#pragma GCC optimize ("Ofast") #include using namespace std; #define MD (1000000007U) template struct cLtraits_identity{ using type = T; } ; template using cLtraits_try_make_signed = typename conditional< is_integral::value, make_signed, cLtraits_identity >::type; struct mint{ static unsigned md; static unsigned W; static unsigned R; static unsigned Rinv; static unsigned mdninv; static unsigned RR; unsigned val; mint(){ val=0; } mint(int a){ val = mulR(a); } mint(unsigned a){ val = mulR(a); } mint(long long a){ val = mulR(a); } mint(unsigned long long a){ val = mulR(a); } int get_inv(long long a, int md){ long long t=a; long long s=md; long long u=1; long long v=0; long long e; while(s){ e=t/s; t-=e*s; u-=e*v; swap(t,s); swap(u,v); } if(u<0){ u+=md; } return u; } void setmod(unsigned m){ int i; unsigned t; W = 32; md = m; R = (1ULL << W) % md; RR = (unsigned long long)R*R % md; switch(m){ case 104857601: Rinv = 2560000; mdninv = 104857599; break; case 998244353: Rinv = 232013824; mdninv = 998244351; break; case 1000000007: Rinv = 518424770; mdninv = 2226617417U; break; case 1000000009: Rinv = 171601999; mdninv = 737024967; break; case 1004535809: Rinv = 234947584; mdninv = 1004535807; break; case 1007681537: Rinv = 236421376; mdninv = 1007681535; break; case 1012924417: Rinv = 238887936; mdninv = 1012924415; break; case 1045430273: Rinv = 254466304; mdninv = 1045430271; break; case 1051721729: Rinv = 257538304; mdninv = 1051721727; break; default: Rinv = get_inv(R, md); mdninv = 0; t = 0; for(i=(0);i<((int)W);i++){ if(t%2==0){ t+=md; mdninv |= (1U<> W); if(t >= md){ t -= md; } return t; } unsigned reduce(unsigned long long T){ unsigned m = (unsigned)T * mdninv; unsigned t = (unsigned)((T + (unsigned long long)m*md) >> W); if(t >= md){ t -= md; } return t; } unsigned get(){ return reduce(val); } inline mint &operator++(){ (*this) += 1; return *this; } inline mint &operator--(){ (*this) -= 1; return *this; } inline mint operator++(int a){ mint res(*this); (*this) += 1; return res; } inline mint operator--(int a){ mint res(*this); (*this) -= 1; return res; } mint &operator+=(mint a){ val += a.val; if(val >= md){ val -= md; } return *this; } mint &operator-=(mint a){ if(val < a.val){ val = val + md - a.val; } else{ val -= a.val; } return *this; } mint &operator*=(mint a){ val = reduce((unsigned long long)val*a.val); return *this; } mint &operator/=(mint a){ return *this *= a.inverse(); } mint operator+(mint a){ return mint(*this)+=a; } mint operator-(mint a){ return mint(*this)-=a; } mint operator*(mint a){ return mint(*this)*=a; } mint operator/(mint a){ return mint(*this)/=a; } mint operator+(int a){ return mint(*this)+=mint(a); } mint operator-(int a){ return mint(*this)-=mint(a); } mint operator*(int a){ return mint(*this)*=mint(a); } mint operator/(int a){ return mint(*this)/=mint(a); } mint operator+(long long a){ return mint(*this)+=mint(a); } mint operator-(long long a){ return mint(*this)-=mint(a); } mint operator*(long long a){ return mint(*this)*=mint(a); } mint operator/(long long a){ return mint(*this)/=mint(a); } mint operator-(void){ mint res; if(val){ res.val=md-val; } else{ res.val=0; } return res; } operator bool(void){ return val!=0; } operator int(void){ return get(); } operator long long(void){ return get(); } mint inverse(){ int a = val; int b = md; int u = 1; int v = 0; int t; mint 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 = (unsigned long long)u*RR % md; return res; } mint pw(unsigned long long b){ mint a(*this); mint res; res.val = R; while(b){ if(b&1){ res *= a; } b >>= 1; a *= a; } return res; } bool operator==(int a){ return mulR(a)==val; } bool operator!=(int a){ return mulR(a)!