結果
| 問題 | No.3105 Parallel Connection and Spanning Trees |
| コンテスト | |
| ユーザー |
 ryoku
|
| 提出日時 | 2026-08-26 00:40:56 |
| 言語 | C++23(gcc16) (gcc 16.1.0 + boost 1.92.0) |
| 結果 |
AC
|
| 実行時間 | 80 ms / 5,000 ms |
| + 417µs | |
| コード長 | 37,503 bytes |
| 記録 | |
| コンパイル時間 | 4,665 ms |
| コンパイル使用メモリ | 330,104 KB |
| 実行使用メモリ | 6,272 KB |
| 最終ジャッジ日時 | 2026-08-26 00:41:07 |
| 合計ジャッジ時間 | 7,484 ms |
|
ジャッジサーバーID （参考情報） |
judge2_0 / judge1_0 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 2 |
| other | AC * 32 |
ソースコード
#define CP_BUNDLED_SOURCE
#ifdef TEMPLATE
#else
#define TEMPLATE
# pragma GCC optimize("O3")
#include <iostream>
#include <iomanip>
#include <cstdio>
#include <string>
#include <cstring>
#include <vector>
#include <list>
#include <queue>
#include <stack>
#include <deque>
#include <set>
#include <map>
#include <unordered_set>
#include <unordered_map>
#include <algorithm>
#include <numeric>
#include <cmath>
#include <climits>
#include <cassert>
#include <functional>
#include <iterator>
#include <utility>
#include <complex>
#include <bitset>
#include <chrono>
#include <random>
#include <limits>
#include <optional>
#include <variant>
#include <any>
#include <array>
#include <bit>
#include <compare>
#include <concepts>
#include <numbers>
#include <ranges>
#include <span>
#include <string_view>
#include <tuple>
#include <type_traits>
#include <version>
using namespace std;
using uint=unsigned;
using ll=long long;
using ull=unsigned long long;
using ld=long double;
using pii=pair<int,int>;
using pll=pair<ll,ll>;
using i128=__int128;
using u128=unsigned __int128;
template<class T>using vc=vector<T>;
template<class T>using vvc=vc<vc<T>>;
template<class T>using vvvc=vvc<vc<T>>;
template<class T>using smpq=priority_queue<T,vector<T>,greater<T>>;
template<class T>using bipq=priority_queue<T>;
#define rep(i,n) for(ll i=0;i<(ll)(n);i++)
#define REP(i,j,n) for(ll i=(j);i<(ll)(n);i++)
#define DREP(i,n,m) for(ll i=(n);i>=(m);i--)
#define drep(i,n) for(ll i=((n)-1);i>=0;i--)
#define rall(x) x.rbegin(),x.rend()
#define mp(...) make_pair(__VA_ARGS__)
#define pb push_back
#define fi first
#define se second
#define is insert
#define bg begin()
#define ed end()
#define all(x) x.begin(),x.end()
void scan(int&a) { cin >> a; }
void scan(ll&a) { cin >> a; }
void scan(string&a) { cin >> a; }
void scan(char&a) { cin >> a; }
void scan(uint&a) { cin >> a; }
void scan(ull&a) { cin >> a; }
void scan(bool&a) { cin >> a; }
void scan(ld&a){ cin>> a;}
template<class T> void scan(vector<T>&a) { for(auto&x:a) scan(x); }
void read() {}
template<class Head, class... Tail> void read(Head&head, Tail&... tail) { scan(head); read(tail...); }
#define INT(...) int __VA_ARGS__; read(__VA_ARGS__);
#define LL(...) ll __VA_ARGS__; read(__VA_ARGS__);
#define ULL(...) ull __VA_ARGS__; read(__VA_ARGS__);
#define STR(...) string __VA_ARGS__; read(__VA_ARGS__);
#define VC(type, name, ...) vector<type> name(__VA_ARGS__); read(name);
#define VVC(type, name, size, ...) vector<vector<type>> name(size, vector<type>(__VA_ARGS__)); read(name);
template<class T>void print(T a) { cout << a; }
template<class T> void print(vector<T>a) { for(int i=0;i<(int)a.size();i++){if(i)cout<<" ";print(a[i]);}cout<<endl;}
void PRT() { cout <<endl; return ; }
template<class T> void PRT(T a) { print(a); cout <<endl; return; }
template<class Head, class... Tail> void PRT(Head head, Tail ... tail) { print(head); cout << " "; PRT(tail...); return; }
template<class T,class F>
bool chmin(T &x, F y){
if(x>y){
x=y;
return true;
}
return false;
}
template<class T, class F>
bool chmax(T &x, F y){
if(x<y){
x=y;
return true;
}
return false;
}
template <typename T>
T floor(T a, T b) {
