list = list(map(int,input().split()))
list.sort()

for i in range(n-1):
	composition = (list[0]+list[1])/2
	list.pop(0)
	list.pop(0)
	list.append(composition)
	list.sort()

print(list[0])

Submission status: Accepted

Solution code:
N = int(input())
vn = [int(i) for i in input().split()]

while 1:
    vn = sorted(vn)
    if len(vn) == 1:
        break
    new = sum(vn[:2])/2
    vn = vn[2:] + [new]

print(vn[0])

Submission status: Accepted

Solution code:
n = input()
a = list(map(int, input().split()))
a.sort()
ans = a[0]
for v in a:
  ans = (ans + v) / 2
print(ans)

Submission status: Accepted

Solution code:
n = int(input())
v = list(map(int, input().split()))

for _ in range(n - 1):
    v = sorted(v)
    value = (v.pop(1) + v.pop(0)) / 2
    v.append(value)

print(v[0])

Submission status: Accepted

Solution code:
N = int(input())
v = list(map(float, input().split()))
v.sort()
ans = v[0]
for i in range(1,N):
    ans = (ans+v[i])/2
print(ans)

Submission status: Accepted

Solution code:
N=int(input())
v=map(int,input().split())

v_sorted= sorted(v)
ans = (v_sorted[0]+v_sorted[1])/2

for i in range(2,N):
  ans = (ans + v_sorted[i])/2

print (ans)

Submission status: Accepted

Solution code:
N = int(input())
v_list = input().split()
v_list = [int(v_list[i]) for i in range(N)]
v_list.sort()
ans = v_list[0]
for i in range(1, N):
    ans = (ans + v_list[i])/2 
print(ans)

Submission status: Accepted

Solution code:
N = int(input())
v_list = input().split()
v_list = [int(v_list[i]) for i in range(N)]
v_list.sort()
ans = int(v_list[0])
for i in range(1, N):
    ans = (ans + int(v_list[i]))/2 
print(ans)

Submission status: Accepted

Solution code:
N = int(input())
listN = list(map(int, input().split(' ')))

listN.sort()
prev = 0
for i in listN:
  if prev == 0:
    prev = i
    continue
  prev = (prev + i ) / 2
  
print(prev)

Submission status: Accepted

Solution code:
N = int(input())
v = sorted(list(map(int,input().split())))
c = v[0]
for i in range(1,len(v)):
  c = (v[i]+c)/2
print(c)

Submission status: Accepted

Solution code:
#ABC138C
N = int(input())
V = list(map(int, input().split()))
sortV = sorted(V)
ans = 0
if N == 2:
    ans = sum(V)/2
else:
    ans = ((sortV[0] +sortV[1])/2)
    for i in range(2, N):
        ans = (ans + sortV[i])/2
print(ans)

Submission status: Accepted

Solution code:
n=int(input())
a=[int(i) for i in input().split()]
a.sort()
ans = (a[0]+a[1])/2
for i in range(2,len(a)):
    ans = (ans+a[i])/2
print(ans)

Submission status: Accepted

Solution code:
n = int(input())
vn = list(map(int, input().split()))

def merge(x, y):
    return (x + y) / 2

for _ in range(n-1):
    vn = sorted(vn)
    x = vn.pop(0)
    y = vn.pop(0)
    vn.append(merge(x, y))

print(vn[0])

Submission status: Accepted

Solution code:
input()
ns = sorted(map(int, input().split()))
s = ns.pop(0)
#print(s, ns)
for n in ns:
    s = (s+n)/2
print(s)

Submission status: Accepted

Solution code:
N = int(input())
numList = list(map(int, input().split()))

numList.sort()

result = numList[0]
i = 1
while i < len(numList):
    result = (result + numList[i]) / 2
    i += 1

print(result)

Submission status: Accepted

Solution code:
N = int(input())
V =sorted([int(i)for i in input().split()])
ans = V.pop(0)
for i in range(N-1):
    ans += V.pop(0)
    ans /= 2
print(ans)

