結果
| 問題 | No.1303 Inconvenient Kingdom |
| ユーザー |
👑  rin204
|
| 提出日時 | 2024-05-05 22:02:01 |
| 言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 9 ms / 3,000 ms |
| コード長 | 29,127 bytes |
| コンパイル時間 | 4,732 ms |
| コンパイル使用メモリ | 287,576 KB |
| 実行使用メモリ | 5,248 KB |
| 最終ジャッジ日時 | 2024-11-27 23:24:38 |
| 合計ジャッジ時間 | 5,798 ms |
|
ジャッジサーバーID （参考情報） |
judge2 / judge4 |
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テストケース
テストケース表示| 入力 | 結果 | 実行時間 実行使用メモリ |
|---|---|---|
| testcase_00 | AC | 2 ms
5,248 KB |
| testcase_01 | AC | 2 ms
5,248 KB |
| testcase_02 | AC | 2 ms
5,248 KB |
| testcase_03 | AC | 2 ms
5,248 KB |
| testcase_04 | AC | 2 ms
5,248 KB |
| testcase_05 | AC | 2 ms
5,248 KB |
| testcase_06 | AC | 2 ms
5,248 KB |
| testcase_07 | AC | 3 ms
5,248 KB |
| testcase_08 | AC | 3 ms
5,248 KB |
| testcase_09 | AC | 9 ms
5,248 KB |
| testcase_10 | AC | 9 ms
5,248 KB |
| testcase_11 | AC | 9 ms
5,248 KB |
| testcase_12 | AC | 9 ms
5,248 KB |
| testcase_13 | AC | 9 ms
5,248 KB |
| testcase_14 | AC | 9 ms
5,248 KB |
| testcase_15 | AC | 9 ms
5,248 KB |
| testcase_16 | AC | 9 ms
5,248 KB |
| testcase_17 | AC | 9 ms
5,248 KB |
| testcase_18 | AC | 9 ms
5,248 KB |
| testcase_19 | AC | 9 ms
5,248 KB |
| testcase_20 | AC | 8 ms
5,248 KB |
| testcase_21 | AC | 9 ms
5,248 KB |
| testcase_22 | AC | 9 ms
5,248 KB |
| testcase_23 | AC | 9 ms
5,248 KB |
| testcase_24 | AC | 9 ms
5,248 KB |
| testcase_25 | AC | 9 ms
5,248 KB |
| testcase_26 | AC | 2 ms
5,248 KB |
| testcase_27 | AC | 2 ms
5,248 KB |
| testcase_28 | AC | 2 ms
5,248 KB |
| testcase_29 | AC | 2 ms
5,248 KB |
| testcase_30 | AC | 2 ms
5,248 KB |
| testcase_31 | AC | 2 ms
5,248 KB |
| testcase_32 | AC | 2 ms
5,248 KB |
| testcase_33 | AC | 2 ms
5,248 KB |
| testcase_34 | AC | 2 ms
5,248 KB |
| testcase_35 | AC | 2 ms
5,248 KB |
| testcase_36 | AC | 2 ms
5,248 KB |
| testcase_37 | AC | 2 ms
5,248 KB |
ソースコード
// #pragma GCC target("avx2")
// #pragma GCC optimize("O3")
// #pragma GCC optimize("unroll-loops")
#include <bits/stdc++.h>
using namespace std;
// #define INTERACTIVE
namespace templates {
// type
using ll = long long;
using ull = unsigned long long;
using Pii = pair<int, int>;
using Pil = pair<int, ll>;
using Pli = pair<ll, int>;
using Pll = pair<ll, ll>;
template <class T>
using pq = priority_queue<T>;
template <class T>
using qp = priority_queue<T, vector<T>, greater<T>>;
// clang-format off
#define vec(T, A, ...) vector<T> A(__VA_ARGS__);
#define vvec(T, A, h, ...) vector<vector<T>> A(h, vector<T>(__VA_ARGS__));
#define vvvec(T, A, h1, h2, ...) vector<vector<vector<T>>> A(h1, vector<vector<T>>(h2, vector<T>(__VA_ARGS__)));
// clang-format on
// for loop
#define fori1(a) for (ll _ = 0; _ < (a); _++)
#define fori2(i, a) for (ll i = 0; i < (a); i++)
#define fori3(i, a, b) for (ll i = (a); i < (b); i++)
#define fori4(i, a, b, c) for (ll i = (a); ((c) > 0 || i > (b)) && ((c) < 0 || i < (b)); i += (c))
#define overload4(a, b, c, d, e, ...) e
