/* author: Kite_kuma created: 2020.09.25 21:53:44 */ // #ifdef LOCAL // #define _GLIBCXX_DEBUG // #endif #include using namespace std; #pragma region aliases #define rep(i, n) for(long long i = 0; i < (n); i++) #define rrep(i, n) for(long long i = (n)-1; i > -1; i--) #define Rep(i, m, n) for(long long i = (m); i < (n); i++) #define rRep(i, m, n) for(long long i = (n)-1; i >= (m); i--) #define REP(i, m, n, p) for(long long i = m; i < n; i += p) #define foa(s, v) for(auto &s : v) #define all(v) (v).begin(), (v).end() #define rall(v) (v).rbegin(), (v).rend() #define bcnt(n) __builtin_popcountll(n) #define endk endl #define ednl endl #define enld endl using ll = long long; using ld = long double; using ull = unsigned long long; using vb = vector; using vi = vector; using vvi = vector>; using vvvi = vector>>; using vll = vector; using vvll = vector; using vvvll = vector; using mll = map; using pll = pair; using qll = queue; using sll = set; using vpll = vector>; template using V = vector; template using VV = V>; template using VVV = V>>; //昇順pq(小さい方から取り出す) template using pqup = priority_queue, greater>; //降順pq(大きい方から取り出す) template using pqdn = priority_queue; #pragma endregion #pragma region constants long long const limLL = 9223372036854775807; // POW(2,63)-1 ~ 9.22e18 long long const dekai = 3e16; const long double pi = acos(-1); const char dl = '\n'; int dx[4] = {1, 0, -1, 0}; int dy[4] = {0, 1, 0, -1}; int ddx[8] = {-1, -1, -1, 0, 0, 1, 1, 1}; int ddy[8] = {-1, 0, 1, -1, 1, -1, 0, 1}; const int mod = 1000000007; // const int mod = 998244353; #pragma endregion #pragma region basic_procedure template inline bool isin(T x, T lef, T rig) { return ((lef <= x) && (x < rig)); } template inline bool chmin(T &a, T b) { if(a > b) { a = b; return true; } return false; } template inline bool chmax(T &a, T b) { if(a < b) { a = b; return true; } return false; } void Yes(bool f = 1) { cout << (f ? "Yes" : "No") << "\n"; } void No() { cout << "No\n"; } void YES(bool f = 1) { cout << (f ? "YES" : "NO") << "\n"; } void NO() { cout << "NO\n"; } template void drop(T answer) { cout << answer << "\n"; exit(0); } void err() { cout << -1 << "\n"; exit(0); } template void vout(vector &v, bool tate = 0) { if(v.size() > 0) { for(auto it = v.begin(); it < v.end(); it++) { cout << *it; if(it != v.end() - 1) { if(tate) cout << endl; else cout << " "; } } } cout << endl; } template void add(vector &v, T val) { //ベクトルの各要素に加算 for(auto &a : v) a += val; return; } // vectorの中身を数える map<要素,個数>を返す template map cntv(vector v) { map m; for(auto &g : v) { if(m.count(g)) m[g]++; else m[g] = 1; } return m; } //配列圧縮 //{1,36,1,3,8,-2,-92}を //{2, 5,2,3,4, 1, 0}にする template vector press(vector &v) { long long n = v.size(); vector w(n); map m; for(T &p : v) m[p] = 0; long long i = 0; for(auto &p : m) { p.second = i; i++; } for(long long i = 0; i < n; i++) w.at(i) = m[v.at(i)]; return w; } // 切り上げ除算 template T dup(T a, T b) { assert(b != 0); T x = abs(a); T y = abs(b); T z = (x + y - 1) / y; if((a < 0 && b > 0) || (a > 0 && b < 0)) return -z; else if(a == 0) return 0; else return z; } long long POW(long long a, long long n) { long long res = 1; while(n > 0) { if(n & 1) res = res * a; a = a * a; n >>= 1; if(res > mod || a > mod) { drop(mod); } } return res; } template T greatest_lower_multiple(T x, T d) { if(d == 0) return 0; if(d < 0) d *= -1; T