=val; } } ; unsigned mint::md; unsigned mint::W; unsigned mint::R; unsigned mint::Rinv; unsigned mint::mdninv; unsigned mint::RR; mint operator+(int a, mint b){ return mint(a)+=b; } mint operator-(int a, mint b){ return mint(a)-=b; } mint operator*(int a, mint b){ return mint(a)*=b; } mint operator/(int a, mint b){ return mint(a)/=b; } mint operator+(long long a, mint b){ return mint(a)+=b; } mint operator-(long long a, mint b){ return mint(a)-=b; } mint operator*(long long a, mint b){ return mint(a)*=b; } mint operator/(long long a, mint b){ return mint(a)/=b; } inline int my_getchar(){ static char buf[1048576]; static int s = 1048576; static int e = 1048576; if(s == e && e == 1048576){ e = fread(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(); if(k=='-'){ m=1; break; } if('0'<=k&&k<='9'){ x=k-'0'; break; } } for(;;){ k = my_getchar(); 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(buf, 1, s, stdout); } } } ; MY_WRITER MY_WRITER_VAR; void my_putchar(int a){ if(MY_WRITER_VAR.s == MY_WRITER_VAR.e){ fwrite(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(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('-'); } while(s--){ my_putchar(f[s]+'0'); } } inline void wt_L(unsigned x){ int s=0; char f[10]; while(x){ f[s++]=x%10; x/=10; } if(!s){ f[s++]=0; } while(s--){ my_putchar(f[s]+'0'); } } inline void wt_L(long long x){ int s=0; int m=0; char f[20]; if(x<0){ m=1; x=-x; } while(x){ f[s++]=x%10; x/=10; } if(!s){ f[s++]=0; } if(m){ my_putchar('-'); } while(s--){ my_putchar(f[s]+'0'); } } inline void wt_L(unsigned long long x){ int s=0; char f[21]; while(x){ f[s++]=x%10; x/=10; } if(!s){ f[s++]=0; } while(s--){ my_putchar(f[s]+'0'); } } inline void wt_L(mint x){ int i; i = (int)x; wt_L(i); } int WRITER_DOUBLE_DIGIT = 15; inline int writerDigit_double(){ return WRITER_DOUBLE_DIGIT; } inline void writerDigit_double(int d){ WRITER_DOUBLE_DIGIT = d; } inline void wt_L(double x){ const int d = WRITER_DOUBLE_DIGIT; int k; int r; double v; if(x!=x || (x==x+1 && x==2*x)){ my_putchar('E'); my_putchar('r'); my_putchar('r'); return; } if(x < 0){ my_putchar('-'); x = -x; } x += 0.5 * pow(0.1, d); r = 0; v = 1; while(x >= 10*v){ v *= 10; r++; } while(r >= 0){ r--; k = floor(x / v); if(k >= 10){ k = 9; } if(k <= -1){ k = 0; } x -= k * v; v *= 0.1; my_putchar(k + '0'); } if(d > 0){ my_putchar('.'); v = 1; for(r=(0);r<(d);r++){ v *= 0.1; k = floor(x / v); if(k >= 10){ k = 9; } if(k <= -1){ k = 0; } x -= k * v; my_putchar(k + '0'); } } } inline void wt_L(const char c[]){ int i=0; for(i=0;c[i]!='\0';i++){ my_putchar(c[i]); } } inline void wt_L(string &x){ int i=0; for(i=0;x[i]!='\0';i++){ my_putchar(x[i]); } } unsigned long long powmod(unsigned long long a, unsigned long long b, unsigned long long m){ unsigned long long r = 1; while(b){ if(b&1){ r = r * a % m; } b>>=1; a = a * a % m; } return r; } template inline T GCD_L(T a, U b){ T r; while(b){ r=a; a=b; b=r%a; } return a; } int N; int K; int c[100]; int d[100]; int* e = &c[1]; int main(){ int i; { mint x; x.setmod(MD); } rd(N); { int PiIOrLma; for(PiIOrLma=(0);PiIOrLma<(9);PiIOrLma++){ rd(e[PiIOrLma]); } } int g = 0; for(i=(0);i<(10);i++){ int j; if(c[i] == 0){ continue; } for(j=(0);j<(10);j++){ if(c[j] == 0){ continue; } g =GCD_L(abs(i-j), g); } } if(g == 0){ long long aout = 0; for(i=(0);i<(10);i++){ if(c[i] != 0){ aout = i; } } mint ans = 0; mint ten =10; ans = mint(aout) * (ten.pw(c[aout]) -1)/mint(9); wt_L(ans); wt_L('\n'); exit(0); } g *= 81; for(i=(1);i<(10);i++){ d[i] = c[i]; d[i] += d[i-1]; } long long ans = 0; for(i=(0);i<(10);i++){ if(c[i] == 0){ continue; } long long tmp = (long long)(i) * powmod(10, d[i-1], g); tmp %= g; tmp *= (powmod(10, c[i], g) - 1); ans += tmp; ans %= g; } wt_L(GCD_L(ans, g)/9); wt_L('\n'); return 0; } // cLay version 20210405-1 // --- original code --- // //no-unlocked // int N, K; // int c[100]; // int d[100]; // int * e = &c[1]; // { // rd(N, e(9)); // int g = 0; // rep(i, 10) // { // if(c[i] == 0) continue; // rep(j, 10){ // if(c[j] == 0) continue; // g = gcd(abs(i-j), g); // } // } // if(g == 0){ // ll aout = 0; // rep(i, 10){ // if(c[i] != 0){ // aout = i; // } // } // mint ans = 0; // mint ten =10; // // ans = mint(aout) * (ten.pw(c[aout]) -1)/mint(9); // wt(ans); // exit(0); // } // g *= 81; // rep(i, 1, 10){ // d[i] = c[i]; // d[i] += d[i-1]; // } // ll ans = 0; // rep(i, 10){ // if(c[i] == 0) continue; // ll tmp = (ll)(i) * powmod(10, d[i-1], g); // tmp %= g; // tmp *= (powmod(10, c[i], g) - 1); // ans += tmp; // ans %= g; // } // wt(gcd(ans,g)/9); // }