This documentation is automatically generated by online-judge-tools/verification-helper
#define PROBLEM "https://judge.yosupo.jp/problem/counting_eulerian_circuits"
#include "../../graph/count_directed_euler_trail.hpp"
#include "../../graph/utility.hpp"
#include "../../modint/modint.hpp"
#include "../../template/template.hpp"
namespace ebi {
using mint = modint998244353;
void main_() {
int n, m;
std::cin >> n >> m;
Graph<int> g(n);
g.read_graph(m, 0);
std::cout << count_directed_euler_circuit<mint>(remove_isolated_vertex(g))
<< '\n';
}
} // namespace ebi
int main() {
ebi::fast_io();
int t = 1;
// std::cin >> t;
while (t--) {
ebi::main_();
}
return 0;
}
#line 1 "test/graph/Counting_Eulerian_Circuits.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/counting_eulerian_circuits"
#line 2 "graph/count_directed_euler_trail.hpp"
#include <vector>
#line 2 "graph/base.hpp"
#include <cassert>
#include <iostream>
#include <ranges>
#line 7 "graph/base.hpp"
#line 2 "data_structure/simple_csr.hpp"
#line 4 "data_structure/simple_csr.hpp"
#include <utility>
#line 6 "data_structure/simple_csr.hpp"
namespace ebi {
template <class E> struct simple_csr {
simple_csr() = default;
simple_csr(int n, const std::vector<std::pair<int, E>>& elements)
: start(n + 1, 0), elist(elements.size()) {
for (auto e : elements) {
start[e.first + 1]++;
}
for (auto i : std::views::iota(0, n)) {
start[i + 1] += start[i];
}
auto counter = start;
for (auto [i, e] : elements) {
elist[counter[i]++] = e;
}
}
simple_csr(const std::vector<std::vector<E>>& es)
: start(es.size() + 1, 0) {
int n = es.size();
for (auto i : std::views::iota(0, n)) {
start[i + 1] = (int)es[i].size() + start[i];
}
elist.resize(start.back());
for (auto i : std::views::iota(0, n)) {
std::copy(es[i].begin(), es[i].end(), elist.begin() + start[i]);
}
}
int size() const {
return (int)start.size() - 1;
}
const auto operator[](int i) const {
return std::ranges::subrange(elist.begin() + start[i],
elist.begin() + start[i + 1]);
}
auto operator[](int i) {
return std::ranges::subrange(elist.begin() + start[i],
elist.begin() + start[i + 1]);
}
const auto operator()(int i, int l, int r) const {
return std::ranges::subrange(elist.begin() + start[i] + l,
elist.begin() + start[i + 1] + r);
}
auto operator()(int i, int l, int r) {
return std::ranges::subrange(elist.begin() + start[i] + l,
elist.begin() + start[i + 1] + r);
}
private:
std::vector<int> start;
std::vector<E> elist;
};
} // namespace ebi
#line 9 "graph/base.hpp"
namespace ebi {
template <class T> struct Edge {
int from, to;
T cost;
int id;
};
template <class E> struct Graph {
using cost_type = E;
using edge_type = Edge<cost_type>;
Graph(int n_) : n(n_) {}
Graph() = default;
void add_edge(int u, int v, cost_type c) {
buff.emplace_back(u, edge_type{u, v, c, m});
edges.emplace_back(edge_type{u, v, c, m++});
}
void add_undirected_edge(int u, int v, cost_type c) {
buff.emplace_back(u, edge_type{u, v, c, m});
buff.emplace_back(v, edge_type{v, u, c, m});
edges.emplace_back(edge_type{u, v, c, m});
m++;
}
void read_tree(int offset = 1, bool is_weighted = false) {
read_graph(n - 1, offset, false, is_weighted);
}
void read_parents(int offset = 1) {
for (auto i : std::views::iota(1, n)) {
