#define AUTO_GENERATED
// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/inverse_matrix
#include "../../../src/lalg/ds/mat/lib.hpp"
#include "../../../src/lalg/mat/ge/lib.hpp"
#include "../../../src/lalg/mat/inv/lib.hpp"
using namespace tifa_libs;
CEXP u32 MOD = 998244353;
#include "../../../src/math/ds/mint/ms/lib.hpp"
using namespace tifa_libs;
using mint = mint_ms<MOD>;
using mat = tifa_libs::matrix<mint>;
int main() {
std::cin.tie(nullptr)->std::ios::sync_with_stdio(false);
u32 n;
std::cin >> n;
mat a(n, n);
std::cin >> a;
auto is_0 = [](cT_(mint) x) { return x.val() == 0; };
auto ge = [&is_0](mat& m, bool f) { return tifa_libs::ge_mat(m, is_0, f); };
auto res = tifa_libs::inv_mat(a, is_0, ge);
if (res)
std::cout << res.value();
else
std::cout << "-1\n";
return 0;
}
#line 1 "test/cpv/library-checker-linear_algebra/inverse_matrix.mints-ms.cpp"
#define AUTO_GENERATED
// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/inverse_matrix
#line 2 "src/lalg/ds/mat/lib.hpp"
#line 2 "src/util/traits/others/lib.hpp"
// clang-format off
#line 2 "src/util/alias/others/lib.hpp"
#line 2 "src/util/consts/lib.hpp"
#line 2 "src/util/alias/num/lib.hpp"
#line 2 "src/util/util/lib.hpp"
// https://github.com/Tiphereth-A/CP-lib
#include <bits/extc++.h>
// clang-format off
namespace tifa_libs {
#define CEXP constexpr
#define CEXPE constexpr explicit
#define CR const&
#define CP const*
#define PC *const
#define CPC const*const
#define TPN typename
#define NE noexcept
#define CNE const noexcept
#define ND [[nodiscard]]
#define cT_(...) std::conditional_t<sizeof(__VA_ARGS__) <= sizeof(size_t) * 2, __VA_ARGS__, __VA_ARGS__ CR>
// NOLINTNEXTLINE(misc-const-correctness)
#define flt_(T, i, l, r, ...) for (T i = (l), i##e = (r)__VA_OPT__(, ) __VA_ARGS__; i < i##e; ++i)
#define retif_(cond, if_true, ...) if cond return if_true __VA_OPT__(; else return __VA_ARGS__)
#ifdef ONLINE_JUDGE
#undef assert
#define assert(x) 42
#endif
using namespace std::ranges;
using namespace std::literals;
template <class T>
CEXP T abs(T x) NE { retif_((x < 0), -x, x); }
} // namespace tifa_libs
// clang-format on
#line 4 "src/util/alias/num/lib.hpp"
// clang-format off
namespace tifa_libs {
#define mk0_(w, t) using w = t; using c##w = const t
#define mk_(w, t) mk0_(w, t); CEXP w operator""_##w(unsigned long long x) NE { return (w)x; }
mk_(i8, int8_t) mk_(u8, uint8_t) mk_(i16, int16_t) mk_(u16, uint16_t) mk_(i32, int32_t) mk_(u32, uint32_t) mk_(i64, int64_t) mk_(u64, uint64_t) mk_(isz, ssize_t) mk_(usz, size_t) mk_(chr, char) mk_(schr, signed char) mk_(uchr, unsigned char) mk_(sint, signed) mk_(uint, unsigned);
mk0_(i128, __int128_t); mk0_(u128, __uint128_t); mk0_(f32, float); mk0_(f64, double); mk0_(f128, long double);
#undef mk0_
#undef mk_
} // namespace tifa_libs
// clang-format on
#line 4 "src/util/consts/lib.hpp"
// clang-format off
namespace tifa_libs {
using std::numbers::pi_v;
template <std::floating_point FP>
inline FP eps_v = std::sqrt(std::numeric_limits<FP>::epsilon());
template <std::floating_point FP>
CEXP void set_eps(FP v) NE { eps_v<FP> = v; }
CEXP u32 TIME = ((__TIME__[0] & 15) << 20) | ((__TIME__[1] & 15) << 16) | ((__TIME__[3] & 15) << 12) | ((__TIME__[4] & 15) << 8) | ((__TIME__[6] & 15) << 4) | (__TIME__[7] & 15);
CEXP auto STR2U16 = [] { std::array<u32, 65536> table{}; table.fill(-1_u32); flt_ (u32, i, 48, 58) flt_ (u32, j, 48, 58) table[i << 8 | j] = (j & 15) * 10 + (i & 15); return table; }();