#define fori(...) overload4(__VA_ARGS__, fori4, fori3, fori2, fori1)(__VA_ARGS__)
// declare and input
// clang-format off
#define INT(...) int __VA_ARGS__; inp(__VA_ARGS__);
#define LL(...) ll __VA_ARGS__; inp(__VA_ARGS__);
#define STRING(...) string __VA_ARGS__; inp(__VA_ARGS__);
#define CHAR(...) char __VA_ARGS__; inp(__VA_ARGS__);
#define DOUBLE(...) double __VA_ARGS__; STRING(str___); __VA_ARGS__ = stod(str___);
#define VEC(T, A, n) vector<T> A(n); inp(A);
#define VVEC(T, A, n, m) vector<vector<T>> A(n, vector<T>(m)); inp(A);
// clang-format on
// const value
const ll MOD1 = 1000000007;
const ll MOD9 = 998244353;
const double PI = acos(-1);
// other macro
#if !defined(RIN__LOCAL) && !defined(INTERACTIVE)
#define endl "\n"
#endif
#define spa ' '
#define len(A) ll(A.size())
#define all(A) begin(A), end(A)
// function
vector<char> stoc(string &S) {
int n = S.size();
vector<char> ret(n);
for (int i = 0; i < n; i++) ret[i] = S[i];
return ret;
}
string ctos(vector<char> &S) {
int n = S.size();
string ret = "";
for (int i = 0; i < n; i++) ret += S[i];
return ret;
}
template <class T>
auto min(const T &a) {
return *min_element(all(a));
}
template <class T>
auto max(const T &a) {
return *max_element(all(a));
}
template <class T, class S>
auto clamp(T &a, const S &l, const S &r) {
return (a > r ? r : a < l ? l : a);
}
template <class T, class S>
inline bool chmax(T &a, const S &b) {
return (a < b ? a = b, 1 : 0);
}
template <class T, class S>
inline bool chmin(T &a, const S &b) {
return (a > b ? a = b, 1 : 0);
}
template <class T, class S>
inline bool chclamp(T &a, const S &l, const S &r) {
auto b = clamp(a, l, r);
return (a != b ? a = b, 1 : 0);
}
template <typename T>
T sum(vector<T> &A) {
T tot = 0;
for (auto a : A) tot += a;
return tot;
}
template <typename T>
vector<T> compression(vector<T> X) {
sort(all(X));
X.erase(unique(all(X)), X.end());
return X;
}
// input and output
namespace io {
// __int128_t
std::ostream &operator<<(std::ostream &dest, __int128_t value) {
std::ostream::sentry s(dest);
if (s) {
__uint128_t tmp = value < 0 ? -value : value;
char buffer[128];
char *d = std::end(buffer);
do {
--d;
*d = "0123456789"[tmp % 10];
tmp /= 10;
} while (tmp != 0);
if (value < 0) {
--d;
*d = '-';
}
int len = std::end(buffer) - d;
if (dest.rdbuf()->sputn(d, len) != len) {
dest.setstate(std::ios_base::badbit);
}
}
return dest;
}
// vector<T>
template <typename T>
istream &operator>>(istream &is, vector<T> &A) {
for (auto &a : A) is >> a;
return is;
}
template <typename T>
ostream &operator<<(ostream &os, vector<T> &A) {
for (size_t i = 0; i < A.size(); i++) {
os << A[i];
if (i != A.size() - 1) os << ' ';
}
return os;
}
// vector<vector<T>>
template <typename T>
istream &operator>>(istream &is, vector<vector<T>> &A) {
for (auto &a : A) is >> a;
return is;
}
template <typename T>
ostream &operator<<(ostream &os, vector<vector<T>> &A) {
for (size_t i = 0; i < A.size(); i++) {
os << A[i];
if (i != A.size() - 1) os << endl;
}
return os;
}
// pair<S, T>
