Piva and Glasses

#include <cstdio>
#include <iostream>
#include <string>
#include <vector>
using namespace std;

const long long BASE = 1000000000;

int main() {
    string s;
    cin >> s;
    vector<int> cnt(26, 0);
    for (char c : s) cnt[c - 'a']++;
    vector<long long> num(1, 1);
    for (int k = 2; k <= (int)s.size(); k++) {
        long long carry = 0;
        for (auto& d : num) {
            long long cur = d * k + carry;
            d = cur % BASE;
            carry = cur / BASE;
        }
        while (carry) {
            num.push_back(carry % BASE);
            carry /= BASE;
        }
    }
    for (int c = 0; c < 26; c++) {
        for (int k = 2; k <= cnt[c]; k++) {
            long long rem = 0;
            for (int i = num.size() - 1; i >= 0; i--) {
                long long cur = num[i] + rem * BASE;
                num[i] = cur / k;
                rem = cur % k;
            }
            while (num.size() > 1 && num.back() == 0) num.pop_back();
        }
    }
    printf("%lld", num.back());
    for (int i = num.size() - 2; i >= 0; i--) printf("%09lld", num[i]);
    printf("\n");
}

Test 1

Verdict: ACCEPTED

Test 2

Verdict: ACCEPTED

Test 3

Verdict: ACCEPTED

Test 4

Verdict: ACCEPTED

Test 5

Verdict: ACCEPTED

Test 6

Verdict: ACCEPTED

Test 7

Verdict: ACCEPTED

Test 8

Verdict: ACCEPTED

Test 9

Verdict: ACCEPTED

Test 10

Verdict: ACCEPTED

Test 11

Verdict: ACCEPTED

Test 12

Verdict: ACCEPTED

Test 13

Verdict: ACCEPTED

Test 14

Verdict: ACCEPTED

Test 15

Verdict: ACCEPTED

Test 16

Verdict: ACCEPTED

Test 17

Verdict: ACCEPTED

Test 18

Verdict: ACCEPTED

Test 19

Verdict: ACCEPTED

Test 20

Verdict: ACCEPTED

Test 21

Verdict: ACCEPTED

Test 22

Verdict: ACCEPTED

Test 23

Verdict: ACCEPTED

Test 24

Verdict: ACCEPTED

Test 25

Verdict: ACCEPTED

Test 26

Verdict: ACCEPTED

Test 27

Verdict: ACCEPTED

Test 28

Verdict: ACCEPTED

Test 29

Verdict: ACCEPTED

Test 30

Verdict: ACCEPTED