inline const auto fn_0 = [](auto&&...) NE {};
inline const auto fn_is0 = [](auto x) NE { return x == 0; };
} // namespace tifa_libs
// clang-format on
#line 4 "src/util/alias/others/lib.hpp"
namespace tifa_libs {
template <class T>
struct chash {
CEXP static u64 C = u64(pi_v<f128> * 2e18) | 71;
CEXP u64 operator()(T x) CNE { return __builtin_bswap64(((u64)x ^ TIME) * C); }
};
// clang-format off
#define mk_(w, t) using w = t; using c##w = const t;
mk_(strn, std::string) mk_(strnv, std::string_view)
#undef mk_
template <class T> struct edge_t { T w; u32 u, v; CEXP auto operator<=>(edge_t CR) const = default; }; template <class T> using cedge_t = const edge_t<T>;
template <class T> struct pt3 { T _0, _1, _2; CEXP auto operator<=>(pt3 CR) const = default; }; template <class T> using cpt3 = const pt3<T>;
template <class T> struct pt4 { T _0, _1, _2, _3; CEXP auto operator<=>(pt4 CR) const = default; }; template <class T> using cpt4 = const pt4<T>;
#define mkT_(w, t, ...) template <class T> using w = t __VA_OPT__(, ) __VA_ARGS__; template <class T> using c##w = const t __VA_OPT__(, ) __VA_ARGS__;
mkT_(ptt, std::pair<T, T>) mkT_(alc, std::pmr::polymorphic_allocator<T>) mkT_(vec, std::vector<T>) mkT_(vvec, vec<vec<T>>) mkT_(v3ec, vvec<vec<T>>) mkT_(vecpt, vec<ptt<T>>) mkT_(vvecpt, vvec<ptt<T>>) mkT_(ptvec, ptt<vec<T>>) mkT_(ptvvec, ptt<vvec<T>>)
#undef mkT_
template <class T> using itl = std ::initializer_list<T>;
template <class T, usz ext = std::dynamic_extent> using spn = std::span<T const, ext>;
template <class T, usz N> using arr = std::array<T, N>; template <class T, usz N> using carr = std::array<const T, N>;
template <class U, class T> using vecp = vec<std::pair<U, T>>; template <class U, class T> using vvecp = vvec<std::pair<U, T>>;
template <class U, class T> using vvecp = vvec<std::pair<U, T>>; template <class U, class T> using vvvecp = vvec<vvec<std::pair<U, T>>>;
#ifdef PB_DS_ASSOC_CNTNR_HPP
template <class T, class C = std::less<T>> using set = __gnu_pbds::tree<T, __gnu_pbds::null_type, C>;
template <class K, class V, class C = std::less<K>> using map = __gnu_pbds::tree<K, V, C>;
// hset<u64> s({}, {}, {}, {}, {1<<16});
template <class T, class HF = chash<T>> using hset = __gnu_pbds::gp_hash_table<T, __gnu_pbds::null_type, HF>;
// hmap<u64, int> s({}, {}, {}, {}, {1<<16});
template <class K, class V, class HF = chash<K>> using hmap = __gnu_pbds::gp_hash_table<K, V, HF>;
#else
using std::set, std::map;
template <class T, class HF = chash<T>> using hset = std::unordered_set<T, HF>;
template <class K, class V, class HF = chash<K>> using hmap = std::unordered_map<K, V, HF>;
#endif
#ifdef PB_DS_PRIORITY_QUEUE_HPP
template <class T, class C = std::less<T>> using pq = __gnu_pbds::priority_queue<T, C>;
#else
template <class T, class C = std::less<T>> using pq = std::priority_queue<T, vec<T>, C>;
#endif
template <class T> using pqg = pq<T, std::greater<T>>;
// clang-format on
#define mk1_(V, A, T) using V##A = V<T>;
#define mk_(V, A, T) mk1_(V, A, T) mk1_(c##V, A, T)
#define mk(A, T) mk_(edge_t, A, T) mk_(ptt, A, T) mk_(pt3, A, T) mk_(pt4, A, T) mk_(vec, A, T) mk_(vvec, A, T) mk_(v3ec, A, T) mk_(vecpt, A, T) mk_(vvecpt, A, T) mk_(ptvec, A, T) mk_(ptvvec, A, T) mk1_(spn, A, T) mk1_(itl, A, T)
mk(b, bool) mk(c, chr) mk(i, i32) mk(u, u32) mk(ii, i64) mk(uu, u64) mk(t, isz) mk(z, usz) mk(f, f32) mk(d, f64) mk(s, strn);
#undef mk
#undef mk_