int p;
std::cin >> p;
p -= offset;
add_undirected_edge(p, i, 1);
}
build();
}
void read_graph(int e, int offset = 1, bool is_directed = false,
bool is_weighted = false) {
for (int i = 0; i < e; i++) {
int u, v;
std::cin >> u >> v;
u -= offset;
v -= offset;
if (is_weighted) {
cost_type c;
std::cin >> c;
if (is_directed) {
add_edge(u, v, c);
} else {
add_undirected_edge(u, v, c);
}
} else {
if (is_directed) {
add_edge(u, v, 1);
} else {
add_undirected_edge(u, v, 1);
}
}
}
build();
}
void build() {
assert(!prepared);
csr = simple_csr<edge_type>(n, buff);
buff.clear();
prepared = true;
}
int size() const {
return n;
}
int node_number() const {
return n;
}
int edge_number() const {
return m;
}
edge_type get_edge(int i) const {
return edges[i];
}
std::vector<edge_type> get_edges() const {
return edges;
}
const auto operator[](int i) const {
return csr[i];
}
auto operator[](int i) {
return csr[i];
}
private:
int n, m = 0;
std::vector<std::pair<int,edge_type>> buff;
std::vector<edge_type> edges;
simple_csr<edge_type> csr;
bool prepared = false;
};
} // namespace ebi
#line 2 "graph/count_spanning_tree.hpp"
#line 5 "graph/count_spanning_tree.hpp"
#line 2 "matrix/base.hpp"
#include <algorithm>
#line 8 "matrix/base.hpp"
namespace ebi {
template <class T> struct matrix;
template <class T> matrix<T> identify_matrix(int n) {
matrix<T> a(n, n);
for (int i = 0; i < n; i++) {
a[i][i] = 1;
}
return a;
}
template <class T> struct matrix {
private:
using Self = matrix<T>;
public:
matrix(int n_, int m_, T init_val = 0)
: n(n_), m(m_), data(n * m, init_val) {}
matrix(const std::vector<std::vector<T>> &a)
: n((int)a.size()), m((int)a[0].size()) {
data = std::vector(n * m);
for (int i = 0; i < n; i++) {
std::copy(a[i].begin(), a[i].end(), data.begin() + i * m);
}
}
Self operator+(Self &rhs) const noexcept {
return Self(*this) += rhs;
}
Self operator-(Self &rhs) const noexcept {
return Self(*this) -= rhs;
}
Self operator*(Self &rhs) const noexcept {
return Self(*this) *= rhs;
}
Self operator/(Self &rhs) const noexcept {
return Self(*this) /= rhs;
}
friend Self operator*(const T &lhs, const Self &rhs) {
return Self(rhs) *= lhs;
}
friend Self operator*(const Self &lhs, const T &rhs) {
return Self(lhs) *= rhs;
}
std::vector<T> operator*(const std::vector<T> &rhs) noexcept {
assert(m == (int)rhs.size());
std::vector<T> res(n, 0);
for (int i = 0; i < n; i++) {
for (int j = 0; j < m; j++) {
res[i] += (*this)[i][j] * rhs[j];
}
}
return res;
}
Self &operator+=(Self &rhs) noexcept {
assert(this->size() == rhs.size());
for (int i = 0; i < n; ++i) {
for (int j = 0; j < m; ++j) {
(*this)[i][j] += rhs[i][j];
}
}
return *this;
}
Self &operator-=(Self &rhs) noexcept {
assert(this->size() == rhs.size());
for (int i = 0; i < n; ++i) {
for (int j = 0; j < m; ++j) {
(*this)[i][j] -= rhs[i][j];
}
}
return *this;
}
Self &operator*=(Self &rhs) noexcept {
int h = n, w = rhs.column_size();
assert(m == rhs.row_size());
Self ret(h, w);
for (int i = 0; i < h; ++i) {
for (int k = 0; k < m; ++k) {
for (int j = 0; j < w; ++j) {
ret[i][j] += (*this)[i][k] * rhs[k][j];
}
}
}
return *this = ret;
}
Self &operator/=(const Self &rhs) noexcept {
auto ret = rhs.inv();
assert(ret);
return *this *= ret.value();