y = x % d; if(y < 0) y += d; return x - y; } template T least_upper_multiple(T x, T d) { return -greatest_lower_multiple(-x, d); } long long modpow(long long a, long long n, long long mod) { // a^n mod if(mod == 1) return 0LL; long long res = 1; while(n > 0) { if(n & 1) res = res * a % mod; a = a * a % mod; n >>= 1; } return res; } // a * x % mod == __gcd(a,mod)なるxを返す // a が modの倍数でないことが条件 long long modinv(long long a, long long mod) { long long b = mod, u = 1, v = 0; while(b) { long long t = a / b; a -= t * b; swap(a, b); u -= t * v; swap(u, v); } u %= mod; if(u < 0) u += mod; return u; } vvll comb(100, vll(100, -1)); long long com(long long n, long long k) { //普通の二項計数(overflowに注意) assert(n < 100 && k < 100); if(n < k || k < 0 || n < 0) return 0; if(comb[n][k] != -1) return comb[n][k]; ll res; if(n - k < k) res = com(n, n - k); else if(k == 0) res = 1; else res = com(n - 1, k - 1) + com(n - 1, k); comb[n][k] = res; return res; } // nCk modを求める const int MAX = 5100000; // この値は求める二項計数の値に応じて変える // MAX=3*10^7のとき1900msほど、ほぼ比例 // MAX=5*10^6程度ならそれほど気にしなくてよい(300ms程) long long fac[MAX], finv[MAX], inv[MAX]; void cominit() { // テーブルを作る前処理 fac[0] = fac[1] = 1; finv[0] = finv[1] = 1; inv[1] = 1; for(int i = 2; i < MAX; i++) { fac[i] = fac[i - 1] * i % mod; inv[i] = mod - inv[mod % i] * (mod / i) % mod; finv[i] = finv[i - 1] * inv[i] % mod; } } long long commod(long long n, long long k) { // 二項係数 if(n < k) return 0; if(n < 0 || k < 0) return 0; return fac[n] * (finv[k] * finv[n - k] % mod) % mod; } long long pmod(long long n, long long k) { // 順列 if(n < k) return 0; if(n < 0 || k < 0) return 0; return fac[n] * finv[n - k] % mod; } // n個の区別しないボールを区別するk個の箱に入れる方法の総数 long long hmod(long long n, long long k) { // 重複組み合わせ return commod(n + k - 1, n); } #pragma endregion #pragma region input #define VEC(type, name, size) \ vector name(size); \ INPUT(name) #define VVEC(type, name, h, w) \ vector> name(h, vector(w)); \ INPUT(name) #define INT(...) \ int __VA_ARGS__; \ INPUT(__VA_ARGS__) #define LL(...) \ long long __VA_ARGS__; \ INPUT(__VA_ARGS__) #define STR(...) \ string __VA_ARGS__; \ INPUT(__VA_ARGS__) #define CHAR(...) \ char __VA_ARGS__; \ INPUT(__VA_ARGS__) #define DOUBLE(...) \ double __VA_ARGS__; \ INPUT(__VA_ARGS__) #define LD(...) \ long double __VA_ARGS__; \ INPUT(__VA_ARGS__) template void scan(T &a) { cin >> a; } template void scan(vector &a) { for(auto &i : a) scan(i); } template void scan(pair &p) { scan(p.first); scan(p.second); } void INPUT() {} template void INPUT(Head &head, Tail &... tail) { scan(head); INPUT(tail...); } template inline void print(T x) { cout << x << '\n'; } template istream &operator>>(istream &is, pair &p) { is >> p.first >> p.second; return is; } #pragma endregion #pragma region debug #pragma region output template ostream &operator<<(ostream &os, const pair &p) { os << p.first << " " << p.second; return os; } template ostream &operator<<(ostream &os, const vector &v) { for(int i = 0; i < (int)v.size(); i++) { if(i) os << " "; os << v[i]; } return os; } #pragma endregion #pragma region view template void view(const T e) { std::cerr << e; } template void view(const std::pair &p) { std::cerr << "("; view(p.first); cerr << ", "; view(p.second); cerr << ")"; } template void view(std::set &s) { if(s.empty()) { cerr << "{ }"; return; } std::cerr << "{ "; for(auto &t : s) { view(t); std::cerr << ", "; } std::cerr << "\b\b }"; } template void view(const std::vector &v) { if(v.empty()) { cerr << "{ }"; return; } std::cerr << "{ "; for(const auto &e : v) { view(e); std::cerr << ", "; } std::cerr << "\b\b }"; } template void view(const std::vector> &vv) { std::cerr << "{\n"; for(const auto &v : vv) { std::cerr << "\t"; view(v); std::cerr << "\n"; } std::cerr << "}"; } template void view(const std::vector> &v) { std::cerr << "{\n"; for(const auto &c : v) { std::cerr << "\t("; view(c.first); cerr << ", "; view(c.second); cerr << ")\n"; } std::cerr << "}"; } template void view(const std::map &m) { std::cerr << "{\n"; for(auto &t : m) { std::cerr << "\t["; view(t.first); cerr << "] : "; view(t.second); cerr << "\n"; } std::cerr << "}"; } #pragma endregion // when debugging : g++ foo.cpp -DLOCAL #ifdef LOCAL void debug_out() {} template void debug_out(Head H, Tail... T) { view(H); cerr << ", "; debug_out(T...); } #define debug(...) \ do { \ cerr << __LINE__ << " [" << #__VA_ARGS__ << "] : ["; \ debug_out(__VA_ARGS__); \ cerr << "\b\b]\n"; \ } while(0) #define dump(x) \ do { \ cerr << __LINE__ << " " << #x << " : "; \ view(x); \ cerr << "\n"; \ } while(0) #else #define debug(...) (void(0)) #define dump(x) (void(0)) #endif #pragma endregion #pragma region modint template struct ModInt { int x; ModInt() : x(0) {} ModInt(long long y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {} ModInt &operator+=(const ModInt &p) { if((x += p.x) >= mod) x -= mod; return *this; } ModInt &operator-=(const ModInt &p) { if((x += mod - p.x) >= mod) x -= mod; return *this; } ModInt &operator*=(const ModInt &p) { x = (int)(1LL * x * p.x % mod); return *this; } ModInt &operator/=(const ModInt &p) { *this *= p.inverse(); return *this; } ModInt operator-() const { return ModInt(-x); } ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; } ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; } ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; } ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; } bool operator==(const ModInt &p) const { return x == p.x; } bool operator!=(const ModInt &p) const { return x != p.x; } ModInt inverse() const { int a = x, b = mod, u = 1, v = 0, t; while(b > 0) { t = a / b; swap(a -= t * b, b); swap(u -= t * v, v); } return ModInt(u); } ModInt pow(long long n) const { ModInt ret(1), mul(x); while(n > 0) { if(n & 1) ret *= mul; mul *= mul; n >>= 1; } return ret; } friend ostream &operator<<(ostream &os, const ModInt &p) { return os << p.x; } friend istream &operator>>(istream &is, ModInt &a) { long long t; is >> t; a = ModInt(t); return (is); } static int get_mod() { return mod; } }; using mint = ModInt; #pragma endregion map soinsuu(long long n) { // map<素因数,個数> map m; long long p = sqrt(n); while(n % 2 == 0) { n /= 2; if(m.count(2)) { m[2]++; } else { m[2] = 1; } } for(long long i = 3; i * i <= n; i += 2) { while(n % i == 0) { n /= i; if(m.count(i)) { m[i]++; } else { m[i] = 1; } } } if(n != 1) m[n] = 1; return m; } int main() { ios::sync_with_stdio(false); cin.tie(nullptr); cout << fixed << setprecision(15); srand((unsigned)time(NULL)); INT(n); VEC(ll, a, n); sort(all(a)); ll res = 1; foa(t, a) { if(t == 0) err(); if(t > 4){ drop(mod); } ll fac = 1; rep(i, t) { fac *= (i + 1); } res *= POW(t, fac); if(res > mod){ drop(mod); } } drop(mod % res); return 0; }