// author: hotman78 // date: 2023/04/09-21:02:09 // --- begin raw code ----------------- // #include"cpplib/util/template.hpp" // #include // // struct matrix{ // using D=long double; // using M=matrix; // array,2>v; // matrix(){ // rep(i,2)v[i].fill(0); // } // M& operator+=(M x){ // rep(i,2)rep(j,2)v[i][j]+=x.v[i][j]; // return *this; // } // M& operator*=(M x){ // M res; // rep(i,2)rep(j,2)rep(k,2)res.v[i][j]+=v[i][k]*x.v[k][j]; // return *this=res; // } // M operator+(M x){ // return M(*this)+=x; // } // M operator*(M x){ // return M(*this)*=x; // } // // static M transpose(M x){ // M res; // rep(i,2)rep(j,2)res.v[i][j]=x.v[j][i]; // return res; // } // // M cbrt(){ // if(abs(v[1][0])<=1e-11){ // M res; // res.v={array{std::cbrt(v[0][0]),0l},array{0l,std::cbrt(v[1][1])}}; // return res; // } // D a=1,b=-v[0][0]-v[1][1],c=v[0][0]*v[1][1]-v[1][0]*v[0][1]; // D d=b*b-4*a*c; // D x1=(-b-sqrt(d))/(2*a); // D x2=abs(x1)<=1e-11?-b:c/x1; // // cerr<=1e-11){ // p.v[0][0]/=sqrt(tmp); // p.v[0][1]/=sqrt(tmp); // ok=1; // } // } // if(!ok){ // p.v[0][0]=v[1][1]-x1; // p.v[0][1]=-v[1][0]; // D tmp=p.v[0][0]*p.v[0][0]+p.v[0][1]*p.v[0][1]; // if(abs(tmp)>=1e-11){ // p.v[0][0]/=sqrt(tmp); // p.v[0][1]/=sqrt(tmp); // ok=1; // } // } // if(!ok){ // p.v[0][0]=1; // p.v[0][1]=0; // fst=1; // } // } // { // bool ok=0; // if(!ok){ // p.v[1][0]=-v[0][1]; // p.v[1][1]=v[0][0]-x2; // D tmp=p.v[1][0]*p.v[1][0]+p.v[1][1]*p.v[1][1]; // // cout<=1e-11){ // p.v[1][0]/=sqrt(tmp); // p.v[1][1]/=sqrt(tmp); // ok=1; // if(fst){ // p.v[0][0]=-p.v[1][1]; // p.v[0][1]=p.v[1][0]; // } // } // } // if(!ok){ // p.v[1][0]=v[1][1]-x2; // p.v[1][1]=-v[1][0]; // D tmp=p.v[0][0]*p.v[0][0]+p.v[0][1]*p.v[0][1]; // if(abs(tmp)>=1e-11){ // p.v[0][0]/=sqrt(tmp); // p.v[0][1]/=sqrt(tmp); // ok=1; // if(fst){ // p.v[0][0]=-p.v[1][1]; // p.v[0][1]=p.v[1][0]; // } // } // } // if(!ok){ // p.v[1][0]=-p.v[0][1]; // p.v[1][1]=p.v[0][0]; // } // } // // rep(i,2){ // // rep(j,2){ // // cout<{std::cbrt(x1),0l},array{0l,std::cbrt(x2)}}; // // rep(i,2){ // // rep(j,2){ // // cout<>t; // while(t--){ // matrix x; // rep(i,2)rep(j,2)cin>>x.v[i][j]; // rep(i,2)rep(j,2)x.v[i][j]*=1000000; // x=x.cbrt(); // rep(i,2){ // rep(j,2){ // cout< using namespace std; #line 1 "cpplib/util/ioutil.hpp" // template // std::ostream& output(std::ostream& out,const Head& head,const Args&... args){ // out>>head; // return output(head,args...); // } // template // std::ostream& output(std::ostream& out,const Head& head){ // out>>head; // return out; // } template std::ostream &operator<<(std::ostream &out, std::pair v) { out << "(" << v.first << "," << v.second << ")"; return out; } // template // ostream& operator<<(ostream& out,std::tuplev){ // std::apply(output,v); // return out; // } #line 8 "cpplib/util/template.hpp" struct __INIT__ { __INIT__() { cin.tie(0); ios::sync_with_stdio(false); cout << fixed << setprecision(15); } } __INIT__; typedef long long lint; constexpr long long INF = 1LL << 60; constexpr int IINF = 1 << 30; constexpr double EPS = 1e-10; #ifndef REACTIVE #define endl '\n'; #endif typedef vector vec; typedef vector> mat; typedef vector>> mat3; typedef vector svec; typedef vector> smat; template using V = vector; template using VV = V>; template inline void output(T t) { bool f = 0; for (auto i : t) { cout << (f ? " " : "") << i; f = 1; } cout << endl; } template