template <typename S, typename T>
istream &operator>>(istream &is, pair<S, T> &A) {
is >> A.first >> A.second;
return is;
}
template <typename S, typename T>
ostream &operator<<(ostream &os, pair<S, T> &A) {
os << A.first << ' ' << A.second;
return os;
}
// vector<pair<S, T>>
template <typename S, typename T>
istream &operator>>(istream &is, vector<pair<S, T>> &A) {
for (size_t i = 0; i < A.size(); i++) {
is >> A[i];
}
return is;
}
template <typename S, typename T>
ostream &operator<<(ostream &os, vector<pair<S, T>> &A) {
for (size_t i = 0; i < A.size(); i++) {
os << A[i];
if (i != A.size() - 1) os << endl;
}
return os;
}
// tuple
template <typename T, size_t N>
struct TuplePrint {
static ostream &print(ostream &os, const T &t) {
TuplePrint<T, N - 1>::print(os, t);
os << ' ' << get<N - 1>(t);
return os;
}
};
template <typename T>
struct TuplePrint<T, 1> {
static ostream &print(ostream &os, const T &t) {
os << get<0>(t);
return os;
}
};
template <typename... Args>
ostream &operator<<(ostream &os, const tuple<Args...> &t) {
TuplePrint<decltype(t), sizeof...(Args)>::print(os, t);
return os;
}
// io functions
void FLUSH() {
cout << flush;
}
void print() {
cout << endl;
}
template <class Head, class... Tail>
void print(Head &&head, Tail &&...tail) {
cout << head;
if (sizeof...(Tail)) cout << spa;
print(std::forward<Tail>(tail)...);
}
template <typename T, typename S>
void prisep(vector<T> &A, S sep) {
int n = A.size();
for (int i = 0; i < n; i++) {
cout << A[i];
if (i != n - 1) cout << sep;
}
cout << endl;
}
template <typename T, typename S>
void priend(T A, S end) {
cout << A << end;
}
template <typename T>
void prispa(T A) {
priend(A, spa);
}
template <typename T, typename S>
bool printif(bool f, T A, S B) {
if (f)
print(A);
else
print(B);
return f;
}
template <class... T>
void inp(T &...a) {
(cin >> ... >> a);
}
} // namespace io
using namespace io;
// read graph
vector<vector<int>> read_edges(int n, int m, bool direct = false, int indexed = 1) {
vector<vector<int>> edges(n, vector<int>());
for (int i = 0; i < m; i++) {
INT(u, v);
u -= indexed;
v -= indexed;
edges[u].push_back(v);
if (!direct) edges[v].push_back(u);
}
return edges;
}
vector<vector<int>> read_tree(int n, int indexed = 1) {
return read_edges(n, n - 1, false, indexed);
}
template <typename T = long long>
vector<vector<pair<int, T>>> read_wedges(int n, int m, bool direct = false, int indexed = 1) {
vector<vector<pair<int, T>>> edges(n, vector<pair<int, T>>());
for (int i = 0; i < m; i++) {
INT(u, v);
T w;
inp(w);
u -= indexed;
v -= indexed;
edges[u].push_back({v, w});
if (!direct) edges[v].push_back({u, w});
}
return edges;
}
template <typename T = long long>
vector<vector<pair<int, T>>> read_wtree(int n, int indexed = 1) {
return read_wedges<T>(n, n - 1, false, indexed);
}
// yes / no
namespace yesno {
// yes
inline bool yes(bool f = true) {
cout << (f ? "yes" : "no") << endl;
return f;
}
inline bool Yes(bool f = true) {
cout << (f ? "Yes" : "No") << endl;
return f;
}