return a / b - (a % b && (a ^ b) < 0);
}
template <typename T>
T ceil(T x, T y) {
return floor(x + y - 1, y);
}
template <typename T>
T bmod(T x, T y) {
return x - y * floor(x, y);
}
template <typename T>
pair<T, T> divmod(T x, T y) {
T q = floor(x, y);
return {q, x - q * y};
}
void YesNo(bool b){
cout<<(b?"Yes":"No")<<endl;
}
void YESNO(bool b){
cout<<(b?"YES":"NO")<<endl;
}
void AliceBob(bool b){
cout<<(b?"Alice":"Bob")<<endl;
}
void TakahashiAoki(bool b){
cout<<(b?"Takahashi":"Aoki")<<endl;
}
void Yes(){
cout<<"Yes"<<endl;
}
void No(){
cout<<"No"<<endl;
}
vc<int>stovi(const string&s,const string&S){
vc<int>v(s.size());
rep(i,s.size()){
auto t=S.find(s[i]);
assert(t!=string::npos);
v[i]=t;
}
return v;
}
template<class T=ll>
T isqrt(T x){
T F=sqrtl(x);
while((F+1)*(F+1)<=x)F++;
while(F*F>x)F--;
return F;
}
template<class T>
vvc<T>trans(const vvc<T>&a){
assert(a.size()&&a[0].size());
vvc<T>b(a[0].size(),vc<T>(a.size()));
rep(i,a.size())rep(j,a[0].size()){
b[j][i]=a[i][j];
}
return b;
}
template<class T>
vc<string>trans(const vc<string>&a){
assert(a.size()&&a[0].size());
vc<string>b(a[0].size(),string(a.size(),0));
rep(i,a.size())rep(j,a[0].size()){
b[j][i]=a[i][j];
}
return b;
}
template<class T>
int popcount(T n){
return __builtin_popcountll(n);
}
template<class T,class L=ll>
L sum(vc<T>&a){
return accumulate(all(a),L(0));
}
template<class T>
vc<T>subset(T S){
vc<T>ans;
for(T x=S;x>0;x=(x-1)&S)ans.pb(x);
ans.pb(0);
return ans;
}
template<class T>
T max(vc<T>&a){
return *max_element(all(a));
}
template<class T>
T min(vc<T>&a){
return *min_element(all(a));
}
#ifndef COMPRESSER_STRUCT
#define COMPRESSER_STRUCT
template<class T>
struct compresser{
vc<T>x;
compresser(int n=0){x.reserve(n);}
compresser(const vc<T>&xs){
x=xs;
}
void push(T p){built=false;x.pb(p);}
bool built=false;
void build(){
if(!chmax(built,1))return;
sort(all(x));
x.erase(unique(all(x)),x.end());
}
int find(T v){
build();
auto itr=lower_bound(all(x),v)-x.begin();
if(itr==x.size()||x[itr]!=v)return -1;
return itr;
}
int find_next(T v){
build();
return lower_bound(all(x),v)-x.begin();
}
int size(){
build();
return x.size();
}
T operator[](int i)const{
assert(0<=i&&i<x.size());
return x[i];
}
};
#endif
template<class T,class L=ll>
vc<L> presum(vc<T> &a){
vc<L> ret(a.size()+1);
rep(i,a.size())ret[i+1]=ret[i]+a[i];
return ret;
}
template<class T, class F>
vc<T> &operator+=(vc<T> &a,F b){
for (auto&v:a)v += b;
return a;
}
template<class T, class F>
vc<T> &operator-=(vc<T>&a,F b){
for (auto&v:a)v-=b;
return a;
}
template<class T, class F>
vc<T> &operator*=(vc<T>&a,F b){
for (auto&v:a)v*=b;
return a;
}
template<class T=ll>
constexpr T pow(T a,T b){
T res=1;
while(b){
if(b&1)res*=a;
a*=a;
b/=2;
}
return res;
}
constexpr ll ten(ll a){
return pow<ll>(10,a);
}
template<typename T>constexpr T inf=numeric_limits<T>::max()/2-1;
template<class T>
int tbit(T x){
using U=make_unsigned_t<T>;
U y=(U)x;
return y?(int)bit_width(y)-1:-1;
}
template<class T>
int lbit(T x){
using U=make_unsigned_t<T>;
U y=(U)x;
return y?(int)countr_zero(y):-1;
}
template<class T>
int tbit(T x,int p){
using U=make_unsigned_t<T>;
constexpr int W=numeric_limits<U>::digits;
U y=(U)x;
if(p<0)return -1;
if(p>=W-1)return tbit(y);
return tbit(y&((U(1)<<(p+1))-1));
}
template<class T>
int lbit(T x,int p){
using U=make_unsigned_t<T>;
constexpr int W=numeric_limits<U>::digits;
U y=(U)x;
if(p<0)return lbit(y);
if(p>=W)return -1;
return lbit(y&(~U(0)<<p));
}
istream& operator>>(istream&is,i128&x){
string s;is>>s;
x=0;
int i=0,neg=0;
if(s[0]=='-')neg=1,i=1;
for(;i<(int)s.size();i++)x=x*10+s[i]-'0';
if(neg)x=-x;
return is;
}
ostream& operator<<(ostream&os,i128 x){