}
Self &operator*=(const T &rhs) noexcept {
for (int i = 0; i < n; i++) {
for (int j = 0; j < m; j++) {
(*this)[i][j] *= rhs;
}
}
return *this;
}
const auto operator[](int i) const {
return std::ranges::subrange(data.begin() + i * m,
data.begin() + (i + 1) * m);
}
auto operator[](int i) {
return std::ranges::subrange(data.begin() + i * m,
data.begin() + (i + 1) * m);
}
void swap(int i, int j) {
std::swap_ranges(data.begin() + i * m, data.begin() + (i + 1) * m,
data.begin() + j * m);
}
int rank() const;
Self transposition() const {
Self res(m, n);
for (int i = 0; i < n; i++) {
for (int j = 0; j < m; j++) {
res[j][i] = (*this)[i][j];
}
}
return res;
}
std::optional<Self> inv() const {
assert(row_size() == column_size());
Self a = *this;
Self b = identify_matrix<T>(n);
for (int r = 0; r < n; r++) {
for (int i = r; i < n; i++) {
if (a[i][r] != 0) {
a.swap(r, i);
b.swap(r, i);
break;
}
}
if (a[r][r] == 0) return std::nullopt;
T x = a[r][r].inv();
for (int j = 0; j < n; j++) {
if (r < j) a[r][j] *= x;
b[r][j] *= x;
}
for (int i = 0; i < n; i++) {
if (i == r) continue;
for (int j = 0; j < n; j++) {
if (r < j) a[i][j] -= a[i][r] * a[r][j];
b[i][j] -= a[i][r] * b[r][j];
}
}
}
return b;
}
Self pow(long long k) const {
assert(row_size() == column_size() && k >= 0);
Self res = identify_matrix<T>(row_size());
Self x = *this;
while (k) {
if (k & 1) res *= x;
x *= x;
k >>= 1;
}
return res;
}
int row_size() const {
return n;
}
int column_size() const {
return m;
}
std::pair<int, int> size() const {
return {n, m};
}
private:
int n, m;
std::vector<T> data;
};
template <class T> T det(matrix<T> a) {
assert(a.row_size() == a.column_size());
T d = 1;
int n = a.row_size();
for (int r = 0; r < n; r++) {
if (a[r][r] == 0) {
for (int i = r + 1; i < n; i++) {
if (a[i][r] != 0) {
a.swap(r, i);
d = -d;
}
}
}
if (a[r][r] == 0) return 0;
d *= a[r][r];
T inv = a[r][r].inv();
for (int i = r + 1; i < n; i++) {
T x = a[i][r] * inv;
for (int j = r; j < n; j++) {
a[i][j] -= x * a[r][j];
}
}
}
return d;
}
template <class T> std::istream &operator>>(std::istream &os, matrix<T> &a) {
for (int i = 0; i < a.row_size(); i++) {
for (int j = 0; j < a.column_size(); j++) {
os >> a[i][j];
}
}
return os;
}
template <class T>
std::ostream &operator<<(std::ostream &os, const matrix<T> &a) {
for (int i = 0; i < a.row_size(); i++) {
for (int j = 0; j < a.column_size(); j++) {
os << a[i][j];
if (j < a.column_size() - 1) os << ' ';
}
if (i < a.row_size() - 1) os << '\n';
}
return os;
}
} // namespace ebi
#line 2 "modint/base.hpp"
#include <concepts>
#line 6 "modint/base.hpp"
namespace ebi {
template <class T>
concept Modint = requires(T a, T b) {
a + b;
a - b;
a * b;
a / b;
a.inv();
a.val();
a.pow(std::declval<long long>());
T::mod();
};
template <Modint mint> std::istream &operator>>(std::istream &os, mint &a) {
long long x;
os >> x;
a = x;
return os;
}
template <Modint mint>
std::ostream &operator<<(std::ostream &os, const mint &a) {
return os << a.val();
}
} // namespace ebi
#line 9 "graph/count_spanning_tree.hpp"
namespace ebi {
template <Modint mint>
mint count_spanning_tree(const std::vector<std::vector<int>> &g) {
const int n = (int)g.size();
if (n == 1) return 1;