Submission status: Accepted

Solution code:
n = int(input())
v = list(map(int,input().split()))
v = sorted(v)
z = v[0]
for i in v[1:]:
    z += i
    z /= 2
print(z)

Submission status: Accepted

Solution code:
n = int(input())
v = list(map(int,input().split()))
z = 0
for i in range(n):
    if len(v) == 1:
        print(z)
    else:
        z = min(v)
        v.remove(z)
        z = (z + min(v))/2
        v.remove(min(v))
        v.append(z)

Submission status: Accepted

Solution code:
n = input()
v_list = sorted(list(map(int, input().split())), reverse=True)
result = 0
for i, v in enumerate(v_list):
    if i + 1 == len(v_list):
        result += v / (2**i)
    else:
        result += v / (2**(i+1))
print(result)

Submission status: Accepted

Solution code:
# coding: utf-8
n = int(input())

a = list(map(float,input().split())) 

a.sort()

for k in range(n-1):
    b=(a[0]+a[1])/2
    a.append(b)
    a.pop(0)
    a.pop(0)
    a.sort()

A =a[0]
print(A)

Submission status: Accepted

Solution code:
n = int(input())
v = list( map(int, input().split(" ")) )
v.sort()
answer = 0

multipilier = 2**(len(v)-1)

for i in range(len(v)):
    answer = (v[i]/multipilier) + answer
    if i!=0:
        multipilier = multipilier/2

print(answer)

Submission status: Accepted

Solution code:
n = int(input())
v = list(map(int, input().split()))
v.sort()
tmp = v[0]
for i in range(n-1):
    tmp = (v[i+1]+tmp)/2
print(tmp)

Submission status: Accepted

Solution code:
N = input()
values = list(map(int, input().split()))
values.sort()

while len(values) > 1:
  values.append((values.pop(0) + values.pop(0)) / 2)
  values.sort()

print(values[0])

Submission status: Accepted

Solution code:
# 早い方が価値は元帥。小さい順に投入する。

import sys
n = sys.stdin.readline()
v = sys.stdin.readline()
n = int(n)
v = v.split()
v = sorted([int(x) for x in v], reverse=True)
ans = sum([(v[i] * (1 / 2 ** (i+1))) for i in range(0,n)]) + v[(n-1)] * (1 / 2 ** (n))
print(ans)

Submission status: Accepted

Solution code:
N = int(input())

v = list(map(int, input().split()))

v = sorted(v, reverse = False)

sum = v[0] / pow(2, N-1)
for i in range(1, N):
    sum += v[i]/pow(2, (N-i))

print(sum)

Submission status: Accepted

Solution code:
N = int(input())
A = list(map(float,input().split()))
A.sort()
tmp = A[0]
for i in range(1,N):
    tmp = (tmp+A[i])/2
print(tmp)

Submission status: Accepted

Solution code:
N = int(input())
v_str = input()
v_list_str = v_str.split(" ")
v_list_float = [0.0] * N
for i in range(N):
    v_list_float[i] = float(v_list_str[i])
#print(v_list_float)

v_list_float.sort(reverse=True)
#print(v_list_float)

ans = 0.0
for i in range(N-1):
    ans += v_list_float[i] / (2 ** (i+1))
ans += v_list_float[N-1] / (2 ** (N-1))

print(ans)

Submission status: Accepted

Solution code:
N=int(input())
v=sorted(list(map(int, input().split())))
a=v[0]
for i in v:
  a=(a+i)/2
print(a)

Submission status: Accepted

Solution code:
N=int(input())
v=list(map(int, input().split()))
v.sort()
for i in range(N-2):
  v1=v
  v=[(v1[0]+v1[1])/2]
  v.extend(v1[2:])
print(sum(v)/2)

