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#define PROBLEM "https://yukicoder.me/problems/no/1303" #include "../../modint.hpp" #include "../../number/dual_number.hpp" #include "../../unionfind/unionfind.hpp" #include "../matrix.hpp" #include <iostream> #include <utility> #include <vector> using namespace std; using mint = ModInt<998244353>; using dual = DualNumber<mint>; mint solve1(int N, const vector<pair<int, int>> &edges) { vector<vector<dual>> d(N, vector<dual>(N)); for (auto p : edges) { int u = p.first, v = p.second; d[u][u] += dual::id(); d[v][v] += dual::id(); d[u][v] -= dual::id(); d[v][u] -= dual::id(); } const dual x = dual(0, 1); for (int i = 0; i < N; ++i) { for (int j = 0; j < i; ++j) { if (d[i][j] == dual()) { d[i][i] += x; d[j][j] += x; d[i][j] -= x; d[j][i] -= x; } } } d.resize(N - 1); for (auto &v : d) v.resize(N - 1); auto ret = matrix<dual>(d).gauss_jordan().determinant_of_upper_triangle(); return ret.a + ret.b; } mint solve2(const vector<int> &vs, const vector<pair<int, int>> &edges) { int D = vs.size(); matrix<mint> mat(D - 1, D - 1); for (auto p : edges) { int i = lower_bound(vs.begin(), vs.end(), p.first) - vs.begin(); int j = lower_bound(vs.begin(), vs.end(), p.second) - vs.begin(); if (i < D - 1) mat[i][i] += 1; if (j < D - 1) mat[j][j] += 1; if (i + 1 < D and j + 1 < D) mat[i][j] -= 1, mat[j][i] -= 1; } return mat.gauss_jordan().determinant_of_upper_triangle(); } int main() { cin.tie(nullptr), ios::sync_with_stdio(false); int N, M; cin >> N >> M; vector<pair<int, int>> edges; UnionFind uf1(N); while (M--) { int u, v; cin >> u >> v; --u, --v; edges.emplace_back(u, v); uf1.unite(u, v); } if (uf1.count(0) == N) { cout << "0\n" << solve1(N, edges) << '\n'; return 0; } int max_red = 0, cntmaxi = 0, fuben = 0; for (int i = 0; i < N; ++i) { for (int j = 0; j < N; ++j) fuben += !uf1.same(i, j); } for (int i = 0; i < N; ++i) { for (int j = 0; j < i; ++j) { if (!uf1.same(i, j)) { int s = uf1.count(i) * uf1.count(j); if (s > max_red) { max_red = s, cntmaxi = 1; } else { if (max_red == s) cntmaxi++; } } } } mint ret = cntmaxi; vector<vector<int>> r2is(N); vector<vector<pair<int, int>>> r2edges(N); for (int i = 0; i < N; ++i) r2is[uf1.find(i)].push_back(i); for (auto p : edges) r2edges[uf1.find(p.first)].push_back(p); for (int r = 0; r < N; ++r) { if (r2is[r].size()) ret *= solve2(r2is[r], r2edges[r]); } cout << fuben - max_red * 2 << '\n' << ret << '\n'; }
#line 1 "linear_algebra_matrix/test/matrix_det_dual_number.yuki1303.test.cpp" #define PROBLEM "https://yukicoder.me/problems/no/1303" #line 2 "modint.hpp" #include <cassert> #include <iostream> #include <set> #include <vector> template <int md> struct ModInt { using lint = long long; constexpr static int mod() { return md; } static int get_primitive_root() { static int primitive_root = 0; if (!primitive_root) { primitive_root = [&]() { std::set<int> fac; int v = md - 1; for (lint i = 2; i * i <= v; i++) while (v % i == 0) fac.insert(i), v /= i; if (v > 1) fac.insert(v); for (int g = 1; g < md; g++) { bool ok = true; for (auto i : fac) if (ModInt(g).pow((md - 1) / i) == 1) { ok = false; break; } if (ok) return g; } return -1; }(); } return primitive_root; } int val_; int val() const noexcept { return val_; } constexpr ModInt() : val_(0) {} constexpr ModInt &_setval(lint v) { return val_ = (v >= md ? v - md : v), *this; } constexpr ModInt(lint v) { _setval(v % md + md); } constexpr explicit operator bool() const { return val_ != 0; } constexpr ModInt operator+(const ModInt &x) const { return ModInt()._setval((lint)val_ + x.val_); } constexpr ModInt operator-(const ModInt &x) const { return ModInt()._setval((lint)val_ - x.val_ + md); } constexpr ModInt operator*(const ModInt &x) const { return ModInt()._setval((lint)val_ * x.val_ % md); } constexpr ModInt operator/(const ModInt &x) const { return ModInt()._setval((lint)val_ * x.inv().val() % md); } constexpr ModInt operator-() const { return ModInt()._setval(md - val_); } constexpr ModInt &operator+=(const ModInt &x) { return *this = *this + x; } constexpr ModInt &operator-=(const ModInt &x) { return *this = *this - x; } constexpr ModInt &operator*=(const ModInt &x) { return *this = *this * x; } constexpr ModInt &operator/=(const ModInt &x) { return *this = *this / x; } friend constexpr ModInt operator+(lint a, const ModInt &x) { return ModInt(a) + x; } friend constexpr ModInt operator-(lint a, const ModInt &x) { return ModInt(a) - x; } friend constexpr ModInt operator*(lint a, const ModInt &x) { return ModInt(a) * x; } friend constexpr ModInt operator/(lint a, const ModInt &x) { return ModInt(a) / x; } constexpr bool operator==(const ModInt &x) const { return val_ == x.val_; } constexpr bool operator!=(const ModInt &x) const { return val_ != x.val_; } constexpr bool operator<(const ModInt &x) const { return val_ < x.val_; } // To use std::map<ModInt, T> friend std::istream &operator>>(std::istream &is, ModInt &x) { lint t; return is >> t, x = ModInt(t), is; } constexpr friend std::ostream &operator<<(std::ostream &os, const ModInt &x) { return os << x.val_; } constexpr ModInt pow(lint n) const { ModInt ans = 1, tmp = *this; while (n) { if (n & 1) ans *= tmp; tmp *= tmp, n >>= 1; } return ans; } static constexpr int cache_limit = std::min(md, 1 << 21); static std::vector<ModInt> facs, facinvs, invs; constexpr static void _precalculation(int N) { const int l0 = facs.size(); if (N > md) N = md; if (N <= l0) return; facs.resize(N), facinvs.resize(N), invs.resize(N); for (int i = l0; i < N; i++) facs[i] = facs[i - 1] * i; facinvs[N - 1] = facs.back().pow(md - 2); for (int i = N - 2; i >= l0; i--) facinvs[i] = facinvs[i + 1] * (i + 1); for (int i = N - 1; i >= l0; i--) invs[i] = facinvs[i] * facs[i - 1]; } constexpr ModInt inv() const { if (this->val_ < cache_limit) { if (facs.empty()) facs = {1}, facinvs = {1}, invs = {0}; while (this->val_ >= int(facs.size())) _precalculation(facs.size() * 2); return invs[this->val_]; } else { return this->pow(md - 2); } } constexpr ModInt fac() const { while (this->val_ >= int(facs.size())) _precalculation(facs.size() * 2); return facs[this->val_]; } constexpr ModInt facinv() const { while (this->val_ >= int(facs.size())) _precalculation(facs.size() * 2); return facinvs[this->val_]; } constexpr ModInt doublefac() const { lint k = (this->val_ + 1) / 2; return (this->val_ & 1) ? ModInt(k * 2).fac() / (ModInt(2).pow(k) * ModInt(k).fac()) : ModInt(k).fac() * ModInt(2).pow(k); } constexpr ModInt nCr(int r) const { if (r < 0 or this->val_ < r) return ModInt(0); return this->fac() * (*this - r).facinv() * ModInt(r).facinv(); } constexpr ModInt nPr(int r) const { if (r < 0 or this->val_ < r) return ModInt(0); return this->fac() * (*this - r).facinv(); } static ModInt binom(int n, int r) { static long long bruteforce_times = 0; if (r < 0 or n < r) return ModInt(0); if (n <= bruteforce_times or n < (int)facs.size()) return ModInt(n).nCr(r); r = std::min(r, n - r); ModInt ret = ModInt(r).facinv(); for (int i = 0; i < r; ++i) ret *= n - i; bruteforce_times += r; return ret; } // Multinomial coefficient, (k_1 + k_2 + ... + k_m)! / (k_1! k_2! ... k_m!) // Complexity: O(sum(ks)) template <class Vec> static ModInt multinomial(const Vec &ks) { ModInt ret{1}; int sum = 0; for (int k : ks) { assert(k >= 0); ret *= ModInt(k).facinv(), sum += k; } return ret * ModInt(sum).fac(); } // Catalan number, C_n = binom(2n, n) / (n + 1) // C_0 = 1, C_1 = 1, C_2 = 2, C_3 = 5, C_4 = 14, ... // https://oeis.org/A000108 // Complexity: O(n) static ModInt catalan(int n) { if (n < 0) return ModInt(0); return ModInt(n * 2).fac() * ModInt(n + 1).facinv() * ModInt(n).facinv(); } ModInt sqrt() const { if (val_ == 0) return 0; if (md == 2) return val_; if (pow((md - 1) / 2) != 1) return 0; ModInt b = 1; while (b.pow((md - 1) / 2) == 1) b += 1; int e = 0, m = md - 1; while (m % 2 == 0) m >>= 1, e++; ModInt x = pow((m - 1) / 2), y = (*this) * x * x; x *= (*this); ModInt z = b.pow(m); while (y != 1) { int j = 0; ModInt t = y; while (t != 1) j++, t *= t; z = z.pow(1LL << (e - j - 1)); x *= z, z *= z, y *= z; e = j; } return ModInt(std::min(x.val_, md - x.val_)); } }; template <int md> std::vector<ModInt<md>> ModInt<md>::facs = {1}; template <int md> std::vector<ModInt<md>> ModInt<md>::facinvs = {1}; template <int md> std::vector<ModInt<md>> ModInt<md>::invs = {0}; using ModInt998244353 = ModInt<998244353>; // using mint = ModInt<998244353>; // using mint = ModInt<1000000007>; #line 1 "number/dual_number.hpp" #include <type_traits> namespace dual_number_ { struct has_id_method_impl { template <class T_> static auto check(T_ *) -> decltype(T_::id(), std::true_type()); template <class T_> static auto check(...) -> std::false_type; }; template <class T_> struct has_id : decltype(has_id_method_impl::check<T_>(nullptr)) {}; } // namespace dual_number_ // Dual number (二重数) // Verified: https://atcoder.jp/contests/abc235/tasks/abc235_f template <class T> struct DualNumber { T a, b; // a + bx template <typename T2, typename std::enable_if<dual_number_::has_id<T2>::value>::type * = nullptr> static T2 _T_id() { return T2::id(); } template <typename T2, typename std::enable_if<!dual_number_::has_id<T2>::value>::type * = nullptr> static T2 _T_id() { return T2(1); } DualNumber(T x = T(), T y = T()) : a(x), b(y) {} static DualNumber id() { return DualNumber(_T_id<T>(), T()); } explicit operator bool() const { return a != T() or b != T(); } DualNumber operator+(const DualNumber &x) const { return DualNumber(a + x.a, b + x.b); } DualNumber operator-(const DualNumber &x) const { return DualNumber(a - x.a, b - x.b); } DualNumber operator*(const DualNumber &x) const { return DualNumber(a * x.a, b * x.a + a * x.b); } DualNumber operator/(const DualNumber &x) const { T cinv = _T_id<T>() / x.a; return DualNumber(a * cinv, (b * x.a - a * x.b) * cinv * cinv); } DualNumber operator-() const { return DualNumber(-a, -b); } DualNumber &operator+=(const DualNumber &x) { return *this = *this + x; } DualNumber &operator-=(const DualNumber &x) { return *this = *this - x; } DualNumber &operator*=(const DualNumber &x) { return *this = *this * x; } DualNumber &operator/=(const DualNumber &x) { return *this = *this / x; } bool operator==(const DualNumber &x) const { return a == x.a and b == x.b; } bool operator!=(const DualNumber &x) const { return !