Aristocracy

#include <bits/stdc++.h>

using namespace std;

typedef uint64_t ll;

int kertoma(ll n, unordered_map<ll, ll> mon) {
    ll mod = 1000000007;

    if (mon.count(n)>0) {
        return mon.at(n);
    } else {
        ll x = (kertoma(n-1, mon)*n)%mod;
        mon.insert({n, x});
        return x;
    }

}
template<class T>
T power(T base, T exp, T mod) {
    T ans = 1;
    base %= mod;

    while(exp > 0) {
        if (exp&1) ans = (ans * base) % mod;
        exp >>= 1;
        base = (base*base)%mod;
    }
    return ans;
}
template<class T>
T modInverse(T a, T m) {
    return power(a, m-2, m);
}

int main() {
    ll mod = 1000000007;
    ll n;
    cin >> n;
    unordered_map<ll, ll> kertomat = {{1, 1}};
    unordered_map<string, ll> monarchs = {};

    for (ll i = 0; i < n; i++) {
        string monarch;
        ll num;

        cin >> monarch >> num;

        if (monarchs.count(monarch)>0) {
            monarchs.at(monarch) += 1;
        } else {
            monarchs.insert({monarch, 1});
        }
    }

    ll tulo = 1;

    for ( auto it = monarchs.begin(); it != monarchs.end(); ++it ) {
        ll x = it->second;
        ll kert = kertoma(x, kertomat);
        tulo = (kert*tulo)%mod;
    }

    ll kert = kertoma(n, kertomat);

    ll modinv = modInverse(tulo, mod);



    cout << (kert*modinv)%mod << endl;

}

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