#include <bits/stdc++.h>
using namespace std;
using lint = long long;
template<class T = int> using V = vector<T>;
template<class T = int> using VV = V< V<T> >;

template<unsigned P> 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<R>;
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<C>& 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<C> 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<R>(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<class Z> void multiply(V<Z>& a, const V<Z>& b) {
  assert(!a.empty() and !b.empty());
  int n = 1 << __lg(2 * (a.size() + b.size() - 1) - 1);
  V<C> c(n);
  for (int i = 0; i < n; ++i) {
    if (i < (int) a.size()) c[i].real(a[i]);
    if (i < (int) b.size()) c[i].imag(b[i]);
  }
  fft(c);
  for (int i = 0; i <= n / 2; ++i) {
    c[i] *= c[i];
    if (i & n / 2 - 1) c[n - i] *= c[n - i];
    c[i] = C(0, -0.25) * (c[i] - conj(c[n - i & n - 1]));
    if (i & n / 2 - 1) c[n - i] = conj(c[i]);
  }
  fft(c, true);
  a.resize(a.size() + b.size() - 1);
  for (int i = 0; i < (int) a.size(); ++i) {
    a[i] = real(c[i]) / n + 0.5;
  }
}

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<lint> 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<lint> 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';
}