inline bool YES(bool f = true) {
cout << (f ? "YES" : "NO") << endl;
return f;
}
// no
inline bool no(bool f = true) {
cout << (!f ? "yes" : "no") << endl;
return f;
}
inline bool No(bool f = true) {
cout << (!f ? "Yes" : "No") << endl;
return f;
}
inline bool NO(bool f = true) {
cout << (!f ? "YES" : "NO") << endl;
return f;
}
// possible
inline bool possible(bool f = true) {
cout << (f ? "possible" : "impossible") << endl;
return f;
}
inline bool Possible(bool f = true) {
cout << (f ? "Possible" : "Impossible") << endl;
return f;
}
inline bool POSSIBLE(bool f = true) {
cout << (f ? "POSSIBLE" : "IMPOSSIBLE") << endl;
return f;
}
// impossible
inline bool impossible(bool f = true) {
cout << (!f ? "possible" : "impossible") << endl;
return f;
}
inline bool Impossible(bool f = true) {
cout << (!f ? "Possible" : "Impossible") << endl;
return f;
}
inline bool IMPOSSIBLE(bool f = true) {
cout << (!f ? "POSSIBLE" : "IMPOSSIBLE") << endl;
return f;
}
// Alice Bob
inline bool Alice(bool f = true) {
cout << (f ? "Alice" : "Bob") << endl;
return f;
}
inline bool Bob(bool f = true) {
cout << (f ? "Bob" : "Alice") << endl;
return f;
}
// Takahashi Aoki
inline bool Takahashi(bool f = true) {
cout << (f ? "Takahashi" : "Aoki") << endl;
return f;
}
inline bool Aoki(bool f = true) {
cout << (f ? "Aoki" : "Takahashi") << endl;
return f;
}
} // namespace yesno
using namespace yesno;
} // namespace templates
using namespace templates;
struct UnionFind {
int n;
std::vector<int> par;
int group;
UnionFind() = default;
UnionFind(int n) : n(n) {
par.assign(n, -1);
group = n;
}
int find(int x) {
if (par[x] < 0) return x;
par[x] = find(par[x]);
return par[x];
}
bool unite(int x, int y) {
x = find(x);
y = find(y);
if (x == y) return false;
if (par[x] > par[y]) std::swap(x, y);
group--;
par[x] += par[y];
par[y] = x;
return true;
}
bool same(int x, int y) {
return find(x) == find(y);
}
int size(int x) {
return -par[find(x)];
}
std::vector<int> roots() {
std::vector<int> ret;
for (int i = 0; i < n; i++) {
if (i == find(i)) ret.push_back(i);
}
return ret;
}
bool isroot(int x) {
return x == find(x);
}
};
template <typename type>
struct Matrix {
int n, m;
std::vector<std::vector<type>> A;
Matrix() = default;
Matrix(int n, int m) : n(n), m(m), A(n, std::vector<type>(m, 0)) {}
Matrix(int n) : n(n), m(n), A(n, std::vector<type>(n, 0)) {}
Matrix(std::vector<std::vector<type>> A) : n(A.size()), m(A[0].size()), A(A) {}
inline const std::vector<type> &operator[](int k) const {
return (A.at(k));
}
inline std::vector<type> &operator[](int k) {
return (A.at(k));
}
Matrix T() {
Matrix<type> B(m, n);
for (int i = 0; i < m; i++)
for (int j = 0; j < n; j++) {
B.A[i][j] = A[j][i];
}
return B;
}
Matrix &operator=(const std::vector<std::vector<type>> &B) {
n = B.size();
m = B[0].size();
A = B;
return *this;
}
Matrix &operator+=(const Matrix &B) {
assert(n == int(B.A.size()));
assert(m == int(B.A[0].size()));
for (int i = 0; i < n; i++)
for (int j = 0; j < m; j++) {
