#pragma GCC target("pclmul", "sse2", "sse4.1") #include #include #include __int64_t clmul(__int64_t x, __int64_t y) { __m128i x_ = _mm_set_epi64x(0, x); __m128i y_ = _mm_set_epi64x(0, y); __m128i z_ = _mm_clmulepi64_si128(x_, y_, 0); return _mm_extract_epi64(z_, 0); } #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using lint = long long; using pint = pair; using plint = pair; struct fast_ios { fast_ios(){ cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(20); }; } fast_ios_; #define ALL(x) (x).begin(), (x).end() #define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i=i##_begin_;i--) #define REP(i, n) FOR(i,0,n) #define IREP(i, n) IFOR(i,0,n) template void ndarray(vector& vec, const V& val, int len) { vec.assign(len, val); } template void ndarray(vector& vec, const V& val, int len, Args... args) { vec.resize(len), for_each(begin(vec), end(vec), [&](T& v) { ndarray(v, val, args...); }); } template bool chmax(T &m, const T q) { return m < q ? (m = q, true) : false; } template bool chmin(T &m, const T q) { return m > q ? (m = q, true) : false; } int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); } template pair operator+(const pair &l, const pair &r) { return make_pair(l.first + r.first, l.second + r.second); } template pair operator-(const pair &l, const pair &r) { return make_pair(l.first - r.first, l.second - r.second); } template vector sort_unique(vector vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; } template int arglb(const std::vector &v, const T &x) { return std::distance(v.begin(), std::lower_bound(v.begin(), v.end(), x)); } template int argub(const std::vector &v, const T &x) { return std::distance(v.begin(), std::upper_bound(v.begin(), v.end(), x)); } template istream &operator>>(istream &is, vector &vec) { for (auto &v : vec) is >> v; return is; } template ostream &operator<<(ostream &os, const vector &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; } template ostream &operator<<(ostream &os, const valarray &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; } template ostream &operator<<(ostream &os, const array &arr) { os << '['; for (auto v : arr) os << v << ','; os << ']'; return os; } #if __cplusplus >= 201703L template istream &operator>>(istream &is, tuple &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; } template ostream &operator<<(ostream &os, const tuple &tpl) { os << '('; std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os << ')'; } #endif template ostream &operator<<(ostream &os, const deque &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; } template ostream &operator<<(ostream &os, const set &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const unordered_set &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const multiset &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const unordered_multiset &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const pair &pa) { os << '(' << pa.first << ',' << pa.second << ')'; return os; } template ostream &operator<<(ostream &os, const map &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const unordered_map &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; } #ifdef HITONANODE_LOCAL const string COLOR_RESET = "\033[0m", BRIGHT_GREEN = "\033[1;32m", BRIGHT_RED = "\033[1;31m", BRIGHT_CYAN = "\033[1;36m", NORMAL_CROSSED = "\033[0;9;37m", RED_BACKGROUND = "\033[1;41m", NORMAL_FAINT = "\033[0;2m"; #define dbg(x) cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << endl #define dbgif(cond, x) ((cond) ? cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << endl : cerr) #else #define dbg(x) 0 #define dbgif(cond, x) 0 #endif #include #include // CUT begin // Fast Walsh-Hadamard transform and its abstraction // Tutorials: // template void abstract_fwht(std::vector &seq, F f) { const int n = seq.size(); assert(__builtin_popcount(n) == 1); for (int w = 1; w < n; w *= 2) { for (int i = 0; i < n; i += w * 2) { for (int j = 0; j < w; j++) { f(seq[i + j], seq[i + j + w]); } } } } template std::vector bitwise_conv(std::vector x, std::vector y, F1 f, F2 finv) { const int n = x.size(); assert(__builtin_popcount(n) == 1); assert(x.size() == y.size()); if (x == y) { abstract_fwht(x, f), y = x; } else { abstract_fwht(x, f), abstract_fwht(y, f); } for (size_t i = 0; i < x.size(); i++) { x[i] *= y[i]; } abstract_fwht(x, finv); return x; } // bitwise xor convolution (FWHT-based) // ret[i] = \sum_j x[j] * y[i ^ j] // if T is integer, ||x||_1 * ||y||_1 * 2 < numeric_limits::max() template std::vector xorconv(std::vector x, std::vector y) { auto f = [](T &lo, T &hi) { T c = lo + hi; hi = lo - hi, lo = c; }; auto finv = [](T &lo, T &hi) { T c = lo + hi; hi = (lo - hi) / 2, lo = c / 2; // Reconsider HEAVY complexity of division by 2 when T is ModInt }; return bitwise_conv(x, y, f, finv); } // bitwise AND conolution // ret[i] = \sum_{(j & k) == i} x[j] * y[k] template std::vector andconv(std::vector x, std::vector y) { return bitwise_conv( x, y, [](T &lo, T &hi) { lo += hi; }, [](T &lo, T &hi) { lo -= hi; }); } // bitwise OR convolution // ret[i] = \sum_{(j | k) == i} x[j] * y[k] template std::vector orconv(std::vector x, std::vector y) { return bitwise_conv( x, y, [](T &lo, T &hi) { hi += lo; }, [](T &lo, T &hi) { hi -= lo; }); } constexpr int D = 32; using Int = __int64_t; __int64_t rd() { __int64_t ret = 0; REP(d, D) { __int64_t b; cin >> b; ret += b << d; } return ret; } #include valarray rdva() { valarray ret(D); for (auto &x : ret) cin >> x; return ret; } int main() { int N; cin >> N; vector> A(1 << N), B(1 << N); for (auto &x : A) x = rdva(); for (auto &x : B) x = rdva(); auto f_xor = [](valarray &lo, valarray &hi) { valarray c(lo.size()); c += lo; c += hi; hi = lo - hi, lo = c; }; abstract_fwht(A, f_xor); abstract_fwht(B, f_xor); REP(i, A.size()) { valarray v(63); REP(d, D) REP(e, D) v[d + e] += A[i][d] * B[i][e]; A[i] = v; } abstract_fwht(A, f_xor); for (auto vec : A) { for (auto x : vec) { cout << abs((x >> N) % 2) << ' '; } cout << '\n'; } }