if(x==0)return os<<0;
if(x<0)os<<"-";
u128 y=x<0?-(u128)x:(u128)x;
string s;
while(y)s.pb('0'+y%10),y/=10;
reverse(all(s));
return os<<s;
}
#ifdef LOCAL
#include "debug/debug.hpp"
#else
#define dbg(...) ((void)0)
#endif
struct template_setup{
template_setup(){
#ifdef LOCAL
freopen("input.txt","r",stdin);
freopen("output.txt","w",stdout);
#endif
cin.tie(0)->sync_with_stdio(0);
#ifdef LOCAL
cout<<fixed<<setprecision(6);
dbg("==============="s);
#else
cout<<fixed<<setprecision(20);
#endif
}
};
inline template_setup template_setup;
#endif
struct barrett{
using u64=uint64_t;
using u32=uint32_t;
using i128=__int128_t;
u64 m;
int mod;
void set(int mod_){
assert(mod_>0);
mod=mod_;
m=(i128(1)<<64)/mod;
}
unsigned reduce(uint64_t x){
assert(mod>0);
x-=(((i128)x*m)>>64)*mod;
return x<mod?x:x-mod;
}
};
template<int id>
struct dynamic_modint{
using u32=uint32_t;
using u64=uint64_t;
u32 val;
dynamic_modint():val(0){}
dynamic_modint(ll x){
ll v=x%get_mod();
if(v<0)v+=get_mod();
val=v;
}
static dynamic_modint raw(int v){
assert(v>=0);
dynamic_modint mi;
mi.val=v;
return mi;
}
dynamic_modint &operator+=(const dynamic_modint&m){
if((val+=m.val)>=get_mod())val-=get_mod();
return *this;
}
dynamic_modint &operator-=(const dynamic_modint&m){
if((val+=(get_mod()-m.val))>=get_mod())val-=get_mod();
return *this;
}
dynamic_modint &operator*=(const dynamic_modint&m){
val=rem(u64(val)*m.val);
return *this;
}
dynamic_modint &operator/=(const dynamic_modint&m){
val=rem(u64(val)*m.inv().val);
return *this;
}
dynamic_modint operator-() const{
return dynamic_modint(val?get_mod()-val:0);
}
dynamic_modint operator+() const {
return *this;
}
friend dynamic_modint operator+(dynamic_modint lhs, const dynamic_modint& rhs){
return lhs+=rhs;
}
friend dynamic_modint operator-(dynamic_modint lhs, const dynamic_modint& rhs){
return lhs-=rhs;
}
friend dynamic_modint operator*(dynamic_modint lhs, const dynamic_modint& rhs){
return lhs*=rhs;
}
friend dynamic_modint operator/(dynamic_modint lhs,const dynamic_modint&rhs){
return lhs/=rhs;
}
bool operator==(const dynamic_modint&p) const{
return p.val==val;
}
bool operator!=(const dynamic_modint&p) const{
return p.val!=val;
}
dynamic_modint pow(int64_t n) const{
dynamic_modint res(1),mul(val);
while(n){
if(n%2)res*=mul;
mul*=mul;
n/=2;
}
return res;
}
friend ostream&operator<<(ostream&os,const dynamic_modint&p){
os<<p.val;
return os;
}
friend istream&operator>>(istream&is,dynamic_modint&p){
int64_t x;
is>>x;
p=dynamic_modint(x);
return is;
}
dynamic_modint inv()const{
int64_t a=val,b=get_mod(),u=1,v=0,t;
#ifdef LOCAL
assert(gcd(a,b)==1);
#endif
while(b>0){
t=a/b;
swap(a-=t*b,b);
swap(u-=t*v,v);
}
return dynamic_modint(u);
}
inline static u32 rem(u64 x){return barrett_reduction().reduce(x);}
static inline int &get_mod(){
static int mod=0;
return mod;
}
static void set_mod(int md){
assert(0<md&&md<=(1ll<<31)-1);
get_mod()=md;
barrett_reduction().set(md);
}
static inline barrett&barrett_reduction(){
static barrett b;
return b;
}
};
template<class,class=void>
struct binom_has_get_mod:false_type{};
template<class mint>
struct binom_has_get_mod<mint,void_t<decltype(mint::get_mod())>>:true_type{};
template<class mint>
struct binom{
private:
static vector<mint>&fact_table(){static vector<mint>v={1};return v;}
static vector<mint>&invfact_table(){static vector<mint>v={1};return v;}
static vector<mint>&invs_table(){static vector<mint>v={0};return v;}
static int&built_mod(){static int mod=-1;return mod;}
public:
static void build(int n){
auto&_fact=fact_table();
auto&_invfact=invfact_table();
auto&_invs=invs_table();
if constexpr(binom_has_get_mod<mint>::value){
auto mod=mint::get_mod();
if(built_mod()!=mod){