this->A[i][j] += B[i][j];
}
return *this;
}
Matrix &operator-=(const Matrix &B) {
assert(n == int(B.A.size()));
assert(m == int(B.A[0].size()));
for (int i = 0; i < n; i++)
for (int j = 0; j < m; j++) {
this->A[i][j] -= B[i][j];
}
return *this;
}
Matrix &operator*=(const Matrix &B) {
int k = B[0].size();
assert(m == int(B.A.size()));
std::vector<std::vector<type>> C(n, std::vector<type>(k, 0));
for (int i = 0; i < n; i++)
for (int j = 0; j < k; j++) {
for (int l = 0; l < m; l++) {
C[i][j] += this->A[i][l] * B[l][j];
}
}
swap(this->A, C);
return *this;
}
std::vector<type> operator*(const std::vector<type> &x) {
assert(m == int(x.size()));
std::vector<type> ret(n, 0);
for (int i = 0; i < n; i++)
for (int j = 0; j < m; j++) ret[i] += this->A[i][j] * x[j];
return ret;
}
template <typename Ti>
Matrix &operator*=(const Ti x) {
for (auto &row : A) {
for (auto &e : row) {
e *= x;
}
}
return *this;
}
Matrix operator-() {
return (Matrix(*this) *= -1);
}
Matrix operator+(const Matrix &B) const {
return (Matrix(*this) += B);
}
Matrix operator-(const Matrix &B) const {
return (Matrix(*this) -= B);
}
Matrix operator*(const Matrix &B) const {
return (Matrix(*this) *= B);
}
type det() {
auto arr = A;
assert(n == m);
type ret = 1;
for (int i = 0; i < n; i++) {
if (arr[i][i] == 0) {
bool ng = true;
for (int j = i + 1; j < n; j++) {
if (arr[j][i] == 0) continue;
swap(arr[i], arr[j]);
ret *= -1;
ng = false;
break;
}
if (ng) return 0;
}
ret *= arr[i][i];
type inv = type(1) / arr[i][i];
for (int j = i; j < n; j++) arr[i][j] *= inv;
for (int j = i + 1; j < n; j++) {
type x = arr[j][i];
for (int k = i; k < n; k++) {
arr[j][k] -= arr[i][k] * x;
}
}
}
return ret;
}
void I() {
assert(n == m);
for (int i = 0; i < n; i++) {
for (int j = 0; j < m; j++) {
if (i == j)
A[i][j] = 1;
else
A[i][j] = 0;
}
}
}
Matrix<type> inv() {
assert(n == m);
Matrix<type> ret(n);
ret.I();
auto &B = ret.A;
auto arr = A;
for (int j = 0; j < n; j++) {
int ii = -1;
for (int i = j; i < n; i++) {
if (arr[i][j] != 0) {
ii = i;
break;
}
}
if (ii == -1) {
return {};
}
swap(arr[j], arr[ii]);
swap(B[j], B[ii]);
ii = j;
type inv = type(1) / arr[ii][j];
for (int jj = 0; jj < n; jj++) {
B[ii][jj] *= inv;
arr[ii][jj] *= inv;
}
for (int i = 0; i < n; i++) {
if (i == ii) continue;
type t = arr[i][j];
for (int jj = 0; jj < n; jj++) {
arr[i][jj] -= arr[ii][jj] * t;
B[i][jj] -= B[ii][jj] * t;
}
}
}
return ret;
}
int choose_pivot(int h, int c) const {
for (int j = h; j < n; j++) {
if (A[j][c] != type(0)) return j;
}
return -1;
}
int rank() const {
auto arr = *this;
if (arr.n < arr.m) {
arr = arr.T();
}
int ret = 0;
for (int i = 0; i < arr.m; i++) {
int j = arr.choose_pivot(ret, i);
if (j == -1) continue;
swap(arr[ret], arr[j]);
type inv = type(1) / arr[ret][i];
for (int k = i; k < arr.m; k++) {
arr[ret][k] *= inv;
}
for (int j = ret + 1; j < arr.n; j++) {
type x = arr[j][i];
for (int k = i; k < arr.m; k++) {
arr[j][k] -= arr[ret][k] * x;
}
}
ret++;
}
return ret;
}
Matrix<type> pow(long long k) {
assert(n == m);