inline void output2(T t) { for (auto i : t) output(i); } template inline void debug(T t) { bool f = 0; for (auto i : t) { cerr << (f ? " " : "") << i; f = 1; } cerr << endl; } template inline void debug2(T t) { for (auto i : t) debug(i); } #define loop(n) for (long long _ = 0; _ < (long long)(n); ++_) #define _overload4(_1, _2, _3, _4, name, ...) name #define __rep(i, a) repi(i, 0, a, 1) #define _rep(i, a, b) repi(i, a, b, 1) #define repi(i, a, b, c) \ for (long long i = (long long)(a); i < (long long)(b); i += c) #define rep(...) _overload4(__VA_ARGS__, repi, _rep, __rep)(__VA_ARGS__) #define _overload3_rev(_1, _2, _3, name, ...) name #define _rep_rev(i, a) repi_rev(i, 0, a) #define repi_rev(i, a, b) \ for (long long i = (long long)(b)-1; i >= (long long)(a); --i) #define rrep(...) _overload3_rev(__VA_ARGS__, repi_rev, _rep_rev)(__VA_ARGS__) #define all(n) begin(n), end(n) template bool chmin(T &s, const E &t) { bool res = s > t; s = min(s, t); return res; } template bool chmax(T &s, const E &t) { bool res = s < t; s = max(s, t); return res; } const vector dx = {1, 0, -1, 0, 1, 1, -1, -1}; const vector dy = {0, 1, 0, -1, 1, -1, 1, -1}; #define SUM(v) accumulate(all(v), 0LL) #if __cplusplus >= 201703L template auto make_vector(T x, int arg, Args... args) { if constexpr (sizeof...(args) == 0) return vector(arg, x); else return vector(arg, make_vector(x, args...)); } #endif #define extrep(v, ...) for (auto v : __MAKE_MAT__({__VA_ARGS__})) #define bit(n, a) ((n >> a) & 1) vector> __MAKE_MAT__(vector v) { if (v.empty()) return vector>(1, vector()); long long n = v.back(); v.pop_back(); vector> ret; vector> tmp = __MAKE_MAT__(v); for (auto e : tmp) for (long long i = 0; i < n; ++i) { ret.push_back(e); ret.back().push_back(i); } return ret; } using graph = vector>; template using graph_w = vector>>; #if __cplusplus >= 201703L constexpr inline long long powll(long long a, long long b) { long long res = 1; while (b--) res *= a; return res; } #endif template pair &operator+=(pair &s, const pair &t) { s.first += t.first; s.second += t.second; return s; } template pair &operator-=(pair &s, const pair &t) { s.first -= t.first; s.second -= t.second; return s; } template pair operator+(const pair &s, const pair &t) { auto res = s; return res += t; } template pair operator-(const pair &s, const pair &t) { auto res = s; return res -= t; } #define BEGIN_STACK_EXTEND(size) \ void *stack_extend_memory_ = malloc(size); \ void *stack_extend_origin_memory_; \ char *stack_extend_dummy_memory_ = (char *)alloca( \ (1 + (int)(((long long)stack_extend_memory_) & 127)) * 16); \ *stack_extend_dummy_memory_ = 0; \ asm volatile("mov %%rsp, %%rbx\nmov %%rax, %%rsp" \ : "=b"(stack_extend_origin_memory_) \ : "a"((char *)stack_extend_memory_ + (size)-1024)); #define END_STACK_EXTEND \ asm volatile("mov %%rax, %%rsp" ::"a"(stack_extend_origin_memory_)); \ free(stack_extend_memory_); #line 2 "main.cpp" #include #include #include #include #include namespace atcoder { namespace internal { std::vector sa_naive(const std::vector &s) { int n = int(s.size()); std::vector sa(n); std::iota(sa.begin(), sa.end(), 0); std::sort(sa.begin(), sa.end(), [&](int l, int r) { if (l == r) return false; while (l < n && r < n) { if (s[l] != s[r]) return s[l] < s[r]; l++; r++; } return l == n; }); return sa; } std::vector sa_doubling(const std::vector &s) { int n = int(s.size()); std::vector sa(n), rnk = s, tmp(n); std::iota(sa.begin(), sa.end(), 0); for (int k = 1; k < n; k *= 2) { auto cmp = [&](int x, int y) { if (rnk[x] != rnk[y]) return rnk[x] < rnk[y]; int rx = x + k < n ? rnk[x + k] : -1; int ry = y + k < n ? rnk[y + k] : -1; return rx < ry; }; std::sort(sa.begin(), sa.end(), cmp); tmp[sa[0]] = 0; for (int i = 1; i < n; i++) { tmp[sa[i]] = tmp[sa[i - 1]] + (cmp(sa[i - 1], sa[i]) ? 