_fact={1};
_invfact={1};
_invs={0};
built_mod()=mod;
}
}
if(n<(int)_fact.size())return;
int old=_fact.size();
_fact.resize(n+1);
_invfact.resize(n+1);
_invs.resize(n+1);
if constexpr(binom_has_get_mod<mint>::value){
auto mod=mint::get_mod();
for(int i=old;i<=n;i++){
_fact[i]=_fact[i-1]*i;
if(i==1)_invs[i]=1;
else _invs[i]=-_invs[mod%i]*(mod/i);
_invfact[i]=_invfact[i-1]*_invs[i];
}
}else{
for(int i=old;i<=n;i++){
_fact[i]=_fact[i-1]*i;
_invs[i]=mint(1)/i;
_invfact[i]=_invfact[i-1]*_invs[i];
}
}
}
static mint fact(int i){
assert(i>=0);
build(i);
return fact_table()[i];
}
static mint invfact(int i){
assert(i>=0);
build(i);
return invfact_table()[i];
}
static mint inv(int i){
assert(i>0);
build(i);
return invs_table()[i];
}
static mint C(int a,int b){//aCb
if(b==0)return 1;
if(a<0||b<0||a-b<0)return mint(0);
build(a);
auto&_fact=fact_table();
auto&_invfact=invfact_table();
return _fact[a]*_invfact[b]*_invfact[a-b];
}
static mint iC(int a,int b){//1/aCb
if(a<0||b<0||a-b<0)return mint(0);
build(a);
auto&_fact=fact_table();
auto&_invfact=invfact_table();
return _fact[b]*_fact[a-b]*_invfact[a];
}
static mint P(int a,int b){
if(a<b||b<0)return 0;
build(a);
auto&_fact=fact_table();
auto&_invfact=invfact_table();
return _fact[a]*_invfact[a-b];
}
static mint H(int a,int b){
return C(a+b-1,b);
}
};
template< typename T >
T extgcd(T a, T b, T &x, T &y) {
T d = a;
if(b != 0) {
d = extgcd(b, a % b, y, x);
y -= (a / b) * x;
} else {
x = 1;
y = 0;
}
return d;
}
template<class T>
pair<T,T> inv(T x,T m){
T a1,a2;
T res=extgcd<ll>(x,m,a1,a2);
T md=m/res;
a1=(a1%md+md)%md;
return {a1,md};
}
template<class T>
pair<T,T> mod_solve(T a,T b,T m){//return x s.t. ax=b mod m
a%=m,b%=m;if(a<0)a+=m;if(b<0)b+=m;
T g=gcd(gcd(a,b),m);
a/=g,b/=g,m/=g;
if(gcd(a,m)>1)return {-1,-1};
return {(inv<ll>(a,m).first*b)%m,inv<ll>(a,m).second};
}
//x^2 ≡ b (mod p)
ll mod_sqrt(ll b,ll p){
static mt19937 mt(random_device{}());
b%=p;if(b<0)b+=p;
if(b==0)return 0;
if(p==2){
return b;
}
assert(p>=3);
using mint=dynamic_modint<20260801>;mint::set_mod(p);
if(mint(b).pow((p-1)/2)==-1){
return -1;
}
if(p%4==3){
return mint(b).pow((p+1)/4).val;
}
ll t=[&](){
ll w;
while(1){
ll t=mt()%p;
w=t*t-b;
if(mint(w).pow((p-1)/2)==mint(-1)){
return t;
}
}
assert(0);
}();
mint w=mint(t*t-b);
using T=pair<mint,mint>;
auto ml=[&](T a,T b)->T{
return T{a.first*b.first+a.second*b.second*w,a.second*b.first+a.first*b.second};
};
ll e=(p+1)/2;
T ans={1,0};
T gy={t,1};
while(e){
if(e%2)ans=ml(ans,gy);
gy=ml(gy,gy);
e/=2;
}
return ans.first.val;
}
template<uint32_t mod>
struct static_modint{
static_assert(0<mod&&mod<=(1u<<31)-1);
using u32=uint32_t;
using u64=uint64_t;
u32 val;
static_modint():val(0){}
static_modint(ll x){
ll v=x%mod;
if(v<0)v+=mod;
val=v;
}
constexpr static uint32_t get_mod(){
return mod;
}
static static_modint raw(int v){
assert(v>=0);
static_modint mi;
mi.val=v;
return mi;
}
static_modint &operator+=(const static_modint&m){
if((val+=m.val)>=mod)val-=mod;
return *this;
}
static_modint &operator-=(const static_modint&m){
if((val+=(mod-m.val))>=mod)val-=mod;
return *this;
}
static_modint &operator*=(const static_modint&m){
val=u64(val)*m.val%mod;
return *this;
}
static_modint &operator/=(const static_modint&m){
val=u64(val)*m.inv().val%mod;
return *this;
}
static_modint operator-() const{
return static_modint(mod-val);
}
static_modint operator+() const {
return *this;
}
friend static_modint operator+(static_modint lhs, const static_modint& rhs){
return lhs+=rhs;
}
friend static_modint operator-(static_modint lhs, const static_modint& rhs){
return lhs-=rhs;
}
friend static_modint operator*(static_modint lhs, const static_modint& rhs){
return lhs*=rhs;
}