Matrix<type> B(n);
B.I();
Matrix<type> A(*this);
while (k) {
if (k & 1) B *= A;
A *= A;
k >>= 1;
}
return B;
}
friend std::ostream &operator<<(std::ostream &os, const Matrix &p) {
for (int i = 0; i < p.n; i++) {
for (auto &x : p.A[i]) {
os << x << " ";
}
if (i != p.n - 1) {
os << "\n";
}
}
return (os);
}
friend std::istream &operator>>(std::istream &is, Matrix &p) {
for (auto &row : p.A) {
for (auto &x : row) {
is >> x;
}
}
return (is);
}
};
template <typename T>
void hessenberg_reduction(Matrix<T> &A) {
assert(A.n == A.m);
for (int r = 0; r < A.n - 2; r++) {
int piv = A.choose_pivot(r + 1, r);
if (piv < 0) continue;
for (int i = 0; i < A.n; i++) {
std::swap(A[r + 1][i], A[piv][i]);
}
for (int i = 0; i < A.n; i++) {
std::swap(A[i][r + 1], A[i][piv]);
}
T inv = T(1) / A[r + 1][r];
for (int i = r + 2; i < A.n; i++) {
T t = A[i][r] * inv;
for (int j = 0; j < A.n; j++) {
A[i][j] -= A[r + 1][j] * t;
}
for (int j = 0; j < A.n; j++) {
A[j][r + 1] += A[j][i] * t;
}
}
}
}
template <typename T>
std::vector<T> characteristic_polynomial(Matrix<T> A) {
hessenberg_reduction(A);
if (A.n == 0) {
return std::vector<T>{T(1)};
}
std::vector<std::vector<T>> P(A.n + 1);
P[0] = {T(1)};
for (int i = 0; i < A.n; i++) {
P[i + 1].assign(i + 2, T(0));
for (int j = 0; j < i + 1; j++) {
P[i + 1][j + 1] += P[i][j];
}
for (int j = 0; j < i + 1; j++) {
P[i + 1][j] -= P[i][j] * A[i][i];
}
T x = T(1);
for (int j = i - 1; j >= 0; j--) {
x *= A[j + 1][j];
T h = -A[j][i] * x;
for (int k = 0; k < j + 1; k++) {
P[i + 1][k] += h * P[j][k];
}
}
}
return P.back();
}
template <typename T>
std::vector<T> determinant_of_first_degree_poly_mat(Matrix<T> M0, Matrix<T> M1) {
int n = M0.n;
int cx = 0;
T detAdetBinv = T(1);
for (int p = 0; p < n; p++) {
int pivot = M1.choose_pivot(p, p);
if (pivot < 0) {
if (++cx > n) {
return std::vector<T>(n + 1);
}
for (int i = 0; i < p; i++) {
T v = M1[i][p];
M1[i][p] = 0;
for (int i2 = 0; i2 < n; i2++) {
M0[i2][p] -= v * M0[i2][i];
}
}
for (int i = 0; i < n; i++) {
std::swap(M0[i][p], M1[i][p]);
}
p--;
continue;
}
if (pivot != p) {
std::swap(M1[pivot], M1[p]);
std::swap(M0[pivot], M0[p]);
detAdetBinv *= -1;
}
T v = M1[p][p];
T vinv = T(1) / v;
detAdetBinv *= v;
for (int j = 0; j < n; j++) {
M0[p][j] *= vinv;
M1[p][j] *= vinv;
}
for (int i = 0; i < n; i++) {
if (i == p) continue;
T v = M1[i][p];
for (int j = 0; j < n; j++) {
M0[i][j] -= v * M0[p][j];
M1[i][j] -= v * M1[p][j];
}
}
}
M0 *= -1;
auto poly = characteristic_polynomial(M0);
poly.erase(poly.begin(), poly.begin() + cx);
for (size_t i = 0; i < poly.size(); i++) {
poly[i] *= detAdetBinv;
}
poly.resize(n + 1);
return poly;
}
template <int MOD>
struct Modint {
int x;
Modint() : x(0) {}
Modint(int64_t y) {
if (y >= 0)
x = y % MOD;
else
x = (y % MOD + MOD) % MOD;
}
Modint &operator+=(const Modint &p) {
x += p.x;
if (x >= MOD) x -= MOD;
return *this;
}
Modint &operator-=(const Modint &p) {
x -= p.x;
if (x < 0) x += MOD;
return *this;
}
Modint &operator*=(const Modint &p) {