Submission status: Accepted

Solution code:
n = int(input())
a = list(map(int, input().split()))
num = 0
while(len(a) > 2):
  n1 = a.pop(a.index(min(a)))
  n2 = a.pop(a.index(min(a)))
  n3 = (n1 + n2) / 2
  a.append(n3)
ans = (a[0]+a[1])/2
print(ans)

Submission status: Accepted

Solution code:
n = int(input())
v = [int(i) for i in input().split()]

v.sort()

for i in range(1,n):
    x = v.pop(0)
    y = v.pop(0)
    xy = (x + y) / 2
    v.append(xy)
    v.sort()

print(v.pop(0))

Submission status: Accepted

Solution code:
n = int(input())
v = sorted(map(int, input().split()), reverse=True)
sum = v[n - 1] / 2 ** (n)
for i in range(n):
    sum += v[i] / 2 ** (i + 1)
print(sum)

Submission status: Accepted

Solution code:
N = int(input())
a = sorted(list(map(int,input().split())),reverse=True)
for i in range(N-1):
    a.append((a.pop()+a.pop())/2)
print(a[0])

Submission status: Accepted

Solution code:
n = int(input())
lst = list(map(int, input().split()))
lst.sort()

for i in range(n):
    if i == 0:
        sum = lst[i]
    else:
        sum = (lst[i]+sum)/2

print(sum)

Submission status: Accepted

Solution code:
n=int(input())
lst=list(map(int,input().split()))
lst.sort()
for i in range(n):
  if i==0:
    sum=lst[i]
  else:
    sum=(sum+lst[i])/2

print(sum)

Submission status: Accepted

Solution code:
n=int(input())
lst=list(map(int,input().split()))

lst.sort()
for i in range(n):
    if i==0:
        sum=lst[i]
    else:
        sum=(sum+lst[i])/2

print(sum)

Submission status: Accepted

Solution code:
n = int(input())
v = list(map(int, input().split()))

v.sort()
ans = v[0]

for i in range(1,n):
    ans = (ans+v[i])/2
print(ans)

Submission status: Accepted

Solution code:
n = int(input())
v = list(map(int,input().split()))
i = 0

v.sort()

while i < n -1:
  a = v.pop(0)
  b = v.pop(0)
  v.insert(0,(a+b) / 2)
  i += 1

print(v[0])

Submission status: Accepted

Solution code:
n  = int(input())
vi = sorted(list(map(float, input().split())), reverse=True)

sum = 0
div = 1
for i in range(n):
  if i != n-1:
    div *= 2
  sum += vi[i]/div
    
print(sum)

Submission status: Accepted

Solution code:
N = int(input())
v = sorted(list(map(int, input().split())))

for _ in range(N-1):
    v = sorted([(v[0]+v[1])/2] + v[2:])

print(v[0])

Submission status: Accepted

Solution code:
import heapq

n = int(input())
l = list(map(float,input().split()))

heapq.heapify(l)

while len(l) > 1:
  a = heapq.heappop(l)
  b = heapq.heappop(l)
  heapq.heappush(l,(a+b)/2)

print(heapq.heappop(l))

Submission status: Accepted

Solution code:
from collections import deque
N = int(input())
v = list(map(int,input().split()))
v.sort()
que = deque(v)
for _ in range(N-1):
  a = que.popleft()
  b = que.popleft()
  c = (a+b)/2
  que.appendleft(c)
print(que.popleft())

Submission status: Accepted

Solution code:
import heapq
n = int(input())
v = list(map(int, input().split()))
v_heap = []
for i in v:
    heapq.heappush(v_heap, i)
for _ in range(n-1):
    heapq.heappush(v_heap, (heapq.heappop(v_heap)+heapq.heappop(v_heap))/2)
print(heapq.heappop(v_heap))

Submission status: Accepted

Solution code:
n = int(input())
list_1 = list(map(int,input().split()))
list_2 = sorted(list_1)
sum = (list_2[0]+(list_2[1]))/2
for i in range(n-2):
    sum = (sum + (list_2[i+2]))/2
print(sum)

