Aristocracy

#include <bits/stdc++.h>
using namespace std;

#ifdef LOCAL
#define D(x) {x;}
#else
#define D(x)
#endif
#define rep(i, a, b) for(int i = a; i < (b); ++i)
#define all(x) begin(x),end(x)
#define sz(x) (int) (x).size()
using ll = long long;
using pii = pair<int, int>;
using vi = vector<int>;

const int M = 1e9 + 7;

ll mpow(ll x, ll e) {
    if (e == 0) return 1;
    ll a = mpow(x, e/2);
    a = (a * a) % M;
    if (e & 1) a = a * x % M;
    return a;
}

ll inv(ll x) {
    return mpow(x, M-2);
}

int main() {
    cin.tie(0) -> sync_with_stdio(0);
    cin.exceptions(cin.failbit);

    int n;
    cin >> n;
    
    vector<pair<string, int>> v(n);
    for (int i = 0; i < n; ++i) {
        cin >> v[i].first >> v[i].second;
    }

    sort(all(v));
    ll ans = 1;
    ll d = 1;
    int c = 1;
    for (int i = 0; i < n; ++i) {
        if (i > 0) {
            if (v[i].first == v[i-1].first) ++c;
            else c = 1;
        }
        ans = (ans * (i+1)) % M;
        d = d * c % M;
    }

    ans = ans * inv(d) % M;
    cout << ans << '\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