friend static_modint operator/(static_modint lhs,const static_modint&rhs){
return lhs/=rhs;
}
bool operator==(const static_modint&p) const{
return p.val==val;
}
bool operator!=(const static_modint&p) const{
return p.val!=val;
}
static_modint pow(int64_t n) const{
static_modint res(1),mul(val);
while(n){
if(n%2)res*=mul;
mul*=mul;
n/=2;
}
return res;
}
friend ostream&operator<<(ostream&os,const static_modint&p){
os<<p.val;
return os;
}
friend istream&operator>>(istream&is,static_modint&p){
int64_t x;
is>>x;
p=static_modint(x);
return is;
}
static_modint inv()const{
int64_t a=val,b=mod,u=1,v=0,t;
#ifdef LOCAL
assert(gcd(a,b)==1);
#endif
while(b>0){
t=a/b;
swap(a-=t*b,b);
swap(u-=t*v,v);
}
return static_modint(u);
}
};
namespace MATMAT{
template <typename T, typename = void>
struct is_mint : std::false_type {};
template <typename T>
struct is_mint<T, std::void_t<decltype(T::get_mod())>> : std::true_type {};
};
template<class T,int N,int M>
struct fixed_matrix;
template<class T>
struct matrix{
int n,m;
vvc<T>a;
matrix()=default;
matrix(vvc<T>b):a(b),n(b.size()),m(0){
if(b.size())m=b[0].size();
for(auto&row:b)assert((int)row.size()==m);
}
matrix(int n,int m):n(n),m(m){
assert(n>=0&&m>=0);
a.assign(n,vc<T>(m));
}
vc<T>&operator[](int i){
assert(0<=i&&i<n);
return a[i];
}
const vc<T>&operator[](int i)const{
assert(0<=i&&i<n);
return a[i];
}
matrix&operator+=(const matrix&mt2){
assert(mt2.n==n&&mt2.m==m);
rep(i,n)rep(j,m)a[i][j]+=mt2[i][j];
return *this;
}
matrix&operator-=(const matrix&mt2){
assert(mt2.n==n&&mt2.m==m);
rep(i,n)rep(j,m)a[i][j]-=mt2[i][j];
return *this;
}
matrix&operator*=(const matrix&mt2){
assert(m==mt2.n);
vc<vc<T>>res(n,vc<T>(mt2.m));
auto Mt2=mt2.trans();
if constexpr(MATMAT::is_mint<T>::value){
rep(i,n)rep(j,mt2.m){
__int128 tmp{};
rep(k,m){
tmp+=(ll)a[i][k].val*Mt2[j][k].val;
}
res[i][j]=tmp%T::get_mod();
}
}else{
rep(i,n)rep(j,mt2.m)rep(k,m){
res[i][j]+=a[i][k]*Mt2[j][k];
}
}
a=move(res);
n=a.size();
m=(n?a[0].size():mt2.m);
return *this;
}
matrix trans()const{
matrix res(m,n);
rep(i,n)rep(j,m)res[j][i]=a[i][j];
return res;
}
int size()const{
return n;
}
int size2()const{
return m;
}
matrix operator-() const{
vvc<T>b=a;
for(auto&x:b)for(auto&e:x)e=-e;
return matrix(b);
}
matrix operator+() const {
return *this;
}
friend matrix operator+(matrix lhs, const matrix& rhs){
return lhs+=rhs;
}
friend matrix operator-(matrix lhs, const matrix& rhs){
return lhs-=rhs;
}
friend matrix operator*(matrix lhs, const matrix& rhs){
return lhs*=rhs;
}
template<int N,int M>
matrix&operator*=(const fixed_matrix<T,N,M>&mt2);
static matrix unit(int n){
assert(n>=0);
matrix mt(n,n);
rep(i,n)mt[i][i]=1;
return mt;
}
matrix pow(ll n){
assert(this->n==this->m);
assert(n>=0);
matrix res=unit(this->n);
matrix mul=a;
while(n){
if(n%2)res*=mul;
mul*=mul;
n/=2;
}
return res;
}
T det()const{
assert(n==m);
auto A=a;
T res=1;
rep(i,n){
if(A[i][i]==0){
REP(j,i+1,n){
if(A[j][i]!=0){
swap(A[i],A[j]);
res=-res;
break;
}
}
}
if(A[i][i]==0)return 0;
res*=A[i][i];
T IN=1/A[i][i];
REP(j,i,n)A[i][j]*=IN;
REP(j,i+1,n){
T coef=A[j][i];
REP(k,i,n){
A[j][k]-=A[i][k]*coef;
}
}
}
return res;
}
int rank()const{
matrix a;
if(n>m)a=matrix(*this).trans();
else a=matrix(*this);
int N=a.n,M=a.m;
int hj=0;
rep(i,N){
int HI{-1},HJ{-1};
REP(hj2,hj,M){
REP(hi,i,N){
if(a[hi][hj2]!=0){
HI=hi,HJ=hj2;
break;
}
}
if(HI!=-1)break;
}
if(HJ==-1){
return i;
}
if(i!=HI)swap(a[i],a[HI]);
T IN=1/a[i][HJ];
REP(j,HJ,M)a[i][j]*=IN;
REP(hi,i+1,N){
T coef=a[hi][HJ];
REP(hj2,HJ,M){
a[hi][hj2]-=a[i][hj2]*coef;
}
}
hj=HJ+1;
}
return N;
}
optional<matrix> inverse()const{
assert(n==m);
auto A=a;
auto res=unit(n);
int hj=0;
rep(i,n){
int HI{-1},HJ{-1};