std::vector<int> deg(n, 0);
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
if (i == j) continue;
assert(g[i][j] == g[j][i]);
deg[i] += g[i][j];
}
}
matrix<mint> L(n - 1, n - 1, 0);
for (int i = 1; i < n; i++) {
for (int j = 1; j < n; j++) {
if (i == j)
L[i - 1][j - 1] = deg[i];
else
L[i - 1][j - 1] -= g[i][j];
}
}
return det(L);
}
template <Modint mint, class T> mint count_spanning_tree(const Graph<T> &g) {
int n = g.node_number();
if (n == 1) return 1;
std::vector a(n, std::vector<int>(n, 0));
for (int i = 0; i < n; i++) {
for (auto e : g[i]) {
a[i][e.to]++;
}
}
return count_spanning_tree<mint>(a);
}
template <Modint mint>
mint count_directed_spanning_tree(const std::vector<std::vector<int>> &g,
int root, bool in = false) {
const int n = (int)g.size();
if (n == 1) return 1;
std::vector<int> d(n, 0);
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
if (i != j) d[i] += in ? g[i][j] : g[j][i];
}
}
matrix<mint> L(n - 1, n - 1, 0);
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
int a = i, b = j;
if (a == root || b == root) continue;
if (root < a) a--;
if (root < b) b--;
if (a == b)
L[a][b] = d[i];
else
L[a][b] = in ? -g[i][j] : -g[j][i];
}
}
return det(L);
}
template <Modint mint, class T>
mint count_directed_spanning_tree(const Graph<T> &g, int root, bool in = false) {
const int n = g.node_number();
if (n == 1) return 1;
std::vector d(n, std::vector<int>(n, 0));
for (int i = 0; i < n; i++) {
for (auto e : g[i]) {
d[i][e.to]++;
}
}
return count_directed_spanning_tree<mint>(d, root, in);
}
} // namespace ebi
#line 2 "math/binomial.hpp"
#include <bit>
#line 5 "math/binomial.hpp"
#include <cstdint>
#line 9 "math/binomial.hpp"
#line 11 "math/binomial.hpp"
namespace ebi {
template <Modint mint> struct Binomial {
private:
static void extend(int len = -1) {
int sz = (int)fact.size();
if (len < 0)
len = 2 * sz;
else if (len <= sz)
return;
else
len = std::max(2 * sz, (int)std::bit_ceil(std::uint32_t(len)));
len = std::min(len, mint::mod());
assert(sz <= len);
fact.resize(len);
inv_fact.resize(len);
for (int i : std::views::iota(sz, len)) {
fact[i] = fact[i - 1] * i;
}
inv_fact[len - 1] = fact[len - 1].inv();
for (int i : std::views::iota(sz, len) | std::views::reverse) {
inv_fact[i - 1] = inv_fact[i] * i;
}
}
public:
Binomial() = default;
Binomial(int n) {
extend(n + 1);
}
static mint f(int n) {
if (n >= (int)fact.size()) [[unlikely]] {
extend(n + 1);
}
return fact[n];
}
static mint inv_f(int n) {
if (n >= (int)fact.size()) [[unlikely]] {
extend(n + 1);
}
return inv_fact[n];
}
static mint c(int n, int r) {
if (r < 0 || n < r) return 0;
return f(n) * inv_f(r) * inv_f(n - r);
}
static mint neg_c(int k, int d) {
assert(d > 0);
return c(k + d - 1, d - 1);
}
static mint p(int n, int r) {
if (r < 0 || n < r) return 0;
return f(n) * inv_f(n - r);
}
static mint catalan_number(int n) {
return c(2 * n, n) * inv(n + 1);
}
static mint inv(int n) {
return inv_f(n) * f(n - 1);
}
static void reserve(int n) {
extend(n + 1);
}
private:
static std::vector<mint> fact, inv_fact;
};
template <Modint mint>
std::vector<mint> Binomial<mint>::fact = std::vector<mint>(2, 1);
template <Modint mint>
std::vector<mint> Binomial<mint>::inv_fact = std::vector<mint>(2, 1);