Submission status: Accepted

Solution code:
import sys
from heapq import *
input = sys.stdin.readline

def main():
    """ main """
    N = int(input())
    VS = list(map(int, input().split()))
    heapify(VS)
    for _ in range(N-1):
        a, b = heappop(VS), heappop(VS)
        new_item = (a+b)/2
        heappush(VS, new_item)
    print(VS[0])

if __name__ == '__main__':
    main()

Submission status: Accepted

Solution code:

N = int(input())
nums = list(map(int,input().split(" ")))
nums.sort()
ans = 0
ans = sum(nums[0:2])/2
if N >= 3:
    for num in nums[2:]:
        ans += num
        ans/=2
print(ans)

Submission status: Accepted

Solution code:
n = int(input())
arr = list(map(int,input().split()))

arr.sort()

prev = arr[0]

for i in range(n-1):
  prev = (prev+arr[i+1])/2
  
print(prev)

Submission status: Accepted

Solution code:
#C - Alchemist(ABC138)
N=int(input())
V=list(map(int, input().split()))
V.sort()
S=V[0]
for i in range(1,N):
    S=(S+V[i])/2
print(S)

Submission status: Accepted

Solution code:
N = int(input())
a = list(map(int,input().split()))
a.sort()
sum=a[0]
for i in range(1,N):
  sum=(sum+a[i])/2
print(sum)

Submission status: Accepted

Solution code:
n=int(input())
v=list(map(int,input().split()))
v.sort()
for i in range(n-1):
    a=(v.pop(1)+v.pop(0))/2
    v.append(a)
    v.sort()
print(*v)

Submission status: Accepted

Solution code:
# coding:utf-8

a = int(input())
n = list(map(int, input().split()))

ind = n.index(min(n))
POT = n.pop(ind)
for i in range(0, len(n)):
    ind = n.index(min(n))
    POT = (POT + n.pop(ind)) / 2

print(POT)

Submission status: Accepted

Solution code:
def resolve():
    N = int(input())
    v = list(map(int,input().split()))
    v.sort()

    for i in range(N-1):
        v[i+1]=(v[i]+v[i+1])/2
    print(v[N-1])
    
resolve()

Submission status: Accepted

Solution code:
# C - Alchemist
 
n = int(input())
v = list(map(int, input().split()))
v.sort()
 
while len(v) > 1:
    v[0] = (v[1] + v[0]) / 2
    v.pop(1)
print(v[0])

Submission status: Accepted

Solution code:
N=int(input())
v=[int(i) for i in input().split()]
v.sort()

res = v[0]
for i in range(1,N):
    res = (res+v[i])/2
print(res)

Submission status: Accepted

Solution code:
n=int(input())
v=list(map(int, input().split()))
v=sorted(v)
ans=v[0]
for i in range(1,len(v)):
    ans=(v[i]+ans)/2
print(ans)

Submission status: Accepted

Solution code:
n=int(input())
vs=list(map(int,input().split()))
vs.sort()

ans=0
for i in range(1,n):
  ans=(vs[i-1]+vs[i])/2
  vs[i]=ans
print(ans)

Submission status: Accepted

Solution code:
N = int(input())
worthly = list(map(int,input().split()))

sum = 0
k = 1
worthly.sort()
worthly.reverse()
for i in worthly:
    sum += i/2**k
    k += 1
sum += worthly[N-1]/2**(N)
print(sum)

Submission status: Accepted

Solution code:
# -*- coding:utf8 -*-

n = int(input())
s = sorted(list(map(int, input().split())))
while len(s) > 1:
    a = (s[0] + s[1]) / 2
    s.append(a)
    s = sorted(s[2:])
print(s[0])

Submission status: Accepted

Solution code:
from heapq import heappush, heappop
N = int(input())
heap = []
for v in map(int, input().split()):
    heappush(heap, v)

for _ in range(N-1):
    x = heappop(heap)
    y = heappop(heap)
    heappush(heap, (x+y)/2)

print(heappop(heap))