x = int(1LL * x * p.x % MOD);
return *this;
}
Modint &operator/=(const Modint &p) {
*this *= p.inverse();
return *this;
}
Modint &operator%=(const Modint &p) {
assert(p.x == 0);
return *this;
}
Modint operator-() const {
return Modint(-x);
}
Modint &operator++() {
x++;
if (x == MOD) x = 0;
return *this;
}
Modint &operator--() {
if (x == 0) x = MOD;
x--;
return *this;
}
Modint operator++(int) {
Modint result = *this;
++*this;
return result;
}
Modint operator--(int) {
Modint result = *this;
--*this;
return result;
}
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 Modint operator%(const Modint &lhs, const Modint &rhs) {
assert(rhs.x == 0);
return Modint(lhs);
}
bool operator==(const Modint &p) const {
return x == p.x;
}
bool operator!=(const Modint &p) const {
return x != p.x;
}
bool operator<(const Modint &rhs) const {
return x < rhs.x;
}
bool operator<=(const Modint &rhs) const {
return x <= rhs.x;
}
bool operator>(const Modint &rhs) const {
return x > rhs.x;
}
bool operator>=(const Modint &rhs) const {
return x >= rhs.x;
}
Modint inverse() const {
int a = x, b = MOD, u = 1, v = 0, t;
while (b > 0) {
t = a / b;
a -= t * b;
u -= t * v;
std::swap(a, b);
std::swap(u, v);
}
return Modint(u);
}
Modint pow(int64_t k) const {
Modint ret(1);
Modint y(x);
while (k > 0) {
if (k & 1) ret *= y;
y *= y;
k >>= 1;
}
return ret;
}
friend std::ostream &operator<<(std::ostream &os, const Modint &p) {
return os << p.x;
}
friend std::istream &operator>>(std::istream &is, Modint &p) {
int64_t y;
is >> y;
p = Modint<MOD>(y);
return (is);
}
static int get_mod() {
return MOD;
}
};
struct Arbitrary_Modint {
int x;
static int MOD;
static void set_mod(int mod) {
MOD = mod;
}
Arbitrary_Modint() : x(0) {}
Arbitrary_Modint(int64_t y) {
if (y >= 0)
x = y % MOD;
else
x = (y % MOD + MOD) % MOD;
}
Arbitrary_Modint &operator+=(const Arbitrary_Modint &p) {
x += p.x;
if (x >= MOD) x -= MOD;
return *this;
}
Arbitrary_Modint &operator-=(const Arbitrary_Modint &p) {
x -= p.x;
if (x < 0) x += MOD;
return *this;
}
Arbitrary_Modint &operator*=(const Arbitrary_Modint &p) {
x = int(1LL * x * p.x % MOD);
return *this;
}
Arbitrary_Modint &operator/=(const Arbitrary_Modint &p) {
*this *= p.inverse();
return *this;
}
Arbitrary_Modint &operator%=(const Arbitrary_Modint &p) {
assert(p.x == 0);
return *this;
}
Arbitrary_Modint operator-() const {
return Arbitrary_Modint(-x);
}
Arbitrary_Modint &operator++() {
x++;
if (x == MOD) x = 0;
return *this;
}
Arbitrary_Modint &operator--() {
if (x == 0) x = MOD;
x--;
return *this;
}
Arbitrary_Modint operator++(int) {
Arbitrary_Modint result = *this;
++*this;
return result;
}
Arbitrary_Modint operator--(int) {
Arbitrary_Modint result = *this;
--*this;
return result;
}
friend Arbitrary_Modint operator+(const Arbitrary_Modint &lhs, const Arbitrary_Modint &rhs) {
return Arbitrary_Modint(lhs) += rhs;
}
friend Arbitrary_Modint operator-(const Arbitrary_Modint &lhs, const Arbitrary_Modint &rhs) {
return Arbitrary_Modint(lhs) -= rhs;
}
