Kertoma

import math
input = input().split(" ")

counts = {}

precalcs = {}

# factorial is fast, reverse is slow
for i in range(0,1000):
    precalcs[math.factorial(10*i)] = 10*i

l = 0

for i, n in enumerate(input):
    n = int(n)
    counts[str(i)] = n
    l += n

min = 10**(l-1)

n = 0

for fact in precalcs:
    if fact >= min:    
        break
    n = precalcs[fact]

fact = math.factorial(n)

while True:
    n += 1
    fact *= n
    if fact > min:
        s = str(fact)
        valid = True
        for c in counts:
            if not s.count(c) == counts[c]:
                valid = False
                break
        if valid:
            print(n)
            break

        
    

Test 1

Group: 1, 2, 3

Verdict: TIME LIMIT EXCEEDED

Test 2

Group: 1, 2, 3

Verdict: TIME LIMIT EXCEEDED

Test 3

Group: 1, 2, 3

Verdict: TIME LIMIT EXCEEDED

Test 4

Group: 1, 2, 3

Verdict: TIME LIMIT EXCEEDED

Test 5

Group: 1, 2, 3

Verdict: TIME LIMIT EXCEEDED

Test 6

Group: 1, 2, 3

Verdict: TIME LIMIT EXCEEDED

Test 7

Group: 2, 3

Verdict: TIME LIMIT EXCEEDED

Test 8

Group: 2, 3

Verdict: TIME LIMIT EXCEEDED

Test 9

Group: 2, 3

Verdict: TIME LIMIT EXCEEDED

Test 10

Group: 2, 3

Verdict: TIME LIMIT EXCEEDED

Test 11

Group: 3

Verdict: TIME LIMIT EXCEEDED

Test 12

Group: 3

Verdict: TIME LIMIT EXCEEDED

Test 13

Group: 3

Verdict: TIME LIMIT EXCEEDED

Test 14

Group: 3

Verdict: TIME LIMIT EXCEEDED

Test 15

Group: 3

Verdict: TIME LIMIT EXCEEDED

Test 16

Group: 3

Verdict: TIME LIMIT EXCEEDED