Kertoma

import math

numbers = input("").split(" ") #[1308, 658, 687, 684, 694, 636, 695, 685, 672, 693]#[5154, 2884, 2973, 2972, 2901, 2993, 2980, 2941, 2961, 2923]#
numbers = [int(i) for i in numbers]
sum = 0
for i in range(0, len(numbers)):
    sum += numbers[i]

answer = 0
runs = 0
firstRun = 0

while len(str(answer)) < sum:
    answer = math.factorial(runs)
    runs += 1000
    firstRun += 1

if sum > 20000:
    runs -= 1000

secondRun = 0
while len(str(answer)) > sum:
    answer = math.factorial(runs)
    runs -= 100
    secondRun += 1
    if runs < 0:
        runs = 0
        break


thirdRun = 0
while len(str(answer)) < sum:
    answer = math.factorial(runs)
    runs += 10
    thirdRun += 1



delta = 0
while True:
    answer = math.factorial(runs)

    if len(str(answer)) == sum:
        numbersInAnswer = [0,0,0,0,0,0,0,0,0,0]

        for value in str(answer):
            numbersInAnswer[int(value)] += 1
        
        if numbersInAnswer == numbers:
            print(runs)
            break

    # Move the delta up and down to find the exact number
    if len(str(answer)) > sum:
        runs -= 1
        delta -= 1
    else:
        runs += 1
        delta += 1

    # Add randomness to fix getting stuck in "ditches"


# Printing the time taken in seconds
#print(time.process_time())

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: 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