from pulp import LpProblem, LpVariable, LpMinimize, lpSum, PULP_CBC_CMD
"""
ok to clarify the solution here:
modelling this as ilp ->
variable for each button representing how many times it is pressed - minimize this!
constraints for each joltage thingy? idk - (buttons that increment it * number of times pressed) *must equal goal so it matches expected value*!
if button doesnt increment 0 * wtv is still 0 so doesnt matter
boom done city
"""


def solve(goal, buttons): # hence another thing i havent done in years
    prob = LpProblem("Operation_Dumbass_Elves", LpMinimize)
    x = [LpVariable(f"x_{i}", lowBound=0, cat='Integer') for i in range(len(buttons))]

    prob += lpSum(x), "Button Presses"

    for i in range(len(goal)):
        constraint = []
        for j in range(len(buttons)):
            M_ij = buttons[j][i]
            constraint.append(M_ij * x[j])
        prob += lpSum(constraint) == goal[i], f"Constraint_{i}"
    
    prob.solve(PULP_CBC_CMD(msg=0))

    return (int(prob.objective.value()))


with open('input.txt', 'r') as file:
    lines = file.readlines()

count = 0

for line in lines:
    line = line.rstrip('\n').split()
    goal = tuple(map(int, line[-1].strip('{}').split(',')))
    buttons = []
    for i in range(1, len(line) - 1):
        incs = map(int, line[i].strip('()').split(','))
        button = [0] * len(goal)
        for inc in incs:
            button[inc] += 1
        buttons.append(tuple(button))
        
    count += solve(goal, buttons)

print(count)