# Input: lines like "[<part1>] (<part2>) ... {<part3>}"
#        part1 = string of . #
#        part2, part3 = comma-separated list of numbers
# Output: each part2 button increases elements of that line's part3 (0-indexed)
#         find fewest # presses to get each line from all 0 to part3
#         ignore part1 for this half

import numpy
from scipy.optimize import LinearConstraint
from scipy.optimize import milp

def minimum_presses(part2_list, part3_list):

  # https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.milp.html

  # minimize total number of presses

  c_coefficients = []
  for part2 in part2_list:
    c_coefficients.append(1)
  c = numpy.array(c_coefficients)

  # effect of a combination of presses on part3

  f_list = []
  for part3_index in range(0, len(part3_list)):
    f = []
    for part2 in part2_list:
      f.append(1 if part3_index in part2 else 0)
    f_list.append(f)
  a = numpy.array(f_list)

  # desired effect

  b_u = numpy.array(part3_list)
  b_l = b_u

  constraints = LinearConstraint(a, b_l, b_u)

  integrality = numpy.ones_like(c) # array of 1's with same shape as c

  res = milp(c=c, constraints=constraints, integrality=integrality)

  return int(res.fun)

def string_without_ends(s):
  return s[1:len(s)-1]

total = 0

file = open("10_input.txt", "r")
for line in file:
  line = line.replace("\n", "")
  chunks = line.split(" ")
  part1 = string_without_ends(chunks.pop(0))
  part3 = string_without_ends(chunks.pop())
  part3_list = []
  for num_str in part3.split(","):
    part3_list.append(int(num_str))
  part2_list = []
  for chunk in chunks:
    part2_str = string_without_ends(chunk)
    part2 = []
    for num_str in part2_str.split(","):
      part2.append(int(num_str))
    part2_list.append(part2)
  total += minimum_presses(part2_list, part3_list)

print (total)