#include #ifdef DEBUG #include #else #define dump(...) #endif /** * @title Modint * @docs mint.md */ template class ModInt{ public: constexpr static uint32_t MOD = M; uint64_t val; constexpr ModInt(): val(0){} constexpr ModInt(int64_t n){ if(n >= M) val = n % M; else if(n < 0) val = n % M + M; else val = n; } inline constexpr auto operator+(const ModInt &a) const {return ModInt(val + a.val);} inline constexpr auto operator-(const ModInt &a) const {return ModInt(val - a.val);} inline constexpr auto operator*(const ModInt &a) const {return ModInt(val * a.val);} inline constexpr auto operator/(const ModInt &a) const {return ModInt(val * a.inv().val);} inline constexpr auto& operator=(const ModInt &a){val = a.val; return *this;} inline constexpr auto& operator+=(const ModInt &a){if((val += a.val) >= M) val -= M; return *this;} inline constexpr auto& operator-=(const ModInt &a){if(val < a.val) val += M; val -= a.val; return *this;} inline constexpr auto& operator*=(const ModInt &a){(val *= a.val) %= M; return *this;} inline constexpr auto& operator/=(const ModInt &a){(val *= a.inv().val) %= M; return *this;} inline constexpr bool operator==(const ModInt &a) const {return val == a.val;} inline constexpr bool operator!=(const ModInt &a) const {return val != a.val;} inline constexpr auto& operator++(){*this += 1; return *this;} inline constexpr auto& operator--(){*this -= 1; return *this;} inline constexpr auto operator++(int){auto t = *this; *this += 1; return t;} inline constexpr auto operator--(int){auto t = *this; *this -= 1; return t;} inline constexpr static ModInt power(int64_t n, int64_t p){ if(p < 0) return power(n, -p).inv(); int64_t ret = 1, e = n % M; for(; p; (e *= e) %= M, p >>= 1) if(p & 1) (ret *= e) %= M; return ret; } inline constexpr static ModInt inv(int64_t a){ int64_t b = M, u = 1, v = 0; while(b){ int64_t t = a / b; a -= t * b; std::swap(a,b); u -= t * v; std::swap(u,v); } u %= M; if(u < 0) u += M; return u; } inline constexpr static auto frac(int64_t a, int64_t b){return ModInt(a) / ModInt(b);} inline constexpr auto power(int64_t p) const {return power(val, p);} inline constexpr auto inv() const {return inv(val);} friend inline constexpr auto operator-(const ModInt &a){return ModInt(-a.val);} friend inline constexpr auto operator+(int64_t a, const ModInt &b){return ModInt(a) + b;} friend inline constexpr auto operator-(int64_t a, const ModInt &b){return ModInt(a) - b;} friend inline constexpr auto operator*(int64_t a, const ModInt &b){return ModInt(a) * b;} friend inline constexpr auto operator/(int64_t a, const ModInt &b){return ModInt(a) / b;} friend std::istream& operator>>(std::istream &s, ModInt &a){s >> a.val; return s;} friend std::ostream& operator<<(std::ostream &s, const ModInt &a){s << a.val; return s;} template inline static auto div(){ static auto value = inv(N); return value; } explicit operator int32_t() const noexcept {return val;} explicit operator int64_t() const noexcept {return val;} }; /** * @title 1D Imos algorithm (Linear addition) * @docs linear_imos_1d.md */ template struct LinearImos1D{ std::vector vec_a, vec_a_end, vec_b, vec; int n; LinearImos1D(int n): vec_a(n+1), vec_a_end(n+1), vec_b(n+1), vec(n+1), n(n){} void add(int s, int t, const T &a, const T &b){ // x∈[s,t)にax+bを加算する。 vec_a[s+1] += a; vec_a[t] -= a; vec_a_end[t] -= a * (t-s-1); vec_b[s] += a * s + b; vec_b[t] -= a * s + b; } void build(){ for(int i = 0; i < n; ++i) vec_a[i+1] += vec_a[i]; for(int i = 0; i <= n; ++i) vec_a[i] += vec_a_end[i]; for(int i = 0; i < n; ++i) vec_a[i+1] += vec_a[i]; for(int i = 0; i < n; ++i) vec_b[i+1] += vec_b[i]; for(int i = 0; i <= n; ++i) vec[i] = vec_a[i] + vec_b[i]; } inline const T operator[](size_t i) const {return vec[i];} }; using mint = ModInt<1000000007>; const int MAX = 1000000000; int main(){ int N; while(std::cin >> N){ std::vector A(N); for(int i = 0; i < N; ++i) std::cin >> A[i]; mint ans = 0; if(std::count(A.begin(), A.end(), 0) == 0){ //std::vector p(N); LinearImos1D p(N); std::vector next(N); for(int i = N-1; i >= 0; --i){ if(A[i] == 1){ if(i == N-1) next[i] = N; else{ if(A[i + 1] == 1){ next[i] = next[i + 1]; }else{ next[i] = i + 1; } } }else{ next[i] = i + 1; } } dump(next); for(int l = 0; l < N; ++l){ int64_t prod = 1; int r = l; for(int i = 0; i < 100; ++i){ if(r == N or prod * A[r] >= MAX) break; prod *= A[r]; r = next[r]; } //for(int i = l; i < r; ++i){ // p[i] += r - i; //} p.add(l, r, -1, r); } p.build(); ans = 1; for(int i = 0; i < N; ++i){ ans *= mint::power(A[i], p[i]); } } std::cout << ans << "\n"; } return 0; }