Aristocracy

import math
line1= input()
firstname = ""
"""
def groupby(iterable, key=None):
    # [k for k, g in groupby('AAAABBBCCDAABBB')] → A B C D A B
    # [list(g) for k, g in groupby('AAAABBBCCD')] → AAAA BBB CC D

    keyfunc = (lambda x: x) if key is None else key
    iterator = iter(iterable)
    exhausted = False

    def _grouper(target_key):
        nonlocal curr_value, curr_key, exhausted
        yield curr_value
        for curr_value in iterator:
            curr_key = keyfunc(curr_value)
            if curr_key != target_key:
                return
            yield curr_value
        exhausted = True

    try:
        curr_value = next(iterator)
    except StopIteration:
        return
    curr_key = keyfunc(curr_value)

    while not exhausted:
        target_key = curr_key
        curr_group = _grouper(target_key)
        yield curr_key, curr_group
        if curr_key == target_key:
            for _ in curr_group:
                pass
hessut = []
"""

namecount = dict()

for x in range(0,int(line1)):
    nimi = input().split()[0]
    if firstname == "":
        firstname = nimi
    if nimi not in namecount:
        namecount[nimi] = 1
    else:
        namecount[nimi] = namecount[nimi] + 1

#naa = groupby(hessut)

#awe = [list(g) for k,g in groupby(hessut)]
#print(awe)

#main = []

#for i in awe:
#    main.append([i[0],len(i)])

#print(main)
d = namecount
#print(d)

n = d.pop(firstname)
#print(n)

res = 1
if len(d) == 0:
    print(n)
else:
    k = n+1
    for i in d.keys():
        m = d[i]
        if k-1 < m:
            temp = m
            m = k-1
            k = temp+1

        res = res * ((k**m) - math.comb(k, m))
        k = k + m
    print(res)

Test 1

Verdict: ACCEPTED

Test 2

Verdict: WRONG ANSWER

Test 3

Verdict: WRONG ANSWER

Test 4

Verdict: WRONG ANSWER

Test 5

Verdict: WRONG ANSWER

Test 6

Verdict: WRONG ANSWER

Test 7

Verdict: TIME LIMIT EXCEEDED

Test 8

Verdict: WRONG ANSWER

Test 9

Verdict: TIME LIMIT EXCEEDED

Test 10

Verdict: WRONG ANSWER

Test 11

Verdict: WRONG ANSWER

Test 12

Verdict: TIME LIMIT EXCEEDED

Test 13

Verdict: WRONG ANSWER

Test 14

Verdict: TIME LIMIT EXCEEDED

Test 15

Verdict: WRONG ANSWER

Test 16

Verdict: WRONG ANSWER

Test 17

Verdict: ACCEPTED