(*this == x); } bool operator<(const DualNumber &x) const { return (a != x.a ? a < x.a : b < x.b); } template <class OStream> friend OStream &operator<<(OStream &os, const DualNumber &x) { return os << '{' << x.a << ',' << x.b << '}'; } T eval(const T &x) const { return a + b * x; } T root() const { return (-a) / b; } // Solve a + bx = 0 (b \neq 0 is assumed) }; #line 2 "unionfind/unionfind.hpp" #include <algorithm> #include <numeric> #include <utility> #line 6 "unionfind/unionfind.hpp" // CUT begin // UnionFind Tree (0-indexed), based on size of each disjoint set struct UnionFind { std::vector<int> par, cou; UnionFind(int N = 0) : par(N), cou(N, 1) { iota(par.begin(), par.end(), 0); } int find(int x) { return (par[x] == x) ? x : (par[x] = find(par[x])); } bool unite(int x, int y) { x = find(x), y = find(y); if (x == y) return false; if (cou[x] < cou[y]) std::swap(x, y); par[y] = x, cou[x] += cou[y]; return true; } int count(int x) { return cou[find(x)]; } bool same(int x, int y) { return find(x) == find(y); } std::vector<std::vector<int>> groups() { std::vector<std::vector<int>> ret(par.size()); for (int i = 0; i < int(par.size()); ++i) ret[find(i)].push_back(i); ret.erase(std::remove_if(ret.begin(), ret.end(), [&](const std::vector<int> &v) { return v.empty(); }), ret.end()); return ret; } }; #line 4 "linear_algebra_matrix/matrix.hpp" #include <cmath> #include <iterator> #line 9 "linear_algebra_matrix/matrix.hpp" namespace matrix_ { struct has_id_method_impl { template <class T_> static auto check(T_ *) -> decltype(T_::id(), std::true_type()); template <class T_> static auto check(...) -> std::false_type; }; template <class T_> struct has_id : decltype(has_id_method_impl::check<T_>(nullptr)) {}; } // namespace matrix_ template <typename T> struct matrix { int H, W; std::vector<T> elem; typename std::vector<T>::iterator operator[](int i) { return elem.begin() + i * W; } inline T &at(int i, int j) { return elem[i * W + j]; } inline T get(int i, int j) const { return elem[i * W + j]; } int height() const { return H; } int width() const { return W; } std::vector<std::vector<T>> vecvec() const { std::vector<std::vector<T>> ret(H); for (int i = 0; i < H; i++) { std::copy(elem.begin() + i * W, elem.begin() + (i + 1) * W, std::back_inserter(ret[i])); } return ret; } operator std::vector<std::vector<T>>() const { return vecvec(); } matrix() = default; matrix(int H, int W) : H(H), W(W), elem(H * W) {} matrix(const std::vector<std::vector<T>> &d) : H(d.size()), W(d.size() ? d[0].size() : 0) { for (auto &raw : d) std::copy(raw.begin(), raw.end(), std::back_inserter(elem)); } template <typename T2, typename std::enable_if<matrix_::has_id<T2>::value>::type * = nullptr> static T2 _T_id() { return T2::id(); } template <typename T2, typename std::enable_if<!matrix_::has_id<T2>::value>::type * = nullptr> static T2 _T_id() { return T2(1); } static matrix Identity(int N) { matrix ret(N, N); for (int i = 0; i < N; i++) ret.at(i, i) = _T_id<T>(); return ret; } matrix operator-() const { matrix ret(H, W); for (int i = 0; i < H * W; i++) ret.elem[i] = -elem[i]; return ret; } matrix operator*(const T &v) const { matrix ret = *this; for (auto &x : ret.elem) x *= v; return ret; } matrix operator/(const T &v) const { matrix ret = *this; const T vinv = _T_id<T>() / v; for (auto &x : ret.elem) x *= vinv; return ret; } matrix operator+(const matrix &r) const { matrix ret = *this; for (int i = 0; i < H * W; i++) ret.elem[i] += r.elem[i]; return ret; } matrix operator-(const matrix &r) const { matrix ret = *this; for (int i = 0; i < H * W; i++) ret.elem[i] -= r.elem[i]; return ret; } matrix operator*(const matrix &r) const { matrix ret(H, r.W); for (int i = 0; i < H; i++) { for (int k = 0; k < W; k++) { for (int j = 0; j < r.W; j++) ret.at(i, j) += this->get(i, k) * r.get(k, j); } } return ret; } matrix &operator*=(const T &v) { return *this = *this * v; } matrix &operator/=(const T &v) { return *this = *this / v; } matrix &operator+=(const matrix &r) { return *this = *this + r; } matrix &operator-=(const matrix &r) { return *this = *this - r; } matrix &operator*=(const matrix &r) { return *this = *this * r; } bool operator==(const matrix &r) const { return H == r.H and W == r.W and elem == r.elem; } bool operator!=(const matrix &r) const { return H != r.H or W != r.W or elem != r.elem; } bool operator<(const matrix &r) const { return elem < r.elem; } matrix pow(int64_t n) const { matrix ret = Identity(H); bool ret_is_id = true; if (n == 0) return ret; for (int i = 63 - __builtin_clzll(n); i >= 0; i--) { if (!ret_is_id) ret *= ret; if ((n >> i) & 1) ret *= (*this), ret_is_id = false; } return ret; } std::vector<T> pow_vec(int64_t n, std::vector<T> vec) const { matrix x = *this; while (n) { if (n & 1) vec = x * vec; x *= x; n >>= 1; } return vec; }; matrix transpose() const { matrix ret(W, H); for (int i = 0; i < H; i++) { for (int j = 0; j < W; j++) ret.at(j, i) = this->get(i, j); } return ret; } // Gauss-Jordan elimination // - Require inverse for every non-zero element // - Complexity: O(H^2 W) template <typename T2, typename std::enable_if<std::is_floating_point<T2>::value>::type * = nullptr> static int choose_pivot(const matrix<T2> &mtr, int h, int c) noexcept { int piv = -1; for (int j = h; j < mtr.H; j++) { if (mtr.get(j, c) and (piv < 0 or std::abs(mtr.get(j, c)) > std::abs(mtr.get(piv, c)))) piv = j; } return piv; } template <typename T2, typename std::enable_if<!std::is_floating_point<T2>::value>::type * = nullptr> static int choose_pivot(const matrix<T2> &mtr, int h, int c) noexcept { for (int j = h; j < mtr.H; j++) { if (mtr.get(j, c) != T2()) return j; } return -1; } matrix gauss_jordan() const { int c = 0; matrix mtr(*this); std::vector<int> ws; ws.reserve(W); for (int h = 0; h < H; h++) { if (c == W) break; int piv = choose_pivot(mtr, h, c); if (piv == -1) { c++; h--; continue; } if (h != piv) { for (int w = 0; w < W; w++) { std::swap(mtr[piv][w], mtr[h][w]); mtr.at(piv, w) *= -_T_id<T>(); // To preserve sign of determinant } } ws.clear(); for (int w = c; w < W; w++) { if (mtr.at(h, w) != T()) ws.emplace_back(w); } const T hcinv = _T_id<T>() / mtr.at(h, c); for (int hh = 0; hh < H; hh++) if (hh != h) { const T coeff = mtr.at(hh, c) * hcinv; for (auto w : ws) mtr.at(hh, w) -= mtr.at(h, w) * coeff; mtr.at(hh, c) = T(); } c++; } return mtr; } int rank_of_gauss_jordan() const { for (int i = H * W - 1; i >= 0; i--) { if (elem[i] != 0) return i / W + 1; } return 0; } int rank() const { return gauss_jordan().rank_of_gauss_jordan(); } T determinant_of_upper_triangle() const { T ret = _T_id<T>(); for (int i = 0; i < H; i++) ret *= get(i, i); return ret; } int inverse() { assert(H == W); std::vector<std::vector<T>> ret = Identity(H), tmp = *this; int rank = 0; for (int i = 0; i < H; i++) { int ti = i; while (ti < H and tmp[ti][i] == T()) ti++; if (ti == H) { continue; } else { rank++; } ret[i].swap(ret[ti]), tmp[i].swap(tmp[ti]); T inv = _T_id<T>() / tmp[i][i]; for (int j = 0; j < W; j++) ret[i][j] *= inv; for (int j = i + 1; j < W; j++) tmp[i][j] *= inv; for (int h = 0; h < H; h++) { if (i == h) continue; const T c = -tmp[h][i]; for (int j = 0; j < W; j++) ret[h][j] += ret[i][j] * c; for (int j = i + 1; j < W; j++) tmp[h][j] += tmp[i][j] * c; } } *this = ret; return rank; } friend std::vector<T> operator*(const matrix &m, const std::vector<T> &v) { assert(m.W == int(v.size())); std::vector<T> ret(m.H); for (int i = 0; i < m.H; i++) { for (int j = 0; j < m.W; j++) ret[i] += m.get(i, j) * v[j]; } return ret; } friend std::vector<T> operator*(const std::vector<T> &v, const matrix &m) { assert(int(v.size()) == m.H); std::vector<T> ret(m.W); for (int i = 0; i < m.H; i++) { for (int j = 0; j < m.W; j++) ret[j] += v[i] * m.get(i, j); } return ret; } std::vector<T> prod(const std::vector<T> &v) const { return (*this) * v; } std::vector<T> prod_left(const std::vector<T> &v) const { return v * (*this); } template <class OStream> friend OStream &operator<<(OStream &os, const matrix &x) { os << "[(" << x.H << " * " << x.W << " matrix)"; os << "\n[column sums: "; for (int j = 0; j < x.W; j++) { T s = T(); for (int i = 0; i < x.H; i++) s += x.get(i, j); os << s << ","; } os << "]"; for (int i = 0; i < x.H; i++) { os << "\n["; for (int j = 0; j < x.W; j++) os << x.get(i, j) << ","; os << "]"; } os << "]\n"; return os; } template <class IStream> friend IStream &operator>>(IStream &is, matrix &x) { for (auto &v : x.elem) is >> v; return is; } }; #line 6 "linear_algebra_matrix/test/matrix_det_dual_number.yuki1303.test.cpp" #line 10 "linear_algebra_matrix/test/matrix_det_dual_number.yuki1303.test.cpp" using namespace std; using mint = ModInt<998244353>; using dual = DualNumber<mint>; mint solve1(int N, const vector<pair<int, int>> &edges) { vector<vector<dual>> d(N, vector<dual>(N)); for (auto p : edges) { int u = p.first, v = p.second; d[u][u] += dual::id(); d[v][v] += dual::id(); d[u][v] -= dual::id(); d[v][u] -= dual::id(); } const dual x = dual(0, 1); for (int i = 0; i < N; ++i) { for (int j = 0; j < i; ++j) { if (d[i][j] == dual()) { d[i][i] += x; d[j][j] += x; d[i][j] -= x; d[j][i] -= x; } } } d.resize(N - 1); for (auto &v : d) v.resize(N - 1); auto ret = matrix<dual>(d).gauss_jordan().determinant_of_upper_triangle(); return ret.a + ret.b; } mint solve2(const vector<int> &vs, const vector<pair<int, int>> &edges) { int D = vs.size(); matrix<mint> mat(D - 1, D - 1); for (auto p : edges) { int i = lower_bound(vs.begin(), vs.end(), p.first) - vs.begin(); int j = lower_bound(vs.begin(), vs.end(), p.second) - vs.begin(); if (i < D - 1) mat[i][i] += 1; if (j < D - 1) mat[j][j] += 1; if (i + 1 < D and j + 1 < D) mat[i][j] -= 1, mat[j][i] -= 1; } return mat.gauss_jordan().determinant_of_upper_triangle(); } int main() { cin.tie(nullptr), ios::sync_with_stdio(false); int N, M; cin >> N >> M; vector<pair<int, int>> edges; UnionFind uf1(N); while (M--) { int u, v; cin >> u >> v; --u, --v; edges.emplace_back(u, v); uf1.unite(u, v); } if (uf1.count(0) == N) { cout << "0\n" << solve1(N, edges) << '\n'; return 0; } int max_red = 0, cntmaxi = 0, fuben = 0; for (int i = 0; i < N; ++i) { for (int j = 0; j < N; ++j) fuben += !uf1.same(i, j); } for (int i = 0; i < N; ++i) { for (int j = 0; j < i; ++j) { if (!uf1.same(i, j)) { int s = uf1.count(i) * uf1.count(j); if (s > max_red) { max_red = s, cntmaxi = 1; } else { if (max_red == s) cntmaxi++; } } } } mint ret = cntmaxi; vector<vector<int>> r2is(N); vector<vector<pair<int, int>>> r2edges(N); for (int i = 0; i < N; ++i) r2is[uf1.find(i)].push_back(i); for (auto p : edges) r2edges[uf1.find(p.first)].push_back(p); for (int r = 0; r < N; ++r) { if (r2is[r].size()) ret *= solve2(r2is[r], r2edges[r]); } cout << fuben - max_red * 2 << '\n' << ret << '\n'; }