} // namespace ebi
#line 9 "graph/count_directed_euler_trail.hpp"
namespace ebi {
template <Modint mint>
mint count_directed_euler_circuit(const std::vector<std::vector<int>> &g) {
int n = (int)g.size();
if (n == 0) return 1;
std::vector<int> indeg(n, 0);
std::vector<int> outdeg(n, 0);
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
indeg[j] += g[i][j];
outdeg[i] += g[i][j];
}
}
for (int i = 0; i < n; i++) {
if (indeg[i] != outdeg[i]) return 0;
}
mint res = count_directed_spanning_tree<mint>(g, 0, true);
for (int i = 0; i < n; i++) {
res *= Binomial<mint>::f(outdeg[i] - 1);
}
return res;
}
template <Modint mint, class T>
mint count_directed_euler_circuit(const Graph<T> &g,
std::vector<int> edge_count = {}) {
int n = g.node_number();
if (edge_count.empty()) edge_count.assign(g.edge_number(), 1);
std::vector a(n, std::vector<int>(n, 0));
for (auto e : g.get_edges()) {
a[e.from][e.to] += edge_count[e.id];
}
return count_directed_euler_circuit<mint>(a);
}
template <Modint mint>
mint count_directed_euler_trail(std::vector<std::vector<int>> g) {
int n = (int)g.size();
if (n == 0) return 1;
std::vector<int> indeg(n, 0);
std::vector<int> outdeg(n, 0);
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
indeg[j] += g[i][j];
outdeg[i] += g[i][j];
}
}
int s = -1, t = -1;
mint m = 0;
for (int v = 0; v < n; v++) {
m += indeg[v];
if (indeg[v] + 1 == outdeg[v]) {
if (s != -1) return 0;
s = v;
} else if (indeg[v] == outdeg[v] + 1) {
if (t != -1) return 0;
t = v;
} else if (indeg[v] == outdeg[v])
continue;
else
return 0;
}
if (s == -1 && t == -1) {
return m * count_directed_euler_circuit<mint>(g);
} else if (s != -1 && t != -1) {
g[t][s]++;
return count_directed_euler_circuit<mint>(g);
} else {
return 0;
}
}
template <Modint mint, class T>
mint count_directed_euler_trail(const Graph<T> &g,
std::vector<int> edge_count = {}) {
int n = g.node_number();
if (edge_count.empty()) edge_count.assign(g.edge_number(), 1);
std::vector a(n, std::vector<int>(n, 0));
for (auto e : g.get_edges()) {
a[e.from][e.to] += edge_count[e.id];
}
return count_directed_euler_trail<mint>(a);
}
} // namespace ebi
#line 2 "graph/utility.hpp"
#line 4 "graph/utility.hpp"
namespace ebi {
template <class T> Graph<T> remove_isolated_vertex(const Graph<T> &g) {
const int n = g.node_number();
std::vector<int> seen(n, -1);
for (auto e : g.get_edges()) {
seen[e.from] = seen[e.to] = 1;
}
int sz = 0;
for (int i = 0; i < n; i++) {
if (seen[i] != -1) seen[i] = sz++;
}
Graph<T> gh(sz);
for (auto e : g.get_edges()) {
gh.add_undirected_edge(seen[e.from], seen[e.to], e.cost);
}
gh.build();
return gh;
}
template <class T>
std::vector<std::vector<T>> remove_isolated_vertex(
const std::vector<std::vector<T>> &g) {
const int n = (int)g.size();
std::vector<int> seen(n, -1);
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
if (g[i][j] != 0) seen[i] = seen[j] = 1;
}
}
int sz = 0;
for (int i = 0; i < n; i++) {
if (seen[i] != -1) seen[i] = sz++;
}
std::vector gh(sz, std::vector<int>(sz, 0));
for (int i = 0; i < n; i++) {
if (seen[i] == -1) continue;
for (int j = 0; j < n; j++) {
if (seen[j] == -1) continue;
gh[seen[i]][seen[j]] += g[i][j];
}
}
return gh;
}
} // namespace ebi
#line 2 "modint/modint.hpp"