REP(hj2,hj,n){
REP(hi,i,n){
if(A[hi][hj2]!=0){
HI=hi,HJ=hj2;
break;
}
}
if(HI!=-1)break;
}
if(HJ==-1){
return nullopt;
}
if(i!=HI)swap(A[i],A[HI]),swap(res[i],res[HI]);
T IN=1/A[i][HJ];
REP(j,0,n)A[i][j]*=IN,res[i][j]*=IN;
REP(hi,i+1,n){
T coef=A[hi][HJ];
rep(hj2,n){
A[hi][hj2]-=A[i][hj2]*coef;
res[hi][hj2]-=res[i][hj2]*coef;
}
}
hj=HJ+1;
}
drep(i,n){
DREP(j,i-1,0){
rep(k,n)res[j][k]-=res[i][k]*A[j][i];
}
}
return res;
}
};
template<class T,int N,int M>
struct fixed_matrix{
static constexpr int n=N,m=M;
array<array<T,M>,N>a{};
fixed_matrix()=default;
fixed_matrix(initializer_list<initializer_list<T>>il){
int i=0;
for(auto&row:il){
int j=0;
for(auto&v:row){assert(j<M);a[i][j++]=v;}
i++;
assert(i<=N);
}
}
array<T,M>&operator[](int i){assert(0<=i&&i<N);return a[i];}
const array<T,M>&operator[](int i)const{assert(0<=i&&i<N);return a[i];}
fixed_matrix&operator+=(const fixed_matrix&mt2){
rep(i,N)rep(j,M)a[i][j]+=mt2[i][j];
return *this;
}
fixed_matrix&operator-=(const fixed_matrix&mt2){
rep(i,N)rep(j,M)a[i][j]-=mt2[i][j];
return *this;
}
template<int K>
fixed_matrix<T,N,K>operator*(const fixed_matrix<T,M,K>&mt2)const{
fixed_matrix<T,N,K>res;
if constexpr(MATMAT::is_mint<T>::value){
auto Mt2=mt2.trans();
rep(i,N)rep(j,K){
__int128 tmp{};
rep(k,M)tmp+=(ll)a[i][k].val*Mt2[j][k].val;
res[i][j]=tmp%T::get_mod();
}
}else{
rep(i,N)rep(j,K)rep(k,M)res[i][j]+=a[i][k]*mt2[k][j];
}
return res;
}
fixed_matrix&operator*=(const fixed_matrix<T,M,M>&mt2){
return *this=*this*mt2;
}
fixed_matrix<T,M,N>trans()const{
fixed_matrix<T,M,N>res;
rep(i,N)rep(j,M)res[j][i]=a[i][j];
return res;
}
fixed_matrix operator-()const{
fixed_matrix res=*this;
for(auto&row:res.a)for(auto&v:row)v=-v;
return res;
}
fixed_matrix operator+()const{return *this;}
friend fixed_matrix operator+(fixed_matrix lhs,const fixed_matrix&rhs){return lhs+=rhs;}
friend fixed_matrix operator-(fixed_matrix lhs,const fixed_matrix&rhs){return lhs-=rhs;}
static fixed_matrix unit(){
static_assert(N==M,"unit requires square");
fixed_matrix res;
rep(i,N)res[i][i]=1;
return res;
}
fixed_matrix pow(ll k)const{
static_assert(N==M,"pow requires square");
fixed_matrix res=unit(),mul=*this;
while(k){
if(k&1)res=res*mul;
mul=mul*mul;
k>>=1;
}
return res;
}
T det()const{
static_assert(N==M,"det requires square");
auto A=a;
T res=1;
rep(i,N){
if(A[i][i]==0){
REP(j,i+1,N){
if(A[j][i]!=0){
swap(A[i],A[j]);
res=-res;
break;
}
}
}
if(A[i][i]==0)return 0;
res*=A[i][i];
T IN=1/A[i][i];
REP(j,i,N)A[i][j]*=IN;
REP(j,i+1,N){
T coef=A[j][i];
REP(k,i,N){
A[j][k]-=A[i][k]*coef;
}
}
}
return res;
}
int rank()const{
auto A=a;
int hj=0;
rep(i,N){
int HI{-1},HJ{-1};
REP(hj2,hj,M){
REP(hi,i,N){
if(A[hi][hj2]!=0){
HI=hi,HJ=hj2;
break;
}
}
if(HI!=-1)break;
}
if(HJ==-1){
return i;
}
if(i!=HI)swap(A[i],A[HI]);
T IN=1/A[i][HJ];
REP(j,HJ,M)A[i][j]*=IN;
REP(hi,i+1,N){
T coef=A[hi][HJ];
REP(hj2,HJ,M){
A[hi][hj2]-=A[i][hj2]*coef;
}
}
hj=HJ+1;
}
return N;
}
optional<fixed_matrix>inverse()const{
static_assert(N==M,"inverse requires square");
auto A=a;
auto res=unit();
int hj=0;
rep(i,N){
int HI{-1},HJ{-1};
REP(hj2,hj,N){
REP(hi,i,N){
if(A[hi][hj2]!=0){
HI=hi,HJ=hj2;
break;
}
}
if(HI!=-1)break;
}
if(HJ==-1){
return nullopt;
}
if(i!=HI)swap(A[i],A[HI]),swap(res[i],res[HI]);
T IN=1/A[i][HJ];
REP(j,0,N)A[i][j]*=IN,res[i][j]*=IN;
REP(hi,i+1,N){
T coef=A[hi][HJ];
rep(hj2,N){
A[hi][hj2]-=A[i][hj2]*coef;
res[hi][hj2]-=res[i][hj2]*coef;
}
}
hj=HJ+1;
}
drep(i,N){
DREP(j,i-1,0){
rep(k,N)res[j][k]-=res[i][k]*A[j][i];
}
}
return res;
}
};
template<class T,int N,int M>
matrix<T>operator*(const fixed_matrix<T,N,M>&mt1,const matrix<T>&mt2){
assert(M==mt2.n);
matrix<T>res(N,mt2.m);
auto Mt2=mt2.trans();