1 : 0); } std::swap(tmp, rnk); } return sa; } template std::vector sa_is(const std::vector &s, int upper) { int n = int(s.size()); if (n == 0) return {}; if (n == 1) return {0}; if (n == 2) { if (s[0] < s[1]) { return {0, 1}; } else { return {1, 0}; } } if (n < THRESHOLD_NAIVE) { return sa_naive(s); } if (n < THRESHOLD_DOUBLING) { return sa_doubling(s); } std::vector sa(n); std::vector ls(n); for (int i = n - 2; i >= 0; i--) { ls[i] = (s[i] == s[i + 1]) ? ls[i + 1] : (s[i] < s[i + 1]); } std::vector sum_l(upper + 1), sum_s(upper + 1); for (int i = 0; i < n; i++) { if (!ls[i]) { sum_s[s[i]]++; } else { sum_l[s[i] + 1]++; } } for (int i = 0; i <= upper; i++) { sum_s[i] += sum_l[i]; if (i < upper) sum_l[i + 1] += sum_s[i]; } auto induce = [&](const std::vector &lms) { std::fill(sa.begin(), sa.end(), -1); std::vector buf(upper + 1); std::copy(sum_s.begin(), sum_s.end(), buf.begin()); for (auto d : lms) { if (d == n) continue; sa[buf[s[d]]++] = d; } std::copy(sum_l.begin(), sum_l.end(), buf.begin()); sa[buf[s[n - 1]]++] = n - 1; for (int i = 0; i < n; i++) { int v = sa[i]; if (v >= 1 && !ls[v - 1]) { sa[buf[s[v - 1]]++] = v - 1; } } std::copy(sum_l.begin(), sum_l.end(), buf.begin()); for (int i = n - 1; i >= 0; i--) { int v = sa[i]; if (v >= 1 && ls[v - 1]) { sa[--buf[s[v - 1] + 1]] = v - 1; } } }; std::vector lms_map(n + 1, -1); int m = 0; for (int i = 1; i < n; i++) { if (!ls[i - 1] && ls[i]) { lms_map[i] = m++; } } std::vector lms; lms.reserve(m); for (int i = 1; i < n; i++) { if (!ls[i - 1] && ls[i]) { lms.push_back(i); } } induce(lms); if (m) { std::vector sorted_lms; sorted_lms.reserve(m); for (int v : sa) { if (lms_map[v] != -1) sorted_lms.push_back(v); } std::vector rec_s(m); int rec_upper = 0; rec_s[lms_map[sorted_lms[0]]] = 0; for (int i = 1; i < m; i++) { int l = sorted_lms[i - 1], r = sorted_lms[i]; int end_l = (lms_map[l] + 1 < m) ? lms[lms_map[l] + 1] : n; int end_r = (lms_map[r] + 1 < m) ? lms[lms_map[r] + 1] : n; bool same = true; if (end_l - l != end_r - r) { same = false; } else { while (l < end_l) { if (s[l] != s[r]) { break; } l++; r++; } if (l == n || s[l] != s[r]) same = false; } if (!same) rec_upper++; rec_s[lms_map[sorted_lms[i]]] = rec_upper; } auto rec_sa = sa_is(rec_s, rec_upper); for (int i = 0; i < m; i++) { sorted_lms[i] = lms[rec_sa[i]]; } induce(sorted_lms); } return sa; } } // namespace internal std::vector suffix_array(const std::vector &s, int upper) { assert(0 <= upper); for (int d : s) { assert(0 <= d && d <= upper); } auto sa = internal::sa_is(s, upper); return sa; } template std::vector suffix_array(const std::vector &s) { int n = int(s.size()); std::vector idx(n); iota(idx.begin(), idx.end(), 0); sort(idx.begin(), idx.end(), [&](int l, int r) { return s[l] < s[r]; }); std::vector s2(n); int now = 0; for (int i = 0; i < n; i++) { if (i && s[idx[i - 1]] != s[idx[i]]) now++; s2[idx[i]] = now; } return internal::sa_is(s2, now); } std::vector