#line 5 "modint/modint.hpp"
#line 7 "modint/modint.hpp"
namespace ebi {
template <int m> struct static_modint {
private:
using modint = static_modint;
public:
static constexpr int mod() {
return m;
}
static constexpr modint raw(int v) {
modint x;
x._v = v;
return x;
}
constexpr static_modint() : _v(0) {}
template <std::signed_integral T> constexpr static_modint(T v) {
long long x = (long long)(v % (long long)(umod()));
if (x < 0) x += umod();
_v = (unsigned int)(x);
}
template <std::unsigned_integral T> constexpr static_modint(T v) {
_v = (unsigned int)(v % umod());
}
constexpr unsigned int val() const {
return _v;
}
constexpr unsigned int value() const {
return val();
}
constexpr modint &operator++() {
_v++;
if (_v == umod()) _v = 0;
return *this;
}
constexpr modint &operator--() {
if (_v == 0) _v = umod();
_v--;
return *this;
}
constexpr modint operator++(int) {
modint res = *this;
++*this;
return res;
}
constexpr modint operator--(int) {
modint res = *this;
--*this;
return res;
}
constexpr modint &operator+=(const modint &rhs) {
_v += rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
constexpr modint &operator-=(const modint &rhs) {
_v -= rhs._v;
if (_v >= umod()) _v += umod();
return *this;
}
constexpr modint &operator*=(const modint &rhs) {
unsigned long long x = _v;
x *= rhs._v;
_v = (unsigned int)(x % (unsigned long long)umod());
return *this;
}
constexpr modint &operator/=(const modint &rhs) {
return *this = *this * rhs.inv();
}
constexpr modint operator+() const {
return *this;
}
constexpr modint operator-() const {
return modint() - *this;
}
constexpr modint pow(long long n) const {
assert(0 <= n);
modint x = *this, res = 1;
while (n) {
if (n & 1) res *= x;
x *= x;
n >>= 1;
}
return res;
}
constexpr modint inv() const {
assert(_v);
return pow(umod() - 2);
}
friend modint operator+(const modint &lhs, const modint &rhs) {
return modint(lhs) += rhs;
}
friend modint operator-(const modint &lhs, const modint &rhs) {
return modint(lhs) -= rhs;
}
friend modint operator*(const modint &lhs, const modint &rhs) {
return modint(lhs) *= rhs;
}
friend modint operator/(const modint &lhs, const modint &rhs) {
return modint(lhs) /= rhs;
}
friend bool operator==(const modint &lhs, const modint &rhs) {
return lhs.val() == rhs.val();
}
friend bool operator!=(const modint &lhs, const modint &rhs) {
return !(lhs == rhs);
}
private:
unsigned int _v = 0;
static constexpr unsigned int umod() {
return m;
}
};
using modint998244353 = static_modint<998244353>;
using modint1000000007 = static_modint<1000000007>;
} // namespace ebi
#line 1 "template/template.hpp"
#include <bits/stdc++.h>
#define rep(i, a, n) for (int i = (int)(a); i < (int)(n); i++)
#define rrep(i, a, n) for (int i = ((int)(n)-1); i >= (int)(a); i--)
#define Rep(i, a, n) for (i64 i = (i64)(a); i < (i64)(n); i++)
#define RRep(i, a, n) for (i64 i = ((i64)(n)-i64(1)); i >= (i64)(a); i--)
#define all(v) (v).begin(), (v).end()
#define rall(v) (v).rbegin(), (v).rend()
#line 2 "template/debug_template.hpp"
#line 4 "template/debug_template.hpp"
namespace ebi {
#ifdef LOCAL
#define debug(...) \
std::cerr << "LINE: " << __LINE__ << " [" << #__VA_ARGS__ << "]:", \
debug_out(__VA_ARGS__)
#else
#define debug(...)