Submission status: Accepted

Solution code:
N = int(input())
vs = [int(i) for i in input().split()]

vs.sort()

def answer(N , vs):
    if N == 1:
        return vs[0]
    else:
        return (answer(N-1, vs) + vs[N-1]) / 2

print(answer(N, vs))

Submission status: Accepted

Solution code:
N = int(input())
v = input().split()
v = [float(i) for i in v]
v.sort(reverse=True)
ans = 0
for i in range(N-1):
    ans+= v[i]/(2**(i+1))
ans += v[N-1]/(2**(i+1))
print(ans)

Submission status: Accepted

Solution code:
n = int(input())
v = [int(i) for i in input().split()]
v.sort()
ans = v[0]
for i in range(n-1):
    ans = (ans+v[i+1])/2
print(ans)

Submission status: Accepted

Solution code:
n = int(input())

v = list(map(int, input().split(' ')))
v.sort()
while len(v) > 1:
    a = v.pop(0)
    b = v.pop(0)
    v.append((a+b)/2)
    v.sort()

print(v[0])

Submission status: Accepted

Solution code:
N=int(input())
A=list(map(int,input().split()))
B=list(sorted(A))
c=B.pop(0)
m=N-1
total=0
if N==2:
    max=sum(A)/2
elif N>2:
    for a in range(0,m):
        total+=B[a]/(2**(m-a))
    max=total+c/(2**m)

print(max)

Submission status: Accepted

Solution code:
N = int(input())
V = list(map(int, input().split()))

while len(V) >= 2:
    V.sort()
    V = [(V[0]+V[1])/2] + V[2:]

print(V[0])

Submission status: Accepted

Solution code:
def main():
    import sys
    input = sys.stdin.readline
    n = int(input().rstrip('\n'))
    v = list(map(int, input().rstrip('\n').split()))
    v.sort()
    t = v[0]
    for i in range(1, n):
        t = (t + v[i]) / 2
    print(t)


if __name__ == '__main__':
    main()

Submission status: Accepted

Solution code:
N = int(input())
V = list(map(int, input().split()))

V = sorted(V)

ans = V[0]

for v in V[1:]:
    ans = float(v+ans) / 2

print(ans)

Submission status: Accepted

Solution code:
N = int(input())
Lists = list(map(int,input().split()))
newLists = sorted(Lists)
k = newLists[0]
for x in range(1,N):
  k += newLists[x]
  k = k/2
print(k)

Submission status: Accepted

Solution code:
n=int(input())
a=[int(i) for i in input().split()]
a.sort()
s=(a[0]+a[1])/2
for i in range(2,n):
    s=(s+a[i])/2
print(s)

Submission status: Accepted

Solution code:
n = int(input())
V = list(map(int,input().split()))
while len(V)!=1:
  V.sort()
  tmp = (V[0]+V[1])/2
  for i in range(2): V.pop(0)
  V.append(tmp)
print(V[0])

Submission status: Accepted

Solution code:
n = int(input())
a = list(map(int,input().split()))
a.sort()
now = a[0]
for i in range(1,n):
  now = ( now + a[i] ) / 2
print(now)

Submission status: Accepted

Solution code:
a = int(input())
value_list = list( map( int, input().split() ) )
value_list.sort()

for i in range(a - 1):
    value_list[i + 1] = ( value_list[i] + value_list[i + 1] )/ 2
print( value_list[-1] )

Submission status: Accepted

Solution code:
#!/usr/bin/env python3
#ABC138 C

import sys
import math
import bisect
sys.setrecursionlimit(1000000000)
from heapq import heappush, heappop,heappushpop
from collections import defaultdict
from itertools import accumulate
from collections import Counter
from collections import deque
from operator import itemgetter
from itertools import permutations
mod = 10**9 + 7
inf = float('inf')
def I(): return int(sys.stdin.readline())
def LI(): return list(map(int,sys.stdin.readline().split()))

n = I()
v = LI()
v.sort()
ans = v[0]
for i in range(1,n):
    ans = (ans+v[i])/2
print(ans)