suffix_array(const std::string &s) { int n = int(s.size()); std::vector s2(n); for (int i = 0; i < n; i++) { s2[i] = s[i]; } return internal::sa_is(s2, 255); } template std::vector lcp_array(const std::vector &s, const std::vector &sa) { int n = int(s.size()); assert(n >= 1); std::vector rnk(n); for (int i = 0; i < n; i++) { rnk[sa[i]] = i; } std::vector lcp(n - 1); int h = 0; for (int i = 0; i < n; i++) { if (h > 0) h--; if (rnk[i] == 0) continue; int j = sa[rnk[i] - 1]; for (; j + h < n && i + h < n; h++) { if (s[j + h] != s[i + h]) break; } lcp[rnk[i] - 1] = h; } return lcp; } std::vector lcp_array(const std::string &s, const std::vector &sa) { int n = int(s.size()); std::vector s2(n); for (int i = 0; i < n; i++) { s2[i] = s[i]; } return lcp_array(s2, sa); } template std::vector z_algorithm(const std::vector &s) { int n = int(s.size()); if (n == 0) return {}; std::vector z(n); z[0] = 0; for (int i = 1, j = 0; i < n; i++) { int &k = z[i]; k = (j + z[j] <= i) ? 0 : std::min(j + z[j] - i, z[i - j]); while (i + k < n && s[k] == s[i + k]) k++; if (j + z[j] < i + z[i]) j = i; } z[0] = n; return z; } std::vector z_algorithm(const std::string &s) { int n = int(s.size()); std::vector s2(n); for (int i = 0; i < n; i++) { s2[i] = s[i]; } return z_algorithm(s2); } } // namespace atcoder struct matrix { using D = long double; using M = matrix; array, 2> v; matrix() { rep(i, 2) v[i].fill(0); } M &operator+=(M x) { rep(i, 2) rep(j, 2) v[i][j] += x.v[i][j]; return *this; } M &operator*=(M x) { M res; rep(i, 2) rep(j, 2) rep(k, 2) res.v[i][j] += v[i][k] * x.v[k][j]; return *this = res; } M operator+(M x) { return M(*this) += x; } M operator*(M x) { return M(*this) *= x; } static M transpose(M x) { M res; rep(i, 2) rep(j, 2) res.v[i][j] = x.v[j][i]; return res; } M cbrt() { if (abs(v[1][0]) <= 1e-11) { M res; res.v = {array{std::cbrt(v[0][0]), 0l}, array{0l, std::cbrt(v[1][1])}}; return res; } D a = 1, b = -v[0][0] - v[1][1], c = v[0][0] * v[1][1] - v[1][0] * v[0][1]; D d = b * b - 4 * a * c; D x1 = (-b - sqrt(d)) / (2 * a); D x2 = abs(x1) <= 1e-11 ? -b : c / x1; // cerr<= 1e-11) { p.v[0][0] /= sqrt(tmp); p.v[0][1] /= sqrt(tmp); ok = 1; } } if (!ok) { p.v[0][0] = v[1][1] - x1; p.v[0][1] = -v[1][0]; D tmp = p.v[0][0] * p.v[0][0] + p.v[0][1] * p.v[0][1]; if (abs(tmp) >= 1e-11) { p.v[0][0] /= sqrt(tmp); p.v[0][1] /= sqrt(tmp); ok = 1; } } if (!ok) { p.v[0][0] = 1; p.v[0][1] = 0; fst = 1; } } { bool ok = 0; if (!ok) { p.v[1][0] = -v[0][1]; p.v[1][1] = v[0][0] - x2; D tmp = p.v[1][0] * p.v[1][0] + p.v[1][1] * p.v[1][1]; // cout<= 1e-11) { p.v[1][0] /= sqrt(tmp); p.v[1][1] /= sqrt(tmp); ok = 1; if (fst) { p.v[0][0] = -p.v[1][1]; p.v[0][1] = p.v[1][0]; } } } if (!ok) { p.v[1][0] = v[1][1] - x2; p.v[1][1] = -v[1][0]; D tmp = p.v[0][0] * p.v[0][0] + p.v[0][1] * p.v[0][1]; if (abs(tmp) >= 1e-11) { p.v[0][0] /= sqrt(tmp); p.v[0][1] /= sqrt(tmp); ok = 1; if (fst) { p.v[0][0] = -p.v[1][1]; p.v[0][1] = p.v[1][0]; } } } if (!ok) { p.v[1][0] = -p.v[0][1]; p.v[1][1] = p.v[0][0]; } } // rep(i,2){ // rep(j,2){ // cout<{std::cbrt(x1), 0l}, array{0l, std::cbrt(x2)}}; // rep(i,2){ // rep(j,2){ // cout<> t; while (t--) { matrix x; rep(i, 2) rep(j, 2) cin >> x.v[i][j]; rep(i, 2) rep(j, 2) x.v[i][j] *= 1000000; x = x.cbrt(); rep(i, 2) { rep(j, 2) { cout << fixed << setprecision(5) << x.v[i][j] * 0.01 << " \n"[j]; } } } }