#undef mk1_
} // namespace tifa_libs
#line 4 "src/util/traits/others/lib.hpp"
namespace tifa_libs {
//! only for template without non-type argument
template <class, template <class...> class> CEXP bool specialized_from_v = false;
template <template <class...> class T, class... Args> CEXP bool specialized_from_v<T<Args...>, T> = true;
static_assert(specialized_from_v<vecu, std::vector>);
template <class T> concept container_c = common_range<T> && !std::is_array_v<std::remove_cvref_t<T>> && !std::same_as<std::remove_cvref_t<T>, strn> && !std::same_as<std::remove_cvref_t<T>, strnv>;
template <class T> concept istream_c = std::derived_from<T, std::istream> || std::derived_from<T, std::wistream> || requires(T is) { is.peek(); };
template <class T> concept ostream_c = std::derived_from<T, std::ostream> || std::derived_from<T, std::wostream> || requires(T os) { os.flush(); };
} // namespace tifa_libs
// clang-format on
#line 4 "src/lalg/ds/mat/lib.hpp"
namespace tifa_libs {
#define FOR1_(i, l, r) for (u32 i = (l), i##ed__ = (r); i < i##ed__; ++i)
#define FOR2_(i, row_l, row_r, j, col_l, col_r) \
FOR1_ (i, row_l, row_r) \
FOR1_ (j, col_l, col_r)
template <class T>
class matrix {
vec<T> d;
u32 r_, c_;
bool tr_;
public:
using val_t = T;
CEXP matrix(u32 row, u32 col, cT_(T) v = T{}) NE : d(row* col, v), r_{row}, c_{col}, tr_{false} { assert(row > 0 && col > 0); }
CEXP matrix(u32 row, u32 col, spn<T> data) NE : d(data), r_{row}, c_{col}, tr_{false} { assert(row > 0 && col > 0 && d.size() == row * col); }
CEXP matrix(vvec<T> CR data) NE : d(data.size() * data[0].size()), r_((u32)data.size()), c_((u32)data[0].size()), tr_{false} {
assert(data.size() > 0 && data[0].size() > 0);
FOR1_ (i, 1, r_) assert((u32)data[i].size() == c_);
FOR2_ (i, 0, r_, j, 0, c_) (*this)(i, j) = data[i][j];
}
ND CEXP u32 row() CNE { retif_((tr_), c_, r_); }
ND CEXP u32 col() CNE { retif_((tr_), r_, c_); }
ND CEXP vec<T> CR data() CNE { return d; }
CEXP vec<T>& data() NE { return d; }
CEXP TPN vec<T>::reference operator()(u32 r, u32 c) NE { retif_((tr_), d[c * c_ + r], d[r * c_ + c]); }
CEXP TPN vec<T>::const_reference operator()(u32 r, u32 c) CNE { retif_((tr_), d[c * c_ + r], d[r * c_ + c]); }
CEXP matrix& trans() NE {
tr_ = !tr_;
return *this;
}
template <class F>
CEXP void apply(F&& f) NE { apply_range(0, row(), 0, col(), std::forward<F>(f)); }
template <class F>
requires requires(F f, u32 i, u32 j, T& val) { f(i, j, val); }
CEXP void apply_range(u32 row_l, u32 row_r, u32 col_l, u32 col_r, F&& f) NE {
assert(row_l < row_r && row_r <= row() && col_l < col_r && col_r <= col());
T val;
FOR2_ (i, row_l, row_r, j, col_l, col_r) f(i, j, val = (*this)(i, j)), (*this)(i, j) = val;
}
friend auto& operator>>(istream_c auto& is, matrix& mat) NE {
cu32 r_ = mat.row(), c_ = mat.col();
FOR2_ (i, 0, r_, j, 0, c_) is >> mat(i, j);
return is;
}
friend auto& operator<<(ostream_c auto& os, matrix CR mat) NE {
cu32 r_ = mat.row(), c_ = mat.col();
FOR2_ (i, 0, r_ - 1, j, 0, c_) os << mat(i, j) << " \n"[j + 1 == c_];
os << mat(r_ - 1, 0);
FOR1_ (j, 1, c_) os << ' ' << mat(r_ - 1, j);
return os;
}
ND CEXP matrix submat(u32 row_l, u32 row_r, u32 col_l, u32 col_r) CNE {
assert(row_l < row_r && row_r <= row() && col_l < col_r && col_r <= col());
matrix ret(row_r - row_l, col_r - col_l);
FOR2_ (i, row_l, row_r, j, col_l, col_r) ret(i - row_l, j - col_l) = (*this)(i, j);
return ret;
}
CEXP void swap_row(u32 r1, u32 r2) NE {
