#include using namespace std; using ll = long long; constexpr char newl = '\n'; // https://noshi91.hatenablog.com/entry/2019/03/31/174006 template struct ModInt { using u64 = std::uint_fast64_t; static constexpr u64 MOD = Modulus; u64 val; constexpr ModInt(const u64 x = 0) noexcept : val(x % MOD) {} constexpr ModInt operator+() const noexcept { return ModInt(*this); } constexpr ModInt operator-() const noexcept { ModInt res(*this); if (res.val != 0) res.val = MOD - res.val; return res; } constexpr bool operator==(const ModInt& rhs) const noexcept { return val == rhs.val; } constexpr bool operator!=(const ModInt& rhs) const noexcept { return val != rhs.val; } // prefix increment/decrement constexpr ModInt& operator++() noexcept { return *this += ModInt(1); } constexpr ModInt& operator--() noexcept { return *this -= ModInt(1); } // postfix increment/decrement constexpr ModInt operator++(int) noexcept { ModInt tmp(*this); ++*this; return tmp; } constexpr ModInt operator--(int) noexcept { ModInt tmp(*this); --*this; return tmp; } constexpr ModInt operator+(const ModInt& rhs) const noexcept { return ModInt(*this) += rhs; } constexpr ModInt operator-(const ModInt& rhs) const noexcept { return ModInt(*this) -= rhs; } constexpr ModInt operator*(const ModInt& rhs) const noexcept { return ModInt(*this) *= rhs; } constexpr ModInt operator/(const ModInt& rhs) const noexcept { return ModInt(*this) /= rhs; } constexpr ModInt& operator+=(const ModInt& rhs) noexcept { val += rhs.val; if (val >= MOD) val -= MOD; return *this; } constexpr ModInt& operator-=(const ModInt& rhs) noexcept { if (val < rhs.val) val += MOD; val -= rhs.val; return *this; } constexpr ModInt& operator*=(const ModInt& rhs) noexcept { val = val * rhs.val % MOD; return *this; } // prime Modulus only constexpr ModInt& operator/=(const ModInt& rhs) noexcept { return *this *= rhs.inv(); } // prime Modulus only constexpr ModInt inv() const noexcept { return pow(*this, MOD - 2); } }; template constexpr ModInt pow(ModInt x, std::uint_fast64_t n) { ModInt res(1); while (n) { if (n & 1) res *= x; x *= x; n >>= 1; } return res; } template istream& operator>>(istream& is, ModInt& x) { std::uint_fast64_t val; is >> val; x = ModInt(val); return is; } template ostream& operator<<(ostream& os, const ModInt& x) { return os << x.val; } using mint = ModInt<1000000007>; // g++ -Wl,--stack,[STACK SIZE] [file] でスタックサイズを増やすか、 // グローバル変数として宣言して使うこと!!! template struct Comb { array fact, fact_inv; constexpr Comb() noexcept { fact[0] = 1; for (size_t i = 1; i <= MAXV; i++) { fact[i] = fact[i - 1] * i; } fact_inv[MAXV] = fact[MAXV].inv(); for (size_t i = MAXV; i > 0; i--) { fact_inv[i - 1] = fact_inv[i] * i; } } constexpr T operator()(int n, int k) const noexcept { if (n < k || n < 0 || k < 0) return 0; return fact[n] * fact_inv[k] * fact_inv[n - k]; } constexpr T perm(int n, int k) const noexcept { if (n < k || n < 0 || k < 0) return 0; return fact[n] * fact_inv[n - k]; } }; const Comb<1000000> comb; template vector divisor(T n) { vector res; for (T i = 1; i * i <= n; i++) { if (n % i == 0) { res.emplace_back(i); if (i != n / i) res.emplace_back(n / i); } } return res; } /* map moebius(int n) { map res; vector primes; for (int i = 2; i * i <= n; i++) { if (n % i == 0) { primes.push_back(i); while (n % i == 0) n /= i; } } if (n != 1) primes.push_back(n); int m = primes.size(); for (int i = 0; i < (1 << m); i++) { int mu = 1, d = 1; for (int j = 0; j < m; j++) { if (i >> j & 1) { mu *= -1; d *= primes[j]; } } res[d] = mu; } return res; }*/ int main() { cin.tie(nullptr); ios::sync_with_stdio(false); int K; cin >> K; int sum = 0; vector c(K); for (int i = 0; i < K; i++) { cin >> c[i]; sum += c[i]; } int g = sum; for (int i = 0; i < K; i++) { g = __gcd(g, c[i]); } vector v = divisor(g); sort(v.begin(), v.end()); int sz = v.size(); // map meb = moebius(sum); mint ans = 0; vector dp(sz, 0); for (int i = sz - 1; i >= 0; i--) { int d = v[i]; int num = sum / d; dp[i] = comb.fact[num]; for (int j = 0; j < K; j++) { dp[i] /= comb.fact[c[j] / d]; } for (int j = i + 1; j < sz; j++) { int num2 = sum / v[j]; if (num % num2 != 0) continue; dp[i] -= dp[j]; } ans += dp[i] / num; } cout << ans << newl; return 0; }