#include using namespace std; using lint = long long; template using V = vector; template using VV = V< V >; template struct ModInt { using M = ModInt; unsigned v; ModInt() : v(0) {} ModInt(auto x) : v(x >= 0 ? x % P : (P - -x % P) % P) {} constexpr ModInt(unsigned v, int) : v(v) {} static constexpr unsigned p() { return P; } M operator+() const { return *this; } M operator-() const { return {v ? P - v : 0, 0}; } explicit operator bool() const noexcept { return v; } bool operator!() const noexcept { return !(bool)*this; } M operator*(M r) const { return M(*this) *= r; } M operator/(M r) const { return M(*this) /= r; } M operator+(M r) const { return M(*this) += r; } M operator-(M r) const { return M(*this) -= r; } bool operator==(M r) const { return v == r.v; } bool operator!=(M r) const { return !(*this == r); } M& operator*=(M r) { v = (uint64_t)v * r.v % P; return *this; } M& operator/=(M r) { return *this *= r.inv(); } M& operator+=(M r) { if ((v += r.v) >= P) v -= P; return *this; } M& operator-=(M r) { if ((v += P - r.v) >= P) v -= P; return *this; } M inv() const { int a = v, b = P, x = 1, u = 0; while (b) { int q = a / b; swap(a -= q * b, b); swap(x -= q * u, u); } assert(a == 1); return x; } M pow(auto n) const { if (n < 0) return pow(-n).inv(); M res = 1; for (M a = *this; n; a *= a, n >>= 1) if (n & 1) res *= a; return res; } friend M operator*(auto l, M r) { return M(l) *= r; } friend M operator/(auto l, M r) { return M(l) /= r; } friend M operator+(auto l, M r) { return M(l) += r; } friend M operator-(auto l, M r) { return M(l) -= r; } friend ostream& operator<<(ostream& os, M r) { return os << r.v; } friend istream& operator>>(istream& is, M& r) { lint x; is >> x; r = x; return is; } friend bool operator==(auto l, M r) { return M(l) == r; } friend bool operator!=(auto l, M r) { return !(l == r); } }; using Mint = ModInt<(unsigned)1e9 + 7>; using R = double; constexpr R pi = acos((R) -1); using C = complex; C& operator*=(C& l, const C& r) { return l = {real(l) * real(r) - imag(l) * imag(r), real(l) * imag(r) + imag(l) * real(r)}; } void fft(V& a, bool inv = false) { int n = a.size(); int j = 0; for (int i = 1; i < n; ++i) { int w = n >> 1; while (j >= w) j -= w, w >>= 1; j += w; if (i < j) swap(a[i], a[j]); } static VV xi(30); for (int k = 0; 1 << k < n; ++k) if (xi[k].empty()) { xi[k].resize(1 << k); for (int i = 0; i < 1 << k; ++i) { xi[k][i] = polar(1, i * pi / (1 << k)); } } for (int k = 0; 1 << k < n; ++k) { const int w = 1 << k; for (int s = 0; s < n; s += 2 * w) { for (int i = s; i < s + w; ++i) { j = i + w; a[j] *= inv ? conj(xi[k][i - s]) : xi[k][i - s]; tie(a[i], a[j]) = make_pair(a[i] + a[j], a[i] - a[j]); } } } } template void multiply(V& a, V b) { if (a.empty() or b.empty()) { a = {}; return; } int n = 1 << __lg(2 * (a.size() + b.size() - 1) - 1); V f(n), g(n); for (int i = 0; i < n; ++i) { if (i < (int) a.size()) f[i].real(a[i].v & ~(~0 << K)), f[i].imag(a[i].v >> K); if (i < (int) b.size()) g[i].real(b[i].v & ~(~0 << K)), g[i].imag(b[i].v >> K); } fft(f), fft(g); V Al(n), Au(n), Bl(n), Bu(n); for (int i = 0; i < n; ++i) { Al[i] = (f[i] + conj(f[-i & n - 1])) / C(2, 0); Au[i] = (f[i] - conj(f[-i & n - 1])) / C(0, 2); Bl[i] = (g[i] + conj(g[-i & n - 1])) / C(2, 0); Bu[i] = (g[i] - conj(g[-i & n - 1])) / C(0, 2); } for (int i = 0; i < n; ++i) { f[i] = Al[i] * Bl[i] + C(0, 1) * Al[i] * Bu[i]; g[i] = Au[i] * Bl[i] + C(0, 1) * Au[i] * Bu[i]; } fft(f, true), fft(g, true); a.resize(a.size() + b.size() - 1); for (int i = 0; i < (int) a.size(); ++i) { lint l = real(f[i]) / n + 0.5; lint m = (imag(f[i]) + real(g[i])) / n + 0.5; lint u = imag(g[i]) / n + 0.5; a[i] = l + m * Mint(1 << K) + u * Mint(1 << 2 * K); } } int main() { cin.tie(nullptr); ios::sync_with_stdio(false); int n; cin >> n; V<> a(n); for (auto&& e : a) cin >> e; Mint res = 1; { V c(1e5 + 1); for (int e : a) c[e] += 1; multiply(c, c); for (int e : a) c[2 * e] -= 1; for (auto&& e : c) e /= 2; for (int i = 2; i <= 2e5; ++i) if (c[i]) { res *= Mint(i).pow(c[i].v); } } { V c(n + 1); for (int i = n - 1; i >= 0; --i) c[i] += a[i] + c[i + 1]; for (int i = 0; i < n; ++i) { res *= Mint(a[i]).pow(c[i + 1]); } } { auto mn = a; for (int i = n - 2; i >= 0; --i) mn[i] = min(a[i], mn[i + 1]); int mi = -1; { long double x = 1e10; for (int i = 0; i < n - 1; ++i) { long double curr = log((long double)a[i] + mn[i + 1]) + mn[i + 1] * log((long double)a[i]); if (curr < x) { x = curr; mi = i; } } } res /= (a[mi] + mn[mi + 1]) * Mint(a[mi]).pow(mn[mi + 1]); } cout << res << '\n'; }