if (assert(r1 < row() && r2 < row()); r1 == r2) return;
FOR1_ (j, 0, col()) swap((*this)(r1, j), (*this)(r2, j));
}
CEXP void swap_col(u32 c1, u32 c2) NE {
if (assert(c1 < col() && c2 < col()); c1 == c2) return;
FOR1_ (i, 0, row()) swap((*this)(i, c1), (*this)(i, c2));
}
CEXP matrix operator-() CNE {
if CEXP (std::is_same_v<T, bool>) return *this;
else {
matrix ret = *this;
ret.apply([](u32, u32, T& v) NE { v = -v; });
return ret;
}
}
friend CEXP matrix operator+(matrix l, cT_(T) v) NE { return l += v; }
friend CEXP matrix operator+(cT_(T) v, matrix l) NE { return l += v; }
CEXP matrix& operator+=(cT_(T) v) NE {
if CEXP (std::is_same_v<T, bool>) apply([&v](u32, u32, auto& val) NE { val = val ^ v; });
else apply([&v](u32, u32, T& val) NE { val += v; });
return *this;
}
friend CEXP matrix operator-(matrix l, cT_(T) v) NE { return l -= v; }
CEXP matrix& operator-=(cT_(T) v) NE {
if CEXP (std::is_same_v<T, bool>) apply([&v](u32, u32, auto& val) NE { val = val ^ v; });
else apply([&v](u32, u32, T& val) NE { val -= v; });
return *this;
}
friend CEXP matrix operator*(matrix l, cT_(T) v) NE { return l *= v; }
friend CEXP matrix operator*(cT_(T) v, matrix l) NE { return l *= v; }
CEXP matrix& operator*=(cT_(T) v) NE {
if CEXP (std::is_same_v<T, bool>) {
if (!v) fill(begin(d), end(d), false);
return *this;
} else apply([&v](u32, u32, T& val) NE { val *= v; });
return *this;
}
friend CEXP matrix operator+(matrix l, matrix CR r) NE { return l += r; }
CEXP matrix& operator+=(matrix CR r) NE {
assert(row() == r.row() && col() == r.col());
if CEXP (std::is_same_v<T, bool>) apply([&r](u32 i, u32 j, auto& val) NE { val = val ^ r(i, j); });
else apply([&r](u32 i, u32 j, T& val) NE { val += r(i, j); });
return *this;
}
friend CEXP matrix operator-(matrix l, matrix CR r) NE { return l -= r; }
CEXP matrix& operator-=(matrix CR r) NE {
assert(row() == r.row() && col() == r.col());
if CEXP (std::is_same_v<T, bool>) apply([&r](u32 i, u32 j, auto& val) NE { val = val ^ r(i, j); });
else apply([&r](u32 i, u32 j, T& val) NE { val -= r(i, j); });
return *this;
}
friend CEXP matrix operator*(matrix CR l, matrix CR r) NE {
cu32 i_ = l.row(), j_ = l.col(), k_ = r.col();
assert(j_ == r.row());
matrix ret(i_, k_);
FOR1_ (i, 0, i_)
FOR1_ (j, 0, j_)
FOR1_ (k, 0, k_)
if CEXP (std::is_same_v<T, bool>) ret(i, k) = ret(i, k) ^ (l(i, j) && r(j, k));
else ret(i, k) += l(i, j) * r(j, k);
return ret;
}
CEXP matrix& operator*=(matrix CR r) NE { return *this = *this * r; }
ND CEXP vec<T> lproj(spn<T> x) CNE {
cu32 r_ = row(), c_ = col();
assert(r_ == x.size());
vec<T> ret(c_);
FOR1_ (j, 0, c_)
if CEXP (std::is_same_v<T, bool>) {
bool v = false;
FOR1_ (i, 0, r_) v = v ^ ((*this)(i, j) && x[i]);
ret[j] = v;
} else {
T v{};
FOR1_ (i, 0, r_) v += (*this)(i, j) * x[i];
ret[j] = v;
}
return ret;
}
CEXP bool operator==(matrix CR r) CNE {
if (row() != r.row() || col() != r.col()) return false;
FOR2_ (i, 0, row(), j, 0, col())
if ((*this)(i, j) != r(i, j)) return false;
return true;
}
};
#undef FOR1_
#undef FOR2_
} // namespace tifa_libs
#line 2 "src/lalg/mat/ge/lib.hpp"
#line 2 "src/util/traits/math/lib.hpp"
// clang-format off
#line 4 "src/util/traits/math/lib.hpp"
namespace tifa_libs {
template <class T> concept char_c = std::same_as<T, char> || std::same_as<T, signed char> || std::same_as<T, unsigned char>;
#pragma GCC diagnostic ignored "-Wpedantic"
template <class T> concept s128_c = std::same_as<T, __int128_t> || std::same_as<T, __int128>;
