Kertoma

import math
import timeit
from typing import Callable
 
 
def I():
    return map(int, input().split())
 
 
# for larger x, x! has an unique number of digits
 
def binarysearch(func: "Callable[[int],bool]", m=0):
    """search the smallest >=m integer x for which func(x) is true.
     (func must be a function that returns False for all >=m integers less than x,
    and True for all >=m integers greater than or equal to x)"""
    k = 1
    m -= 2  # y>m-2 where y is the greatest integer for which func(y) is False
    while not func(k * 2 + m):
        k *= 2
    #                k//2 < out <= k
    x = k + m
    k //= 2
    while k:
        if not func(x + k):
            x += k
        k //= 2
    return x + 1
 
 
def factorial_digits(x):
    a = 1
    b = 1
    for i in range(1, x + 1):
        a *= i
        while a >= 10:
            a /= 10
            b += 1
    return b
 
 
def find_factorial_with_digit_amount(x: int):
    """x is the amount of digits y! has. finds y \n
    x has to be 4 or greater"""
    if x < 4:
        raise ValueError
 
    def func(a: int):
        return factorial_digits(a) >= x
    y = binarysearch(func)
    return y
 
 
def find_factorial(appearances):
    digits = sum(appearances)
    if digits <= 3:
        if digits == 1:
            if appearances[1]:
                return 1
            elif appearances[2]:
                return 2
            else:
                return 3
        elif digits == 2:
            return 4
        else:
            if appearances[1]:
                return 5
            else:
                return 6
    else:
        return find_factorial_with_digit_amount(digits)
 
 
def main():
 
    appearances = list(I())
    print(find_factorial(appearances))
 
 
main()

Test 1

Group: 1, 2, 3

Verdict: ACCEPTED

Test 2

Group: 1, 2, 3

Verdict: ACCEPTED

Test 3

Group: 1, 2, 3

Verdict: ACCEPTED

Test 4

Group: 1, 2, 3

Verdict: ACCEPTED

Test 5

Group: 1, 2, 3

Verdict: ACCEPTED

Test 6

Group: 1, 2, 3

Verdict: ACCEPTED

Test 7

Group: 2, 3

Verdict: ACCEPTED

Test 8

Group: 2, 3

Verdict: ACCEPTED

Test 9

Group: 2, 3

Verdict: ACCEPTED

Test 10

Group: 2, 3

Verdict: ACCEPTED

Test 11

Group: 3

Verdict: ACCEPTED

Test 12

Group: 3

Verdict: ACCEPTED

Test 13

Group: 3

Verdict: ACCEPTED

Test 14

Group: 3

Verdict: ACCEPTED

Test 15

Group: 3

Verdict: ACCEPTED

Test 16

Group: 3

Verdict: ACCEPTED