Aristocracy

#include <bits/stdc++.h>

using namespace std;

using ll = long long;

const ll MOD   = 1e9 + 7;
const ll MAX_N = 1e5 + 123;

ll factorial[MAX_N];
ll inv_factorial[MAX_N];

ll binpow(ll a, ll n)
{
    if (n == 0) return 1LL;
    if (n % 2 == 0)
    {
        ll tmp = binpow(a, n / 2);
        return (tmp * tmp) % MOD;
    }
    return (a * binpow(a, n - 1)) % MOD;
}

ll cnk(ll n, ll k)
{
    return ((factorial[n] * inv_factorial[k]) % MOD * inv_factorial[n - k]) % MOD;
}

int main()
{
    ios_base::sync_with_stdio(false);

    factorial[0]     = 1LL;
    inv_factorial[0] = binpow(factorial[0], MOD - 2);
    for (ll i = 1; i < MAX_N; i++)
    {
        factorial[i]     = (factorial[i - 1] * i) % MOD;
        inv_factorial[i] = binpow(factorial[i], MOD - 2);
    }

    ll n;
    cin >> n;

    map<string, ll> data;
    for (ll i = 0; i < n; i++)
    {
        string name;
        cin >> name;
        ll number;
        cin >> number;
        data[name]++;
    }

    ll cnt_orders = 1LL;
    ll already_placed = 0LL;
    for (const auto& it : data)
    {
        ll x = it.second;
        assert(n >= already_placed);
        assert((n - already_placed) >= x);
        cnt_orders = (cnt_orders * cnk(n - already_placed, x)) % MOD;
        already_placed += x;
    }

    cout << cnt_orders << '\n';

    return 0;
}

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