// #pragma GCC optimize("O3,unroll-loops") #include // #include using namespace std; #if __cplusplus >= 202002L using namespace numbers; #endif template struct modular_unfixed_base{ #define IS_INTEGRAL(T) (is_integral_v || is_same_v || is_same_v) #define IS_UNSIGNED(T) (is_unsigned_v || is_same_v) static_assert(IS_UNSIGNED(data_t) && IS_UNSIGNED(wider_data_t)); static constexpr bool VARIATE_MOD_FLAG = true; static data_t _mod; static wider_data_t _inverse_mod; static data_t &mod(){ return _mod; } static void precalc_barrett(){ _inverse_mod = (wider_data_t)-1 / _mod + 1; } static void setup(data_t mod = 0){ if(!mod) cin >> mod; _mod = mod; assert(_mod >= 1); precalc_barrett(); } template static vector precalc_power(T base, int SZ){ vector res(SZ + 1, 1); for(auto i = 1; i <= SZ; ++ i) res[i] = res[i - 1] * base; return res; } static vector _INV; static void precalc_inverse(int SZ){ if(_INV.empty()) _INV.assign(2, 1); for(auto x = _INV.size(); x <= SZ; ++ x) _INV.push_back(_mod / x * -_INV[_mod % x]); } // _mod must be a prime static modular_unfixed_base _primitive_root; static modular_unfixed_base primitive_root(){ if(_primitive_root) return _primitive_root; if(_mod == 2) return _primitive_root = 1; if(_mod == 998244353) return _primitive_root = 3; data_t divs[20] = {}; divs[0] = 2; int cnt = 1; data_t x = (_mod - 1) / 2; while(x % 2 == 0) x /= 2; for(auto i = 3; 1LL * i * i <= x; i += 2){ if(x % i == 0){ divs[cnt ++] = i; while(x % i == 0) x /= i; } } if(x > 1) divs[cnt ++] = x; for(auto g = 2; ; ++ g){ bool ok = true; for(auto i = 0; i < cnt; ++ i){ if((modular_unfixed_base(g).power((_mod - 1) / divs[i])) == 1){ ok = false; break; } } if(ok) return _primitive_root = g; } } constexpr modular_unfixed_base(){ } modular_unfixed_base(const double &x){ data = _normalize(llround(x)); } modular_unfixed_base(const long double &x){ data = _normalize(llround(x)); } template::type* = nullptr> modular_unfixed_base(const T &x){ data = _normalize(x); } template::type* = nullptr> static data_t _normalize(const T &x){ if(_mod == 1) return 0; if constexpr(is_same_v){ assert(_inverse_mod); int sign = x >= 0 ? 1 : -1; data_t v = _mod <= sign * x ? sign * x - ((__uint128_t)(sign * x) * _inverse_mod >> 64) * _mod : sign * x; if(v >= _mod) v += _mod; if(sign == -1 && v) v = _mod - v; return v; } else{ int sign = x >= 0 ? 1 : -1; data_t v = _mod <= sign * x ? sign * x % _mod : sign * x; if(sign == -1 && v) v = _mod - v; return v; } } const data_t &operator()() const{ return data; } template::type* = nullptr> operator T() const{ return data; } modular_unfixed_base &operator+=(const modular_unfixed_base &otr){ if((data += otr.data) >= _mod) data -= _mod; return *this; } modular_unfixed_base &operator-=(const modular_unfixed_base &otr){ if((data += _mod - otr.data) >= _mod) data -= _mod; return *this; } template::type* = nullptr> modular_unfixed_base &operator+=(const T &otr){ return *this += modular_unfixed_base(otr); } template::type* = nullptr> modular_unfixed_base &operator-=(const T &otr){ return *this -= modular_unfixed_base(otr); } modular_unfixed_base &operator++(){ return *this += 1; } modular_unfixed_base &operator--(){ return *this += _mod - 1; } modular_unfixed_base operator++(int){ modular_unfixed_base result(*this); *this += 1; return result; } modular_unfixed_base operator--(int){ modular_unfixed_base result(*this); *this += _mod - 1; return result; } modular_unfixed_base operator-() const{ return modular_unfixed_base(_mod - data); } modular_unfixed_base &operator*=(const modular_unfixed_base &rhs){ if constexpr(is_same_v){ long long res = data * rhs.data - _mod * (unsigned long long)(1.L / _mod * data * rhs.data); data = res + _mod * (res < 0) - _mod * (res >= (long long)_mod); } else data = _normalize((wider_data_t)data * rhs.data); return *this; } template::type* = nullptr> modular_unfixed_base &inplace_power(T e){ if(e == 0) return *this = 1; if(data == 0) return *this = {}; if(data == 1) return *this; if(data == mod() - 1) return e % 2 ? *this : *this = -*this; if(e < 0) *this = 1 / *this, e = -e; modular_unfixed_base res = 1; for(; e; *this *= *this, e >>= 1) if(e & 1) res *= *this; return *this = res; } template::type* = nullptr> modular_unfixed_base power(T e) const{ return modular_unfixed_base(*this).inplace_power(e); } modular_unfixed_base &operator/=(const modular_unfixed_base &otr){ make_signed_t a = otr.data, m = _mod, u = 0, v = 1; if(a < _INV.size()) return *this *= _INV[a]; while(a){ make_signed_t t = m / a; m -= t * a; swap(a, m); u -= t * v; swap(u, v); } assert(m == 1); return *this *= u; } #define ARITHMETIC_OP(op, apply_op)\ modular_unfixed_base operator op(const modular_unfixed_base &x) const{ return modular_unfixed_base(*this) apply_op x; }\ template::type* = nullptr>\ modular_unfixed_base operator op(const T &x) const{ return modular_unfixed_base(*this) apply_op modular_unfixed_base(x); }\ template::type* = nullptr>\ friend modular_unfixed_base operator op(const T &x, const modular_unfixed_base &y){ return modular_unfixed_base(x) apply_op y; } ARITHMETIC_OP(+, +=) ARITHMETIC_OP(-, -=) ARITHMETIC_OP(*, *=) ARITHMETIC_OP(/, /=) #undef ARITHMETIC_OP #define COMPARE_OP(op)\ bool operator op(const modular_unfixed_base &x) const{ return data op x.data; }\ template::type* = nullptr>\ bool operator op(const T &x) const{ return data op modular_unfixed_base(x).data; }\ template::type* = nullptr>\ friend bool operator op(const T &x, const modular_unfixed_base &y){ return modular_unfixed_base(x).data op y.data; } COMPARE_OP(==) COMPARE_OP(!=) COMPARE_OP(<) COMPARE_OP(<=) COMPARE_OP(>) COMPARE_OP(>=) #undef COMPARE_OP friend istream &operator>>(istream &in, modular_unfixed_base &number){ long long x; in >> x; number.data = modular_unfixed_base::_normalize(x); return in; } //#define _SHOW_FRACTION friend ostream &operator<<(ostream &out, const modular_unfixed_base &number){ out << number.data; #if defined(LOCAL) && defined(_SHOW_FRACTION) cerr << "("; for(auto d = 1; ; ++ d){ if((number * d).data <= 1000000){ cerr << (number * d).data; if(d != 1) cerr << "/" << d; break; } else if((-number * d).data <= 1000000){ cerr << "-" << (-number * d).data; if(d != 1) cerr << "/" << d; break; } } cerr << ")"; #endif return out; } data_t data = 0; #undef _SHOW_FRACTION #undef IS_INTEGRAL #undef IS_SIGNED }; template data_t modular_unfixed_base::_mod; template wider_data_t modular_unfixed_base::_inverse_mod; template vector> modular_unfixed_base::_INV; template modular_unfixed_base modular_unfixed_base::_primitive_root; using modular = modular_unfixed_base<0, unsigned int, unsigned long long>; // using modular = modular_unfixed_base<0, unsigned long long, __uint128_t>; int main(){ cin.tie(0)->sync_with_stdio(0); cin.exceptions(ios::badbit | ios::failbit); auto __solve_tc = [&](auto __tc_num)->int{ string n; cin >> n; modular::setup(); auto inc = [&](string x)->string{ int i = (int)x.size() - 1; while(i >= 0 && x[i] == '9'){ x[i] = '0'; -- i; } if(i >= 0){ ++ x[i]; } else{ x.insert(x.begin(), '1'); } return x; }; auto half = [&](string x)->string{ assert(~(x.back() - '0')); int carry = 0; for(auto i = 0; i < (int)x.size(); ++ i){ int d = x[i] - '0' + 10 * carry; carry = d % 2; x[i] = d / 2 + '0'; } return x; }; auto compute = [&](string x)->modular{ modular res = 0; for(auto d: x){ res = 10 * res + d - '0'; } return res; }; if(n.back() - '0' & 1){ cout << compute(n) * compute(half(inc(n))) << "\n"; } else{ cout << compute(half(n)) * compute(inc(n)) << "\n"; } return 0; }; int __tc_cnt; cin >> __tc_cnt; for(auto __tc_num = 0; __tc_num < __tc_cnt; ++ __tc_num){ __solve_tc(__tc_num); } return 0; } /* */