if constexpr(MATMAT::is_mint<T>::value){
rep(i,N)rep(j,mt2.m){
__int128 tmp{};
rep(k,M)tmp+=(ll)mt1[i][k].val*Mt2[j][k].val;
res[i][j]=tmp%T::get_mod();
}
}else{
rep(i,N)rep(j,mt2.m)rep(k,M)res[i][j]+=mt1[i][k]*Mt2[j][k];
}
return res;
}
template<class T,int N,int M>
matrix<T>operator*(const matrix<T>&mt1,const fixed_matrix<T,N,M>&mt2){
assert(mt1.m==N);
matrix<T>res(mt1.n,M);
auto Mt2=mt2.trans();
if constexpr(MATMAT::is_mint<T>::value){
rep(i,mt1.n)rep(j,M){
__int128 tmp{};
rep(k,N)tmp+=(ll)mt1[i][k].val*Mt2[j][k].val;
res[i][j]=tmp%T::get_mod();
}
}else{
rep(i,mt1.n)rep(j,M)rep(k,N)res[i][j]+=mt1[i][k]*Mt2[j][k];
}
return res;
}
template<class T>
template<int N,int M>
matrix<T>&matrix<T>::operator*=(const fixed_matrix<T,N,M>&mt2){
return *this=*this*mt2;
}
template<class mint,class Graph>
mint counting_spanning_tree(const Graph&g){
assert(Graph::directed()==false);
int n=g.size();
matrix<mint>mt(n-1,n-1);
REP(i,1,n){
mt[i-1][i-1]=g[i].size();
for(auto&e:g[i]){
if(e.to)mt[i-1][e.to-1]-=1;
}
}
rep(i,n-1)rep(j,n-1)dbg(mt[i][j]);
return mt.det();
}
#include<type_traits>
struct unweighted{
unweighted()=default;
unweighted(int){}
operator int()const{return 1;}
};
template<class T=unweighted>
struct edge{
int from,to,id;
[[no_unique_address]] T cost;
#ifdef LOCAL
friend ostream&operator<<(ostream&os,const edge&e){
return os<<"{from:"<<e.from<<",to:"<<e.to<<",id:"<<e.id<<",cost:"<<e.cost<<"}";
}
#endif
};
template<class T,class=void>struct is_edge:false_type{};
template<class T>struct is_edge<T,void_t<decltype(declval<T>().from),decltype(declval<T>().to),decltype(declval<T>().id),decltype(declval<T>().cost)>>:true_type{};
struct empty_storage{};
template<bool is_directed,class T=unweighted>
struct static_graph{
constexpr static bool directed(){return is_directed;}
using edge=conditional_t<is_edge<T>::value,T,::edge<T>>;
using cost_t=decltype(declval<edge>().cost);
private:
int n,m,added=0;
mutable bool csr_built=false;
[[no_unique_address]] mutable conditional_t<is_directed,bool,empty_storage> inv_built{};
vc<edge>_all_edges;
mutable vc<int>csr_start;
mutable vc<edge>csr_edge;
[[no_unique_address]] mutable conditional_t<is_directed,vc<int>,empty_storage>inv_start;
[[no_unique_address]] mutable conditional_t<is_directed,vc<edge>,empty_storage>inv_edge;
public:
static_graph(int n):n(n),m(-1){assert(n>=0);csr_start.resize(n+1);}
static_graph(int n,int m):n(n),m(m){assert(n>=0&&m>=0);csr_start.resize(n+1);_all_edges.reserve(m);}
void resize(int size){
assert(n<=size);
assert(!csr_built);
n=size;
csr_start.resize(n+1);
}
void add_edge(const edge&e){
assert(0<=e.from&&e.from<n&&0<=e.to&&e.to<n);
assert(m==-1||added<m);
_all_edges.push_back(e);
csr_built=false;
if constexpr(is_directed)inv_built=false;
if(++added==m)build();
}
void add_edge(int a,int b,cost_t cost=1,int id=-1){
assert(0<=a&&a<n&&0<=b&&b<n);
assert(m==-1||added<m);
if(id==-1)id=(int)_all_edges.size();
_all_edges.push_back({a,b,id,cost});
csr_built=false;
if constexpr(is_directed)inv_built=false;
if(++added==m)build();
}
template<int substract=0>
void input(int edge_count){
assert(edge_count>=0);
rep(i,edge_count){
INT(a,b);
a-=substract;
b-=substract;
add_edge(a,b);
}
}
void build()const{
if(csr_built)return;
csr_built=true;
csr_start.assign(n+1,0);
for(auto&e:_all_edges){
csr_start[e.from]++;
if constexpr(!is_directed)csr_start[e.to]++;
}
rep(i,n)csr_start[i+1]+=csr_start[i];
csr_edge.resize(csr_start[n]);
for(auto it=_all_edges.rbegin();it!=_all_edges.rend();++it){
auto&e=*it;
csr_edge[--csr_start[e.from]]=e;
if constexpr(!is_directed)csr_edge[--csr_start[e.to]]={e.to,e.from,e.id,e.cost};
}
}
void build_inv()const{
if constexpr(!is_directed){
build();
