Lucky prefixes

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef vector<ll> vi;
#define til(n) for(ll i = 0; i < n; i++)

constexpr ll mod = 1e9+7;


ll euclid(ll a, ll b, ll& x, ll& y){
    if (!b) return x=1,y=0,a;
    ll d = euclid(b,a%b,y,x);
    return y-=a/b * x, d;
}

struct Mod {
    ll x;
    Mod(ll xx) : x(xx) {}
    Mod operator* (Mod b) { return Mod((x * b.x) % mod); }
    Mod operator/ (Mod b) { return *this * invert(b); }
    Mod invert(Mod a) {
        ll x,y,g = euclid(a.x,mod,x,y);
        assert (g==1);
        return Mod((x+mod) % mod);
    }
};

auto fac(ll n) {
    auto total = Mod(1);
    til(n) {
        total = (total * (i + 1));
    }
    return total;
}

int main() {
    cin.tie(0)->sync_with_stdio(false);
    cout.tie(0)->sync_with_stdio(false);
    ll n;
    unordered_map<string,ll> m;
    cin >> n;
    til(n) {
        string s;
        ll _;
        cin >> s >> _;
        m[s]++;
    }
    auto total = fac(n);
    for (auto [k, v] : m) {
        total = total / fac(v);
    }
    cout << total.x << '\n';
}

Test 1

Verdict: WRONG ANSWER

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: WRONG ANSWER

Test 8

Verdict: WRONG ANSWER

Test 9

Verdict: WRONG ANSWER

Test 10

Verdict: WRONG ANSWER

Test 11

Verdict: WRONG ANSWER

Test 12

Verdict: WRONG ANSWER

Test 13

Verdict: WRONG ANSWER

Test 14

Verdict: WRONG ANSWER

Test 15

Verdict: WRONG ANSWER

Test 16

Verdict: WRONG ANSWER