#pragma GCC optimize ("Ofast") #include using namespace std; #define MD (1000000007U) struct Modint{ unsigned val; Modint(){ val=0; } Modint(int a){ val = ord(a); } Modint(unsigned a){ val = ord(a); } Modint(long long a){ val = ord(a); } Modint(unsigned long long a){ val = ord(a); } inline unsigned ord(unsigned a){ return a%MD; } inline unsigned ord(int a){ a %= (int)MD; if(a < 0){ a += MD; } return a; } inline unsigned ord(unsigned long long a){ return a%MD; } inline unsigned ord(long long a){ a %= (int)MD; if(a < 0){ a += MD; } return a; } inline unsigned get(){ return val; } inline Modint &operator+=(Modint a){ val += a.val; if(val >= MD){ val -= MD; } return *this; } inline Modint &operator-=(Modint a){ if(val < a.val){ val = val + MD - a.val; } else{ val -= a.val; } return *this; } inline Modint &operator*=(Modint a){ val = ((unsigned long long)val*a.val)%MD; return *this; } inline Modint &operator/=(Modint a){ return *this *= a.inverse(); } inline Modint operator+(Modint a){ return Modint(*this)+=a; } inline Modint operator-(Modint a){ return Modint(*this)-=a; } inline Modint operator*(Modint a){ return Modint(*this)*=a; } inline Modint operator/(Modint a){ return Modint(*this)/=a; } inline Modint operator+(int a){ return Modint(*this)+=Modint(a); } inline Modint operator-(int a){ return Modint(*this)-=Modint(a); } inline Modint operator*(int a){ return Modint(*this)*=Modint(a); } inline Modint operator/(int a){ return Modint(*this)/=Modint(a); } inline Modint operator+(long long a){ return Modint(*this)+=Modint(a); } inline Modint operator-(long long a){ return Modint(*this)-=Modint(a); } inline Modint operator*(long long a){ return Modint(*this)*=Modint(a); } inline Modint operator/(long long a){ return Modint(*this)/=Modint(a); } inline Modint operator-(void){ Modint res; if(val){ res.val=MD-val; } else{ res.val=0; } return res; } inline operator bool(void){ return val!=0; } inline operator int(void){ return get(); } inline operator long long(void){ return get(); } inline Modint inverse(){ int a = val; int b = MD; int u = 1; int v = 0; int t; Modint res; while(b){ t = a / b; a -= t * b; swap(a, b); u -= t * v; swap(u, v); } if(u < 0){ u += MD; } res.val = u; return res; } inline Modint pw(unsigned long long b){ Modint a(*this); Modint res; res.val = 1; while(b){ if(b&1){ res *= a; } b >>= 1; a *= a; } return res; } inline bool operator==(int a){ return ord(a)==val; } inline bool operator!=(int a){ return ord(a)!=val; } } ; inline Modint operator+(int a, Modint b){ return Modint(a)+=b; } inline Modint operator-(int a, Modint b){ return Modint(a)-=b; } inline Modint operator*(int a, Modint b){ return Modint(a)*=b; } inline Modint operator/(int a, Modint b){ return Modint(a)/=b; } inline Modint operator+(long long a, Modint b){ return Modint(a)+=b; } inline Modint operator-(long long a, Modint b){ return Modint(a)-=b; } inline Modint operator*(long long a, Modint b){ return Modint(a)*=b; } inline Modint operator/(long long a, Modint b){ return Modint(a)/=b; } inline int my_getchar_unlocked(){ static char buf[1048576]; static int s = 1048576; static int e = 