// includes #include using namespace std; // macros #define pb emplace_back #define mk make_pair #define FOR(i, a, b) for(int i=(a);i<(b);++i) #define rep(i, n) FOR(i, 0, n) #define rrep(i, n) for(int i=((int)(n)-1);i>=0;i--) #define irep(itr, st) for(auto itr = (st).begin(); itr != (st).end(); ++itr) #define irrep(itr, st) for(auto itr = (st).rbegin(); itr != (st).rend(); ++itr) #define all(x) (x).begin(),(x).end() #define sz(x) ((int)(x).size()) #define UNIQUE(v) v.erase(unique(v.begin(), v.end()), v.end()) #define bit(n) (1LL<<(n)) // functions template bool chmax(T &a, const T &b){if(a < b){a = b; return 1;} return 0;} template bool chmin(T &a, const T &b){if(a > b){a = b; return 1;} return 0;} template istream &operator>>(istream &is, vector &vec){for(auto &v: vec)is >> v; return is;} template ostream &operator<<(ostream &os, const vector& vec){for(int i = 0; i < vec.size(); i++){ os << vec[i]; if(i + 1 != vec.size())os << " ";} return os;} template ostream &operator<<(ostream &os, const set& st){for(auto itr = st.begin(); itr != st.end(); ++itr){ os << *itr; auto titr = itr; if(++titr != st.end())os << " ";} return os;} template ostream &operator<<(ostream &os, const unordered_set& st){for(auto itr = st.begin(); itr != st.end(); ++itr){ os << *itr; auto titr = itr; if(++titr != st.end())os << " ";} return os;} template ostream &operator<<(ostream &os, const multiset& st){for(auto itr = st.begin(); itr != st.end(); ++itr){ os << *itr; auto titr = itr; if(++titr != st.end())os << " ";} return os;} template ostream &operator<<(ostream &os, const unordered_multiset& st){for(auto itr = st.begin(); itr != st.end(); ++itr){ os << *itr; auto titr = itr; if(++titr != st.end())os << " ";} return os;} template ostream &operator<<(ostream &os, const pair &p){os << p.first << " " << p.second; return os;} template ostream &operator<<(ostream &os, const map &mp){for(auto itr = mp.begin(); itr != mp.end(); ++itr){ os << itr->first << ":" << itr->second; auto titr = itr; if(++titr != mp.end())os << " "; } return os;} template ostream &operator<<(ostream &os, const unordered_map &mp){for(auto itr = mp.begin(); itr != mp.end(); ++itr){ os << itr->first << ":" << itr->second; auto titr = itr; if(++titr != mp.end())os << " "; } return os;} // types using ll = long long int; using P = pair; // constants const int inf = 1e9; const ll linf = 1LL << 50; const double EPS = 1e-10; const int mod = 1000000007; const int dx[4] = {-1, 0, 1, 0}; const int dy[4] = {0, -1, 0, 1}; // io struct fast_io{ fast_io(){ios_base::sync_with_stdio(false); cin.tie(0); cout << fixed << setprecision(20);} } fast_io_; template T power(T a, T n, T mod) { T res = 1; T tmp = n; T curr = a; while(tmp){ if(tmp % 2 == 1){ res = (T)(res * curr % mod); } curr = (T)(curr * curr % mod); tmp >>= 1; } return res; } struct Factorial{ int n = 0; static const long long mod_default = 1e9 + 7; long long MOD = mod_default; vector fac; vector inv_; explicit Factorial(){} explicit Factorial(int n, long long mod_=mod_default): n(n), MOD(mod_){ assert(MOD > 0 && n < MOD); fac.resize(n + 1); inv_.resize(n + 1); calc_factorial(); calc_inv(); } void calc_factorial(){ fac[0] = 1; for(int i = 1; i <= n; i++){ fac[i] = i * fac[i-1] % MOD; } } void calc_inv(){ inv_[n] = power(fac[n], MOD - 2, MOD); for(int i = n - 1; i >= 0; i--){ inv_[i] = (i + 1) * inv_[i+1] % MOD; } } long long& operator[](size_t i){ if((int)i > n){ cerr << "list index out of range" << endl; abort(); } return fac[i]; } long long inv(size_t i){ if((int)i > n){ cerr << "list index out of range" << endl; abort(); } return inv_[i]; } long long comb(int n, int k){ if(n < 0 || k < 0 || n < k)return 0; long long res = fac[n]; res = res * inv_[n-k] % MOD; res = res * inv_[k] % MOD; return res; } long long perm(int n, int k){ if(n < 0 || k < 0 || n < k)return 0; long long res = fac[n]; res = res * inv_[n-k] % MOD; return res; } long long h(int n, int k){ if(n == 0 && k == 0)return 1; return comb(n + k - 1, k); } }; ll dp[5010][5010]; int cnt[5010]; int main(int argc, char const* argv[]) { Factorial fac(5010); int n; cin >> n; int c = 0; rep(i, n){ int a; cin >> a; cnt[a]++; if(a >= n)c++; } dp[0][c] = 1; int curr = c; rep(i, n){ rep(j, curr + 1){ int k = cnt[i]; (dp[i+1][j+k] += dp[i][j]) %= mod; if(j > 0)(dp[i+1][j+k-1] += dp[i][j] * j % mod) %= mod; FOR(l, 1, min(k, i + j - curr) + 1){ (dp[i+1][j+k-l] += (dp[i][j] * fac.comb(i+j-curr, l) % mod) * fac.perm(k, l) % mod) %= mod; if(j > 0)(dp[i+1][j+k-l-1] += ((dp[i][j] * j % mod) * fac.comb(i+j-curr, l) % mod) * fac.perm(k, l) % mod) %= mod; } } curr += cnt[i]; } /*rep(i, n + 1){ rep(j, n + 1){ cerr << i << " " << j << " " << dp[i][j] << endl; } }*/ cout << dp[n][0] << endl; return 0; }