#include #include #include #define REP(i,s,n) for(int i=(int)(s);i<(int)(n);i++) using namespace std; typedef long long int ll; typedef vector VI; typedef vector VL; const ll mod = 1e9 + 7; const int W = 10000; ll fact[W]; // \sum_{S, |S| = v} \prod{i in S} kind[i] vector comb(const VI &kind) { int n = kind.size(); VL ret(n + 1); ret[0] = 1; REP(b, 0, n) { for (int i = n - 1; i >= 0; --i) { ret[i + 1] += ret[i] * kind[b]; ret[i + 1] %= mod; } } return ret; } int main(void){ int n; cin >> n; VI a(n); VI kind(n); REP(i, 0, n) { cin >> a[i]; if (a[i] < n) { kind[a[i]]++; } } fact[0] = 1; REP(i, 1, W) { fact[i] = fact[i - 1] * i % mod; } ll sum = 0; VL cb = comb(kind); REP(i, 0, n + 1) { ll tmp = fact[n - i]; if (i % 2 == 1) { tmp = (mod - tmp) % mod; } tmp *= cb[i]; sum += tmp; sum %= mod; } cout << sum << endl; }