day 19 part 2

work, _ = open("input").read().split('\n\n')
workflows = {name: rules[:-1].split(',') for name, rules in (line.split('{') for line in work.splitlines())}

def find_rules(current, rules):
    if current == 'A':
        regole.append(rules)
    elif current != 'R':
        rul = []
        for rule in workflows[current][:-1]:
            if rule not in 'AR':
                next_workflow = rule.split(':')[1]
                find_rules(next_workflow, rules + rul + [rule.split(':')[0]])
                if rule[1] == '<':
                    rul.append(rule.split(':')[0].split('<')[0] + '>=' + rule.split(':')[0].split('<')[1])
                elif rule[1] == '>':
                    rul.append(rule.split(':')[0].split('>')[0] + '<=' + rule.split(':')[0].split('>')[1])
        else:
            next_workflow = workflows[current][-1]
            find_rules(next_workflow, rules + rul)

regole = []
find_rules('in', [])
somma = 0
for r in regole:
    maxs = {x: 4001 for x in 'xmas'}
    mins = {x: 0 for x in 'xmas'}
    for s in r:
        if s[0] in 'xmas' and s[1] == '<':
            maxs[s[0]] = min(maxs[s[0]], int(s[2:])) if s[2] != '=' else min(maxs[s[0]], int(s[3:]) + 1)
        elif s[0] in 'xmas' and s[1] == '>':
            mins[s[0]] = max(mins[s[0]], int(s[2:])) if s[2] != '=' else max(mins[s[0]], int(s[3:]) - 1)
    p = 1
    for key in maxs:
        p *= (maxs[key] - mins[key] - 1)
    somma += p
print(somma)