#endif
void debug_out() {
std::cerr << std::endl;
}
template <typename Head, typename... Tail> void debug_out(Head h, Tail... t) {
std::cerr << " " << h;
if (sizeof...(t) > 0) std::cerr << " :";
debug_out(t...);
}
} // namespace ebi
#line 2 "template/int_alias.hpp"
#line 4 "template/int_alias.hpp"
namespace ebi {
using ld = long double;
using std::size_t;
using i8 = std::int8_t;
using u8 = std::uint8_t;
using i16 = std::int16_t;
using u16 = std::uint16_t;
using i32 = std::int32_t;
using u32 = std::uint32_t;
using i64 = std::int64_t;
using u64 = std::uint64_t;
using i128 = __int128_t;
using u128 = __uint128_t;
} // namespace ebi
#line 2 "template/io.hpp"
#line 5 "template/io.hpp"
#include <optional>
#line 7 "template/io.hpp"
namespace ebi {
template <typename T1, typename T2>
std::ostream &operator<<(std::ostream &os, const std::pair<T1, T2> &pa) {
return os << pa.first << " " << pa.second;
}
template <typename T1, typename T2>
std::istream &operator>>(std::istream &os, std::pair<T1, T2> &pa) {
return os >> pa.first >> pa.second;
}
template <typename T>
std::ostream &operator<<(std::ostream &os, const std::vector<T> &vec) {
for (std::size_t i = 0; i < vec.size(); i++)
os << vec[i] << (i + 1 == vec.size() ? "" : " ");
return os;
}
template <typename T>
std::istream &operator>>(std::istream &os, std::vector<T> &vec) {
for (T &e : vec) std::cin >> e;
return os;
}
template <typename T>
std::ostream &operator<<(std::ostream &os, const std::optional<T> &opt) {
if (opt) {
os << opt.value();
} else {
os << "invalid value";
}
return os;
}
void fast_io() {
std::cout << std::fixed << std::setprecision(15);
std::cin.tie(nullptr);
std::ios::sync_with_stdio(false);
}
} // namespace ebi
#line 2 "template/utility.hpp"
#line 5 "template/utility.hpp"
#line 8 "template/utility.hpp"
namespace ebi {
template <class T> inline bool chmin(T &a, T b) {
if (a > b) {
a = b;
return true;
}
return false;
}
template <class T> inline bool chmax(T &a, T b) {
if (a < b) {
a = b;
return true;
}
return false;
}
template <class T> T safe_ceil(T a, T b) {
if (a % b == 0)
return a / b;
else if (a >= 0)
return (a / b) + 1;
else
return -((-a) / b);
}
template <class T> T safe_floor(T a, T b) {
if (a % b == 0)
return a / b;
else if (a >= 0)
return a / b;
else
return -((-a) / b) - 1;
}
constexpr i64 LNF = std::numeric_limits<i64>::max() / 4;
constexpr int INF = std::numeric_limits<int>::max() / 2;
const std::vector<int> dy = {1, 0, -1, 0, 1, 1, -1, -1};
const std::vector<int> dx = {0, 1, 0, -1, 1, -1, 1, -1};
} // namespace ebi
#line 7 "test/graph/Counting_Eulerian_Circuits.test.cpp"
namespace ebi {
using mint = modint998244353;
void main_() {
int n, m;
std::cin >> n >> m;
Graph<int> g(n);
g.read_graph(m, 0);
std::cout << count_directed_euler_circuit<mint>(remove_isolated_vertex(g))
<< '\n';
}
} // namespace ebi
int main() {
ebi::fast_io();
int t = 1;
// std::cin >> t;
while (t--) {
ebi::main_();
}
return 0;
}