from math import sqrt

# n = int(input())
# point_array = []
# for i in range(0, n):
#     point = input()
#     point = point.split(" ")
#     point = list(map(int, point))
#     point_array.append(point)
points_array = [[1, 1], [1, 2]]
print(points_array)
def perimeter(points):
        perimeter = 0
        for i in range(len(points)):
            start = points[i - 1]
            end = points[i]
            side = sqrt((end[0] - start[0])**2 + (end[1] - start[1])**2)
            perimeter += side
        return perimeter

def rotate(A,B,C):
  return (B[0]-A[0])*(C[1]-B[1])-(B[1]-A[1])*(C[0]-B[0])

def jarvismarch(A):
  n = len(A)
  P = [x for x in range(n)]
  # start point
  for i in range(1,n):
    if A[P[i]][0]<A[P[0]][0]:
      P[i], P[0] = P[0], P[i]
  H = [P[0]]
  del P[0]
  P.append(H[0])
  while True:
    right = 0
    for i in range(1,len(P)):
      if rotate(A[H[-1]],A[P[right]],A[P[i]])<0:
        right = i
    if P[right]==H[0]:
      break
    else:
      H.append(P[right])
      del P[right]
  return H
polygon = []
needed = jarvismarch(points_array)
# Берем минимальное выпуклое множество и строим из него такое, которое подойдет к условию
for el in needed:
    polygon.append(points_array[el])
print(polygon)
print(perimeter(polygon))
for i in range(len(polygon)):
    point = polygon[i]
    temp = polygon
    temp.append([point[0], point[1] + 1])
    if len(jarvismarch(temp)) == len(needed):
        polygon[i] = [point[0], point[1]+1]
        continue
    temp = polygon
    temp.append([point[0], point[1] - 1])
    if len(jarvismarch(temp)) == len(needed):
        polygon[i] = [point[0], point[1]-1]
        continue
    temp = polygon
    temp.append([point[0] + 1, point[1]])
    if len(jarvismarch(temp)) == len(needed):
        polygon[i] = [point[0] + 1, point[1]]
        continue
    temp = polygon
    temp.append([point[0] - 1, point[1]])
    if len(jarvismarch(temp)) == len(needed):
        polygon[i] = [point[0] - 1, point[1]]
        continue
print(perimeter(polygon) / 2)