template <class T> concept u128_c = std::same_as<T, __uint128_t> || std::same_as<T, unsigned __int128>;
template <class T> concept i128_c = s128_c<T> || u128_c<T>;
#pragma GCC diagnostic warning "-Wpedantic"
template <class T> concept imost64_c = std::integral<T> && sizeof(T) * __CHAR_BIT__ <= 64;
template <class T> concept smost64_c = imost64_c<T> && std::signed_integral<T>;
template <class T> concept umost64_c = imost64_c<T> && std::unsigned_integral<T>;
template <class T> concept int_c = i128_c<T> || imost64_c<T>;
template <class T> concept sint_c = s128_c<T> || smost64_c<T>;
template <class T> concept uint_c = u128_c<T> || umost64_c<T>;
template <class T> concept arithm_c = std::is_arithmetic_v<T> || int_c<T>;
template <class T> concept mint_c = requires(T x) { {x.mod()} -> uint_c; {x.val()} -> uint_c; };
template <class T> concept dft_c = requires(T x, std::vector<TPN T::data_t> v, u32 n) { {x.size()} -> std::same_as<u32>; x.bzr(n); x.dif(v, n); x.dit(v, n); };
template <class T> concept ntt_c = dft_c<T> && requires(T x) { T::max_size; T::G; };
template <class T> struct to_sint : std::make_signed<T> {};
template <> struct to_sint<u128> { using type = i128; };
template <> struct to_sint<i128> { using type = i128; };
template <class T> using to_sint_t = TPN to_sint<T>::type;
template <class T> struct to_uint : std::make_unsigned<T> {};
template <> struct to_uint<u128> { using type = u128; };
template <> struct to_uint<i128> { using type = u128; };
template <class T> using to_uint_t = TPN to_uint<T>::type;
template <arithm_c T> struct to_bigger : std::make_unsigned<T> {};
#define _(w,ww) template <> struct to_bigger<w> { using type = ww; }
#define _2(w,ww) _(i##w,i##ww); _(u##w,u##ww);
_2(8, 16); _2(16, 32); _2(32, 64); _2(64, 128); _(f32, f64); _(f64, f128);
#undef _2
#undef _
template <class T> using to_bigger_t = TPN to_bigger<T>::type;
template <arithm_c T> CEXP T inf_v = [] {
if CEXP(sint_c<T>) return T(to_uint_t<T>(-1) / 4 - 1);
else if CEXP(uint_c<T>) return T(-1) / 2 - 1;
else return std::numeric_limits<T>::max() / 2 - 1;
}();
} // namespace tifa_libs
// clang-format on
#line 5 "src/lalg/mat/ge/lib.hpp"
namespace tifa_libs {
template <class T, class Is0, bool euclid = int_c<T>>
requires(!euclid || !std::is_floating_point_v<T>) && requires(Is0 is0, T t) {
{ is0(t) } -> std::same_as<bool>;
}
CEXP i32 ge_mat(matrix<T>& mat, Is0 is0, bool clear_u = true) NE {
cu32 R = mat.row(), C = mat.col(), rk_max = min(R, C);
u32 rk = 0;
bool neg = false;
auto swapr = [&](u32 i, u32 c) NE {
u32 i2 = i;
flt_ (u32, r, i + 1, R) {
bool better = false;
flt_ (u32, k, c, C) {
if (mat(r, k) == mat(i2, k)) continue;
better = mat(i2, k) < mat(r, k);
break;
}
if (better) i2 = r;
}
if (i != i2) {
mat.swap_row(i, i2);
return true;
}
return false;
};
for (u32 i = 0, c = 0; i < R; c = max(c, ++i)) {
if CEXP (!euclid && !mint_c<T>) neg ^= swapr(i, c);
else if (is0(mat(i, c))) neg ^= swapr(i, c);
while (c < C && is0(mat(i, c))) ++c;
if (c == C) break;
flt_ (u32, j, clear_u ? 0 : i + 1, R) {
if (i == j || is0(mat(j, c))) continue;
if CEXP (std::same_as<T, bool>)
flt_ (u32, k, c, C) mat(j, k) = !mat(j, k);
else if CEXP (euclid) {
while (true) {
if (is0(mat(j, c))) break;
T _;
if CEXP (mint_c<T>) _ = mat(i, c).val() / mat(j, c).val();
else _ = mat(i, c) / mat(j, c);
flt_ (u32, k, c, C) mat(i, k) -= _ * mat(j, k);
mat.swap_row(i, j), neg ^= 1;