Submission status: Accepted

Solution code:
n=input().strip()
n=int(n)
if n>=2 and n<=50:
    num=list(map(int,input().strip().split()))
num.sort()

if n==2:
    print(sum(num)/2)
else:
    num.append((num[0]+num[1])/2)
    num=num[2:]
    for i in range(len(num)-1):
        num.append((num[-1]+num[0])/2)
        num=num[1:]
    print(num[-1])

Submission status: Accepted

Solution code:
n=int(input())
c=list(map(float,input().split()))
c.sort()
k=n
for i in range(n-2):
  v=(c[0]+c[1])/2
  c=c[2:]
  if c[k-3]<v:
    c.append(v)
    break
  for j in range(k-2):
    if c[j]>=v:
      c.insert(j,v)
      break
  k=k-1
print((c[0]+c[1])/2)

Submission status: Accepted

Solution code:
n = int(input())
v = list(map(int, input().split()))
# print(n)
# print(v)

#vを小さい順に並べる任意の並べ方にする
v.sort()

#左から徐々に計算する
for i in range(n):
    
    #もう計算できないときはbreak
    if len(v) == 1:
        break
        
    v = [(float(v[0]) + float(v[1]))/2] + v[2:]
    
#結果を格納
print(v[0])

Submission status: Accepted

Solution code:
N = int(input())
Vs = input().split()

if N == 2:
    print(sum([int(x) for x in Vs])/N)
else:
    lists = [int(x) for x in Vs]
    while N > 1:
        lists.sort()
        x = (lists.pop(0) + lists.pop(0)) / 2
        lists.insert(0, x)
        N -= 1

    print(lists[0])

Submission status: Accepted

Solution code:
n = int(input())
v = list(map(int, input().split()))

v = sorted(v)

while True:
    if len(v) == 1:
        break
    val = (v[0] + v[1]) / 2
    v.pop(0)
    v.pop(0)
    v.insert(0, val)

print(v[0])

Submission status: Accepted

Solution code:
n = int(input())
v = list(map(int, input().split()))
v = sorted(v)
s = v[0]
for i in range(n-1):
    s = (s + v[i+1])/2
print(s)

Submission status: Accepted

Solution code:
N = int(input())
num_lis = list(map(int,input().split()))

num_lis.sort(reverse = True)
total = 0
for n in range(N):
    if n < (N-1):
        total += num_lis[n] * (1/2)**(n+1)
    else:
        total += num_lis[n] * (1/2)**(n)
print(total)

Submission status: Accepted

Solution code:
N = int(input())
A = list(map(int, input().split()))
while len(A) >= 2:
  A.sort()
  A.append((A[0] + A[1])/2.0)
  A = A[2:]
print(A[0])

Submission status: Accepted

Solution code:
N = int(input())
a = sorted(list(map(float, input().split())))
at = a.pop(0)

for i in a:
  at = (at + i) / 2

print("%.5f" % at)

Submission status: Accepted

Solution code:
N = int(input())
nums = list(map(int,input().split()))
nums.sort()
score = nums[0]
for i in range(N-1):
    score = (score + nums[i+1])/2
print(score)

Submission status: Accepted

Solution code:
##C problem
N = int(input())
v = list(map(float, input().split()))

vs = sorted(v)

for i in range(N-1):

    a=vs[0]

    b=vs[1]
    c=(a+b)/2
    vs.remove(b)
    vs.insert(0,c)
    vs.remove(a)
    #print(i)
    #print(vs)

print(vs[0])

Submission status: Accepted

Solution code:
n = int(input())
v = list(map(int, input().split()))
v_sort = sorted(v)
c = v_sort[0]
for i in range(1,n):
    c = (c + v_sort[i])/2
print(c)

