#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; namespace { using Integer = long long; //__int128; template istream& operator >> (istream& is, vector& vec){for(T& val: vec) is >> val; return is;} template istream& operator , (istream& is, T& val){ return is >> val;} template ostream& operator << (ostream& os, const vector& vec){for(int i=0; i ostream& operator , (ostream& os, const T& val){ return os << " " << val;} template void print(const H& head){ cout << head; } template void print(const H& head, const T& ... tail){ cout << head << " "; print(tail...); } template void println(const T& ... values){ print(values...); cout << endl; } template void eprint(const H& head){ cerr << head; } template void eprint(const H& head, const T& ... tail){ cerr << head << " "; eprint(tail...); } template void eprintln(const T& ... values){ eprint(values...); cerr << endl; } class range{ long long start_, end_, step_; public: struct range_iterator{ long long val, step_; range_iterator(long long v, long long step) : val(v), step_(step) {} long long operator * (){return val;} void operator ++ (){val += step_;} bool operator != (range_iterator& x){return step_ > 0 ? val < x.val : val > x.val;} }; range(long long len) : start_(0), end_(len), step_(1) {} range(long long start, long long end) : start_(start), end_(end), step_(1) {} range(long long start, long long end, long long step) : start_(start), end_(end), step_(step) {} range_iterator begin(){ return range_iterator(start_, step_); } range_iterator end(){ return range_iterator( end_, step_); } }; string operator "" _s (const char* str, size_t size){ return move(string(str)); } constexpr Integer my_pow(Integer x, Integer k, Integer z=1){return k==0 ? z : k==1 ? z*x : (k&1) ? my_pow(x*x,k>>1,z*x) : my_pow(x*x,k>>1,z);} constexpr Integer my_pow_mod(Integer x, Integer k, Integer M, Integer z=1){return k==0 ? z%M : k==1 ? z*x%M : (k&1) ? my_pow_mod(x*x%M,k>>1,M,z*x%M) : my_pow_mod(x*x%M,k>>1,M,z);} constexpr unsigned long long operator "" _ten (unsigned long long value){ return my_pow(10,value); } inline int k_bit(Integer x, int k){return (x>>k)&1;} //0-indexed mt19937 mt(chrono::duration_cast(chrono::steady_clock::now().time_since_epoch()).count()); template string join(const vector& v, const string& sep){ stringstream ss; for(int i=0; i0) ss << sep; ss << v[i]; } return ss.str(); } string operator * (string s, int k){ string ret; while(k){ if(k&1) ret += s; s += s; k >>= 1; } return ret; } } constexpr long long mod = 9_ten + 7; int main(){ int t; cin >> t; vector> fact(200001, vector(9, 0)); vector prime(200001); iota(prime.begin(), prime.end(), 0); prime[0] = prime[1] = 1; for(long long i=2; i> s; if(count(s.begin(), s.end(), '0') == s.size()){ println(0); continue; } int ans = 0; int x = s.size()-1; for(int i : range(s.size())){ int val = 1; vector tmp(9, 0); for(auto k : range(9)){ tmp[k] = fact[x][k] - fact[x-i][k] - fact[i][k]; val *= my_pow_mod(k, tmp[k], 9); val %= 9; } (ans += val * (s[i]-'0')) %= 9; } println(ans == 0 ? 9 : ans); } return 0; }