}
} else {
T _ = mat(j, c) / mat(i, c);
mat(j, c) = 0;
flt_ (u32, k, c + 1, C) mat(j, k) -= mat(i, k) * _;
}
}
if (++rk >= rk_max) break;
}
retif_((neg), -((i32)rk), (i32)rk);
}
} // namespace tifa_libs
#line 2 "src/lalg/mat/inv/lib.hpp"
#line 2 "src/lalg/mat/merge_lr/lib.hpp"
#line 4 "src/lalg/mat/merge_lr/lib.hpp"
namespace tifa_libs {
// [l] [r] -> [l r]
template <class T>
CEXP matrix<T> merge_lr_mat(matrix<T> CR l, matrix<T> CR r) NE {
cu32 r_ = l.row();
assert(r_ == r.row());
cu32 lc_ = l.col(), rc_ = r.col(), c_ = lc_ + rc_;
matrix<T> ret(r_, c_);
ret.apply_range(0, r_, 0, lc_, [&l](u32 i, u32 j, T& val) NE { val = l(i, j); });
ret.apply_range(0, r_, lc_, c_, [lc_, &r](u32 i, u32 j, T& val) NE { val = r(i, j - lc_); });
return ret;
}
} // namespace tifa_libs
#line 4 "src/lalg/mat/inv/lib.hpp"
namespace tifa_libs {
template <class T, class Is0, class Ge, bool calc_det = false>
requires requires(Is0 is0, Ge ge, T t, matrix<T> A, bool clear_u) {
{ is0(t) } -> std::same_as<bool>;
{ ge(A, clear_u) } -> std::same_as<i32>;
}
CEXP auto inv_mat(matrix<T> CR mat, Is0&& is0, Ge&& ge) NE {
cu32 n = mat.row();
std::optional<std::conditional_t<calc_det, std::pair<T, matrix<T>>, matrix<T>>> ret;
if (n != mat.col()) return ret;
matrix<T> ans(n, n);
flt_ (u32, i, 0, n) ans(i, i) = 1;
auto rk = ge(ans = merge_lr_mat(mat, ans), true);
if ((u64)abs(rk) != n) return ret;
flt_ (u32, i, 0, n)
if (is0(ans(i, i))) return ret;
if CEXP (!std::is_same_v<T, bool>) ans.apply_range(0, n, n, n * 2, [&ans](u32 i, u32, T& val) NE { val /= ans(i, i); });
if CEXP (calc_det) {
T det{ans(0, 0)};
flt_ (u32, i, 1, n) det *= ans(i, i);
ret.emplace(rk < 0 ? -det : det, ans.submat(0, n, n, n * 2));
return ret;
} else {
ret.emplace(ans.submat(0, n, n, n * 2));
return ret;
}
}
} // namespace tifa_libs
#line 6 "test/cpv/library-checker-linear_algebra/inverse_matrix.mints-ms.cpp"
using namespace tifa_libs;
CEXP u32 MOD = 998244353;
#line 2 "src/math/ds/mint/ms/lib.hpp"
#line 2 "src/nt/mod/montgomery/lib.hpp"
#line 4 "src/nt/mod/montgomery/lib.hpp"
namespace tifa_libs {
template <u32 MOD>
struct montgomery {
static CEXP u32 MOD2 = MOD << 1, R2 = -(u64)(MOD) % MOD, R = [] {
u32 iv = MOD * (2 - MOD * MOD);
iv *= 2 - MOD * iv, iv *= 2 - MOD * iv;
return iv * (MOD * iv - 2);
}();
static_assert(MOD & 1);
static_assert(-R * MOD == 1);
static_assert((MOD >> 30) == 0);
static_assert(MOD != 1);
static CEXP u32 reduce(u64 x) NE { return u32((x + u64((u32)x * R) * MOD) >> 32); }
static CEXP u32 norm(u32 x) NE { return x - (MOD & -((MOD - 1 - x) >> 31)); }
};
template <> // dynamic
struct montgomery<0> {
u32 R, R2, MOD, MOD_ODD, OFFSET, MASK;
CEXP montgomery() NE = default;
CEXPE montgomery(u32 m) NE { reset(m); }
CEXP void reset(u32 m) NE {
for (assert(!(m == 1 || m >> 31)), MOD = MOD_ODD = m, OFFSET = 0; (MOD_ODD & 1) == 0; ++OFFSET, MOD_ODD /= 2);
MASK = (1_u32 << OFFSET) - 1_u32;
u32 iv = MOD_ODD * (2 - MOD_ODD * MOD_ODD);
iv *= 2 - MOD_ODD * iv, iv *= 2 - MOD_ODD * iv, R = iv * (MOD_ODD * iv - 2), R2 = u32(-u64(MOD_ODD) % MOD_ODD);
}
ND CEXP u32 norm(i32 x) CNE { return u32(x + (-(x < 0) & (i32)MOD)); }
ND CEXP u32 reduce(u64 x) CNE {
cu32 t = u32((x + u64((u32)x * R) * MOD_ODD) >> 32);
return t - (MOD_ODD & -((MOD_ODD - 1 - t) >> 31));
}
ND CEXP u32 tsf(u32 x) CNE { retif_((!OFFSET) [[likely]], reduce(u64(x) * R2), reduce(u64(x % MOD_ODD) * R2) << OFFSET | (x & MASK)); }
};
} // namespace tifa_libs