1048576; if(s == e && e == 1048576){ e = fread_unlocked(buf, 1, 1048576, stdin); s = 0; } if(s == e){ return EOF; } return buf[s++]; } inline void rd(int &x){ int k; int m=0; x=0; for(;;){ k = my_getchar_unlocked(); if(k=='-'){ m=1; break; } if('0'<=k&&k<='9'){ x=k-'0'; break; } } for(;;){ k = my_getchar_unlocked(); if(k<'0'||k>'9'){ break; } x=x*10+k-'0'; } if(m){ x=-x; } } inline void rd(long long &x){ int k; int m=0; x=0; for(;;){ k = my_getchar_unlocked(); if(k=='-'){ m=1; break; } if('0'<=k&&k<='9'){ x=k-'0'; break; } } for(;;){ k = my_getchar_unlocked(); if(k<'0'||k>'9'){ break; } x=x*10+k-'0'; } if(m){ x=-x; } } struct MY_WRITER{ char buf[1048576]; int s; int e; MY_WRITER(){ s = 0; e = 1048576; } ~MY_WRITER(){ if(s){ fwrite_unlocked(buf, 1, s, stdout); } } } ; MY_WRITER MY_WRITER_VAR; void my_putchar_unlocked(int a){ if(MY_WRITER_VAR.s == MY_WRITER_VAR.e){ fwrite_unlocked(MY_WRITER_VAR.buf, 1, MY_WRITER_VAR.s, stdout); MY_WRITER_VAR.s = 0; } MY_WRITER_VAR.buf[MY_WRITER_VAR.s++] = a; } inline void wt_L(char a){ my_putchar_unlocked(a); } inline void wt_L(int x){ int s=0; int m=0; char f[10]; if(x<0){ m=1; x=-x; } while(x){ f[s++]=x%10; x/=10; } if(!s){ f[s++]=0; } if(m){ my_putchar_unlocked('-'); } while(s--){ my_putchar_unlocked(f[s]+'0'); } } inline void wt_L(Modint x){ int i; i = (int)x; wt_L(i); } template inline T pow_L(T a, S b){ T res = 1; res = 1; for(;;){ if(b&1){ res *= a; } b >>= 1; if(b==0){ break; } a *= a; } return res; } inline double pow_L(double a, double b){ return pow(a,b); } int N; long long A[100000]; long long sm[100000+1]; long long dm[100000+1]; Modint solve(int N, long long A[]){ int i; int j; long long m = 1; long long t; Modint res = 1; if(N==0){ return res; } for(i=(0);i<(N+1);i++){ sm[i] = 0; } j = 0; for(i=(0);i<(N);i++){ while(j < N && m * A[j] < 1000000000){ m *= A[j++]; } if(j){ dm[j-1]++; } if(i){ dm[i-1]--; } if(i){ sm[i-1] -= j-i; } m /= A[i]; } for(i=(N)-1;i>=(0);i--){ sm[i] += sm[i+1]; } t = m = 0; for(i=(N)-1;i>=(0);i--){ m += dm[i]; t += m; sm[i] += t; } for(i=(0);i<(N);i++){ res *=(pow_L(Modint(A[i]),sm[i])); } return res; } int main(){ int i; int j; long long m = 1; Modint res = 1; rd(N); { int tU__gIr_; for(tU__gIr_=(0);tU__gIr_<(N);tU__gIr_++){ rd(A[tU__gIr_]); } } j = 0; for(i=(0);i<(N+1);i++){ if(i==N || A[i]==0){ res *= solve(i-j, A+j); j = i+1; } } wt_L(res); wt_L('\n'); return 0; } // cLay varsion 20200509-1 // --- original code --- // int N; // ll A[1d5]; // ll sm[1d5+1], dm[1d5+1]; // // Modint solve(int N, ll A[]){ // int i, j; // ll m = 1, t; // Modint res = 1; // // if(N==0) return res; // rep(i,N+1) sm[i] = 0; // // j = 0; // rep(i,N){ // while(j < N && m * A[j] < 1d9) m *= A[j++]; // if(j) dm[j-1]++; // if(i) dm[i-1]--; // if(i) sm[i-1] -= j-i; // m /= A[i]; // } // // rrep(i,N) sm[i] += sm[i+1]; // // t = m = 0; // rrep(i,N){ // m += dm[i]; // t += m; // sm[i] += t; // } // rep(i,N) res *= Modint(A[i]) ** sm[i]; // return res; // } // // { // int i, j; // ll m = 1; // Modint res = 1; // // rd(N,A(N)); // j = 0; // rep(i,N+1) if(i==N || A[i]==0){ // res *= solve(i-j, A+j); // j = i+1; // } // // wt(res); // }