return;
}else{
if(inv_built)return;
inv_built=true;
inv_start.assign(n+1,0);
for(auto&e:_all_edges){
inv_start[e.to]++;
}
rep(i,n)inv_start[i+1]+=inv_start[i];
inv_edge.resize(inv_start[n]);
for(auto it=_all_edges.rbegin();it!=_all_edges.rend();++it){
auto&e=*it;
inv_edge[--inv_start[e.to]]={e.to,e.from,e.id,e.cost};
}
}
}
const vc<edge>&all_edges()const{return _all_edges;}
int edge_size()const{return (int)_all_edges.size();}
edge get_edge(int id)const{
assert(0<=id&&id<edge_size());
return _all_edges[id];
}
int out_deg(int u)const{assert(0<=u&&u<n);build();return csr_start[u+1]-csr_start[u];}
int in_deg(int u)const{
assert(0<=u&&u<n);
if constexpr(!is_directed){
return out_deg(u);
}else{
build_inv();
return inv_start[u+1]-inv_start[u];
}
}
int deg(int u)const{return out_deg(u);}
template<class E>
struct span{
E*l; E* r;
E*begin()const{return l;}
E*end()const{return r;}
int size()const{return r-l;}
E&back()const{return r[-1];}
E&operator[](int i){return l[i];}
const E&operator[](int i)const{return l[i];}
};
auto operator[](int u){
assert(0<=u&&u<n);build();
return span<edge>{csr_edge.data()+csr_start[u],csr_edge.data()+csr_start[u+1]};
}
auto operator[](int u)const{
assert(0<=u&&u<n);build();
return span<const edge>{csr_edge.data()+csr_start[u],csr_edge.data()+csr_start[u+1]};
}
auto inv(int u){
assert(0<=u&&u<n);
if constexpr(!is_directed){
return (*this)[u];
}else{
build_inv();
return span<edge>{inv_edge.data()+inv_start[u],inv_edge.data()+inv_start[u+1]};
}
}
auto inv(int u)const{
assert(0<=u&&u<n);
if constexpr(!is_directed){
return (*this)[u];
}else{
build_inv();
return span<const edge>{inv_edge.data()+inv_start[u],inv_edge.data()+inv_start[u+1]};
}
}
int size()const{return n;}
template<class F>vvc<F>adj()const{
vvc<F>res(n,vc<F>(n));
for(auto&e:all_edges()){
res[e.from][e.to]=e.cost;
if(directed()==false)res[e.to][e.from]=e.cost;
}
return res;
}
void clear(){
added=0;
csr_built=false;
if constexpr(is_directed)inv_built=false;
_all_edges.clear();_all_edges.shrink_to_fit();
csr_start.assign(n+1,0);csr_start.shrink_to_fit();
csr_edge.clear();csr_edge.shrink_to_fit();
if constexpr(is_directed){
inv_start.clear();inv_start.shrink_to_fit();
inv_edge.clear();inv_edge.shrink_to_fit();
}
}
template<class F>
void sort(int i,F f){
assert(0<=i&&i<n);
build();
sort(csr_edge.begin()+csr_start[i],csr_edge.begin()+csr_start[i+1],f);
}
template<class F>
void sort_inv(int i,F f){
assert(0<=i&&i<n);
if constexpr(!is_directed){
build();
sort(csr_edge.begin()+csr_start[i],csr_edge.begin()+csr_start[i+1],f);
return;
}
build_inv();
sort(inv_edge.begin()+inv_start[i],inv_edge.begin()+inv_start[i+1],f);
}
template<class F>
static_graph<is_directed,T>extract(F f)const{
static_graph<is_directed,T>res(n);
for(auto&e:_all_edges)if(f(e))res.add_edge(e);
return res;
}
template<class F>
static_graph<1,T>reorder(F f)const{
static_graph<1,T>res(n);
for(auto&e:_all_edges){
if(f(e))res.add_edge(e);
else res.add_edge({e.to,e.from,e.id,e.cost});
}
return res;
}
};
using mint=static_modint<998244353>;
using B=binom<mint>;
void solve(){
LL(k);
array<mint,2>dp{};
dp[0]=1;
while(k--){
array<mint,2>ndp{};
INT(n,m);
static_graph<0>g(n);
g.input<1>(m);
mint onetwo=counting_spanning_tree<mint>(g);
static_graph<0>ng(n-1);
auto convert=[&](ll a){
return max(a-1,0ll);
};
rep(i,n){
for(auto&e:g[i]){
if(i<e.to)ng.add_edge(convert(e.from),convert(e.to));
}
}
rep(i,n)for(auto&e:g[i]){
if(i<e.to)dbg(i,e.to);
}
mint sy=counting_spanning_tree<mint>(ng);
dbg(sy,onetwo);
ndp[0]+=dp[0]*(sy+onetwo*2);
ndp[1]+=dp[0]*onetwo;
ndp[1]+=dp[1]*(onetwo*2+sy);
dp=move(ndp);
dbg(dp);
}
PRT(dp[1]);
}
signed main(){
int t=1;
// cin >> t;
while(t--)solve();
}