Submission status: Accepted

Solution code:
def alchemist(N: int, V: list)->float:
    V.sort()
    s = V[0]

    for v in V[1:]:
        s = (s + v) / 2

    return s


if __name__ == "__main__":
    N = int(input())
    V = list(map(int, input().split()))

    ans = alchemist(N, V)
    print(ans)

Submission status: Accepted

Solution code:
#C

n = int(input())
v = [int(x) for x in input().split()]

v.sort()

s = v[0]
for i in v[1:]:
    s = (s+i)/2
print(s)

Submission status: Accepted

Solution code:
n=int(input())
v_list=[int(s) for s in input().split()]
v_list.sort()
ans=v_list[0]
for i in range(1,n):
    ans=(ans+v_list[i])/2
print(ans)

Submission status: Accepted

Solution code:
n = int(input())
v = [int(i) for i in input().split()]
sorted_v = sorted(v)
ans = (sorted_v[0] + sorted_v[1]) / 2
for i in sorted_v[2:]:
    ans = (ans + i) / 2
print(ans)

Submission status: Accepted

Solution code:
from heapq import heappush, heappop
import re
from collections import deque
import sys
import math
input = sys.stdin.readline


def int_raw():
    return int(input())

def str_in():
    return input().strip("\n")

def ss_raw():
    return input().split()


def ints_raw():
    return tuple(map(int, ss_raw()))


DIV = 10**9+7


def mod_inv_prime(a, mod=DIV):
    return pow(a, mod-2, mod)


def mod_inv(a, b):
    r = a
    w = b
    u = 1
    v = 0
    while w != 0:
        t = r//w
        r -= t*w
        r, w = w, r
        u -= t*v
        u, v = v, u
    return (u % b+b) % b


def ncr(n, r, mod=DIV):
	r = min(r, n-r)
	ret = 1
	for i in range(1, r+1):
		ret = ret * (n-i+1) % mod
		ret = ret * mod_inv(i, mod) % mod
	return ret


class UnionFind:
    def __init__(self, n):
        self.par = [i for i in range(n+1)]
        self.rank = [0] * (n+1)
        self.mini = [i for i in range(n+1)]

    def find(self, x):
        if self.par[x] == x:
            return x
        else:
            self.par[x] = self.find(self.par[x])
            return self.par[x]

    def union(self, x, y):
        x = self.find(x)
        y = self.find(y)
        if self.rank[x] < self.rank[y]:
            self.par[x] = y
        else:
            self.par[y] = x
            if self.rank[x] == self.rank[y]:
                self.rank[x] += 1
        mini = min(self.mini[x],self.mini[y])
        self.mini[x]=mini
        self.mini[y]=mini
    
    def same_check(self, x, y):
        return self.find(x) == self.find(y)

def main():
    n = int_raw()
    As = list(ints_raw())
    As.sort()
    ans = As[0]
    for a in As[1:]:
        ans = (ans+a)/2.0
    return ans
print(main())

Submission status: Accepted

Solution code:
N = input()
v = [int(i) for i in input().strip().split()]

while True:
    v.sort(reverse=True)
    x1 = v.pop()
    x2 = v.pop()
    x = (x1 + x2) / 2
    v.append(x)

    if len(v) == 1:
        break

print(v[0])

Submission status: Accepted

Solution code:
N=int(input())
values=[int(thing) for thing in input().split(" ")]
values.sort()
ret=0
for i in values:
    if ret!=0:
        ret=(i+ret)*0.5
    else:
        ret=i
print(ret)

Submission status: Accepted

Solution code:
n = int(input())
v = sorted(list(map(int, input().split())))
while len(v) > 1:
  v.insert(0, (v.pop(0) + v.pop(0)) / 2)
print(v[0])

Submission status: Accepted

Solution code:
# -*- coding: utf-8 -*-
n = int(input())
v = sorted(list(map(float, input().split())))

while len(v) > 1:
    v.insert(0, (v.pop(0) + v.pop(0)) / 2)

print(v[0])