#line 2 "src/math/ds/mint/_base/lib.hpp"
#line 2 "src/nt/inverse/lib.hpp"
#line 2 "src/nt/gl/inv_gcd/lib.hpp"
#line 2 "src/math/safe_mod/lib.hpp"
#line 4 "src/math/safe_mod/lib.hpp"
namespace tifa_libs {
template <int_c T>
CEXP T safe_mod(T x, to_uint_t<T> mod) NE {
if CEXP (sint_c<T>) {
if (x <= -(T)mod || x >= (T)mod) x %= (T)mod;
retif_((x < 0), x + (T)mod, x);
} else {
retif_((x >= mod), x % mod, x);
}
}
} // namespace tifa_libs
#line 2 "src/nt/gl/exgcd/lib.hpp"
#line 4 "src/nt/gl/exgcd/lib.hpp"
namespace tifa_libs {
// Binary exgcd
template <uint_c U, bool only_x = false>
CEXP auto exgcd_b(U a, U b) NE {
using T = to_sint_t<U>;
if CEXP (only_x) {
if (!a) return std::make_tuple(b, (T)0);
if (!b) return std::make_tuple(a, (T)1);
} else {
if (!a) return std::make_tuple(b, (T)0, (T) !!b);
if (!b) return std::make_tuple(a, (T)1, (T)0);
}
auto r = std::__countr_zero(a | b);
a >>= r, b >>= r;
T x = (T)a, y = (T)b, s = 1, t = 0, u = 0, v = 1;
while (x) {
while (!(x & 1))
if (x /= 2; !((s | t) & 1)) s /= 2, t /= 2;
else s = (s + (T)b) / 2, t = (t - (T)a) / 2;
while (!(y & 1))
if (y /= 2; !((u | v) & 1)) u /= 2, v /= 2;
else u = (u + (T)b) / 2, v = (v - (T)a) / 2;
if (x >= y) x -= y, s -= u, t -= v;
else y -= x, u -= s, v -= t;
}
if (y > 1) a /= (U)y, b /= (U)y;
if (a && (U)abs(v) >= a) {
const T _ = v / (T)a;
v -= _ * (T)a, u += _ * (T)b;
}
if (b && (U)abs(u) >= b) {
const T _ = u / (T)b;
u -= _ * (T)b, v += _ * (T)a;
}
if (const T u_ = u + (T)b, v_ = v - (T)a; abs(u_) + abs(v_) <= abs(u) + abs(v)) u = u_, v = v_;
if (const T u_ = u - (T)b, v_ = v + (T)a; abs(u_) + abs(v_) <= abs(u) + abs(v)) u = u_, v = v_;
if CEXP (only_x) return std::make_tuple(U(y << r), u);
else return std::make_tuple(U(y << r), u, v);
}
// @return then return tuple(g, x[, y]) s.t. g = gcd(a, b), xa + yb = g, |x| + |y| is the minimal (primary) and x <= y (secondarily)
template <sint_c T, bool only_x = false>
CEXP auto exgcd(T a, T b) NE {
using U = to_uint_t<T>;
if (auto [x, y] = minmax(a, b); x >= 0 && y <= T(U(-1) >> sizeof(U))) return exgcd_b<U, only_x>((U)a, (U)b);
if CEXP (only_x) {
T s = 1, u = 0;
while (b) {
T c = a / b;
std::tie(s, u, a, b) = std::make_tuple(u, s - u * c, b, a - b * c);
}
return std::make_tuple((U)a, s);
} else {
T s = 1, t = 0, u = 0, v = 1;
while (b) {
T c = a / b;
std::tie(s, t, u, v, a, b) = std::make_tuple(u, v, s - u * c, t - v * c, b, a - b * c);
}
return std::make_tuple((U)a, s, t);
}
}
} // namespace tifa_libs
#line 6 "src/nt/gl/inv_gcd/lib.hpp"
namespace tifa_libs {
template <uint_c T>
CEXP ptt<T> inv_gcd(T n, T mod) NE {
using U = to_sint_t<T>;
auto [g, x] = exgcd<U, true>(U(n % mod), (U)mod);
return {g, safe_mod(x, mod)};
}
} // namespace tifa_libs
#line 4 "src/nt/inverse/lib.hpp"
namespace tifa_libs {
// simple but slower: inv(n, mod) -> 1 < n ? mod - inv(mod % n, n) * mod / n : 1;
template <uint_c T, uint_c U>
CEXP U inverse(T n, U mod) NE {
auto [g, x] = inv_gcd(U(n % mod), mod);
assert(g == 1);
return x;
}
} // namespace tifa_libs
#line 5 "src/math/ds/mint/_base/lib.hpp"
namespace tifa_libs::mint_impl_ {
struct mint_tag_base {};
template <std::derived_from<mint_tag_base> tag_t>
struct mint : tag_t {
CEXP mint() = default;
CEXP mint(int_c auto v) NE : tag_t(v) {}
using raw_t = tag_t::raw_t;
using sraw_t = to_sint_t<raw_t>;
static CEXP sraw_t smod() NE { return (sraw_t)tag_t::mod(); }
ND CEXP sraw_t sval() CNE { return (sraw_t)tag_t::val(); }