friend Arbitrary_Modint operator*(const Arbitrary_Modint &lhs, const Arbitrary_Modint &rhs) {
return Arbitrary_Modint(lhs) *= rhs;
}
friend Arbitrary_Modint operator/(const Arbitrary_Modint &lhs, const Arbitrary_Modint &rhs) {
return Arbitrary_Modint(lhs) /= rhs;
}
friend Arbitrary_Modint operator%(const Arbitrary_Modint &lhs, const Arbitrary_Modint &rhs) {
assert(rhs.x == 0);
return Arbitrary_Modint(lhs);
}
bool operator==(const Arbitrary_Modint &p) const {
return x == p.x;
}
bool operator!=(const Arbitrary_Modint &p) const {
return x != p.x;
}
bool operator<(const Arbitrary_Modint &rhs) {
return x < rhs.x;
}
bool operator<=(const Arbitrary_Modint &rhs) {
return x <= rhs.x;
}
bool operator>(const Arbitrary_Modint &rhs) {
return x > rhs.x;
}
bool operator>=(const Arbitrary_Modint &rhs) {
return x >= rhs.x;
}
Arbitrary_Modint inverse() const {
int a = x, b = MOD, u = 1, v = 0, t;
while (b > 0) {
t = a / b;
a -= t * b;
u -= t * v;
std::swap(a, b);
std::swap(u, v);
}
return Arbitrary_Modint(u);
}
Arbitrary_Modint pow(int64_t k) const {
Arbitrary_Modint ret(1);
Arbitrary_Modint y(x);
while (k > 0) {
if (k & 1) ret *= y;
y *= y;
k >>= 1;
}
return ret;
}
friend std::ostream &operator<<(std::ostream &os, const Arbitrary_Modint &p) {
return os << p.x;
}
friend std::istream &operator>>(std::istream &is, Arbitrary_Modint &p) {
int64_t y;
is >> y;
p = Arbitrary_Modint(y);
return (is);
}
static int get_mod() {
return MOD;
}
};
int Arbitrary_Modint::MOD = 998244353;
using modint9 = Modint<998244353>;
using modint1 = Modint<1000000007>;
using modint = Arbitrary_Modint;
using mint = modint9;
void solve() {
LL(n, m);
UnionFind UF(n);
vvec(bool, E, n, n, false);
fori(m) {
INT(u, v);
u--;
v--;
E[u][v] = true;
UF.unite(u, v);
}
if (UF.group == 1) {
print(0);
Matrix<mint> A(n - 1), B(n - 1);
fori(i, n) fori(j, i + 1, n) {
if (E[i][j]) {
A[i][i]++;
if (j != n - 1) {
A[i][j]--;
A[j][i]--;
A[j][j]++;
}
} else {
B[i][i]++;
if (j != n - 1) {
B[i][j]--;
B[j][i]--;
B[j][j]++;
}
}
}
auto res = determinant_of_first_degree_poly_mat(A, B);
print(res[0] + res[1]);
} else {
vvec(int, group, n);
fori(i, n) {
group[UF.find(i)].push_back(i);
}
vec(ll, S, n, 0);
fori(i, n) S[i] = group[i].size();
sort(all(S));
reverse(all(S));
{
mint c = n * (n - 1);
fori(i, 2, n) {
c -= S[i] * (S[i] - 1);
}
c -= (S[0] + S[1]) * (S[0] + S[1] - 1);
print(c);
}
mint ans = 1;
for (auto &g : group) {
ll nn = g.size();
if (nn <= 1) continue;
Matrix<mint> A(nn - 1);
fori(i, nn) fori(j, i + 1, nn) {
if (E[g[i]][g[j]]) {
A[i][i]++;
if (j != nn - 1) {
A[i][j]--;
A[j][i]--;
A[j][j]++;
}
}
}
ans *= A.det();
}
ll c = 0;
for (auto s : S) {
if (s == S[0]) c++;
}
if (c >= 2) {
ans *= mint(c) * (c - 1) / 2 * S[0] * S[0];
} else {
ll c2 = 0;
for (auto s : S) {
if (s == S[1]) c2++;
}
ans *= mint(c) * c2 * S[0] * S[1];
}
print(ans);
}
}
int main() {
#ifndef INTERACTIVE
cin.tie(0)->sync_with_stdio(0);
#endif
// cout << fixed << setprecision(12);
int t;
t = 1;
// cin >> t;
while (t--) solve();
return 0;
}