template <int_c T>
CEXPE operator T() CNE { return (T)tag_t::val(); }
CEXP mint& operator+=(mint CR r) NE {
mint::add(r);
return *this;
}
CEXP mint& operator-=(mint CR r) NE {
mint::sub(r);
return *this;
}
CEXP mint& operator*=(mint CR r) NE {
mint::mul(r);
return *this;
}
CEXP mint& operator/=(mint CR r) NE { return *this = *this * r.inv(); }
CEXP mint CR operator+() CNE { return *this; }
CEXP mint operator-() CNE { return tag_t::template neg<mint>(); }
ND CEXP mint inv() CNE { return inverse(tag_t::val(), tag_t::mod()); }
friend CEXP mint operator+(mint l, mint CR r) NE { return l += r; }
friend CEXP mint operator-(mint l, mint CR r) NE { return l -= r; }
friend CEXP mint operator*(mint l, mint CR r) NE { return l *= r; }
friend CEXP mint operator/(mint l, mint CR r) NE { return l /= r; }
friend CEXP bool operator==(mint CR l, mint CR r) NE { return l.val() == r.val(); }
friend CEXP auto operator<=>(mint CR l, mint CR r) NE { return l.sval() <=> r.sval(); }
friend auto& operator>>(istream_c auto& is, mint& x) NE {
i64 _;
is >> _, x = mint(_);
return is;
}
friend auto& operator<<(ostream_c auto& os, mint CR x) NE { return os << x.val(); }
friend CEXP auto abs(mint CR x) NE { return x.val(); }
};
} // namespace tifa_libs::mint_impl_
#line 5 "src/math/ds/mint/ms/lib.hpp"
namespace tifa_libs {
template <u64 MOD_>
class mint_ms_tag : public mint_impl_::mint_tag_base {
static_assert(MOD_ <= UINT32_MAX);
using core = montgomery<MOD_>;
public:
static CEXP bool FIXED_MOD = true;
protected:
using raw_t = u32;
raw_t v_{};
CEXP mint_ms_tag() NE = default;
CEXP mint_ms_tag(int_c auto v) NE : v_{mod(v)} {}
public:
static CEXP raw_t mod(sint_c auto v) NE {
if CEXP (smost64_c<decltype(v)>) {
retif_((v >= 0 && (u64)v < mod()) [[likely]], core::reduce(u64((raw_t)v) * core::R2));
}
return core::reduce(u64(i32(v % (i32)mod()) + (i32)mod()) * core::R2);
}
static CEXP raw_t mod(uint_c auto v) NE {
if CEXP (umost64_c<decltype(v)>) {
retif_((cu64 x = (u64)v; x < mod()) [[likely]], core::reduce(x * core::R2), core::reduce(u64(x % mod()) * core::R2));
} else retif_((v < mod()) [[likely]], core::reduce(u64((raw_t)v) * core::R2), core::reduce(u64((raw_t)(v % mod())) * core::R2));
}
static CEXP raw_t mod() NE { return MOD_; }
ND CEXP raw_t val() CNE { return core::norm(core::reduce(v_)); }
CEXP raw_t& data() NE { return v_; }
protected:
template <class mint>
ND CEXP auto neg() CNE {
mint res;
res.v_ = (core::MOD2 & -raw_t(v_ != 0)) - v_;
return res;
}
CEXP void add(mint_ms_tag CR r) NE { v_ += r.v_ - core::MOD2, v_ += core::MOD2 & -(v_ >> 31); }
CEXP void sub(mint_ms_tag CR r) NE { v_ -= r.v_, v_ += core::MOD2 & -(v_ >> 31); }
CEXP void mul(mint_ms_tag CR r) NE { v_ = core::reduce(u64(v_) * r.v_); }
};
template <u64 MOD>
using mint_ms = mint_impl_::mint<mint_ms_tag<MOD>>;
} // namespace tifa_libs
#line 11 "test/cpv/library-checker-linear_algebra/inverse_matrix.mints-ms.cpp"
using namespace tifa_libs;
using mint = mint_ms<MOD>;
using mat = tifa_libs::matrix<mint>;
int main() {
std::cin.tie(nullptr)->std::ios::sync_with_stdio(false);
u32 n;
std::cin >> n;
mat a(n, n);
std::cin >> a;
auto is_0 = [](cT_(mint) x) { return x.val() == 0; };
auto ge = [&is_0](mat& m, bool f) { return tifa_libs::ge_mat(m, is_0, f); };
auto res = tifa_libs::inv_mat(a, is_0, ge);
if (res)
std::cout << res.value();
else
std::cout << "-1\n";
return 0;
}
test/cpv/library-checker-linear_algebra/inverse_matrix.mints-ms.cpp