結果

問題 No.1303 Inconvenient Kingdom
ユーザー maroon_kuri
提出日時 2020-11-27 21:36:26
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 150 ms / 3,000 ms
コード長 10,325 bytes
コンパイル時間 2,706 ms
コンパイル使用メモリ 225,104 KB
最終ジャッジ日時 2025-01-16 06:41:11
ジャッジサーバーID
（参考情報） 		judge1 / judge2
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 4
other AC * 34
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ソースコード

diff #
プレゼンテーションモードにする

#include <bits/stdc++.h>
using namespace std;
using ll=long long;
#define int ll
#define rng(i,a,b) for(int i=int(a);i<int(b);i++)
#define rep(i,b) rng(i,0,b)
#define gnr(i,a,b) for(int i=int(b)-1;i>=int(a);i--)
#define per(i,b) gnr(i,0,b)
#define pb push_back
#define eb emplace_back
#define a first
#define b second
#define bg begin()
#define ed end()
#define all(x) x.bg,x.ed
#define si(x) int(x.size())
#ifdef LOCAL
#define dmp(x) cerr<<__LINE__<<" "<<#x<<" "<<x<<endl
#else
#define dmp(x) void(0)
#endif
template<class t,class u> void chmax(t&a,u b){if(a<b)a=b;}
template<class t,class u> void chmin(t&a,u b){if(b<a)a=b;}
template<class t> using vc=vector<t>;
template<class t> using vvc=vc<vc<t>>;
using pi=pair<int,int>;
using vi=vc<int>;
template<class t,class u>
ostream& operator<<(ostream& os,const pair<t,u>& p){
    return os<<"{"<<p.a<<","<<p.b<<"}";
}
template<class t> ostream& operator<<(ostream& os,const vc<t>& v){
    os<<"{";
    for(auto e:v)os<<e<<",";
    return os<<"}";
}
#define mp make_pair
#define mt make_tuple
#define one(x) memset(x,-1,sizeof(x))
#define zero(x) memset(x,0,sizeof(x))
#ifdef LOCAL
void dmpr(ostream&os){os<<endl;}
template<class T,class... Args>
void dmpr(ostream&os,const T&t,const Args&... args){
    os<<t<<" ";
    dmpr(os,args...);
}
#define dmp2(...) dmpr(cerr,__LINE__,##__VA_ARGS__)
#else
#define dmp2(...) void(0)
#endif
using uint=unsigned;
using ull=unsigned long long;
template<class t,size_t n>
ostream& operator<<(ostream&os,const array<t,n>&a){
    return os<<vc<t>(all(a));
}
template<int i,class T>
void print_tuple(ostream&,const T&){
}
template<int i,class T,class H,class ...Args>
void print_tuple(ostream&os,const T&t){
    if(i)os<<",";
    os<<get<i>(t);
    print_tuple<i+1,T,Args...>(os,t);
}
template<class ...Args>
ostream& operator<<(ostream&os,const tuple<Args...>&t){
    os<<"{";
    print_tuple<0,tuple<Args...>,Args...>(os,t);
    return os<<"}";
}
template<class t>
void print(t x,int suc=1){
    cout<<x;
    if(suc==1)
        cout<<"\n";
    if(suc==2)
        cout<<" ";
}
ll read(){
    ll i;
    cin>>i;
    return i;
}
vi readvi(int n,int off=0){
    vi v(n);
    rep(i,n)v[i]=read()+off;
    return v;
}
pi readpi(int off=0){
    int a,b;cin>>a>>b;
    return pi(a+off,b+off);
}
template<class T>
void print(const vector<T>&v,int suc=1){
    rep(i,v.size())
        print(v[i],i==int(v.size())-1?suc:2);
}
string readString(){
    string s;
    cin>>s;
    return s;
}
template<class T>
T sq(const T& t){
    return t*t;
}
//#define CAPITAL
void yes(bool ex=true){
    #ifdef CAPITAL
    cout<<"YES"<<"\n";
    #else
    cout<<"Yes"<<"\n";
    #endif
    if(ex)exit(0);
    #ifdef LOCAL
    cout.flush();
    #endif
}
void no(bool ex=true){
    #ifdef CAPITAL
    cout<<"NO"<<"\n";
    #else
    cout<<"No"<<"\n";
    #endif
    if(ex)exit(0);
    #ifdef LOCAL
    cout.flush();
    #endif
}
void possible(bool ex=true){
    #ifdef CAPITAL
    cout<<"POSSIBLE"<<"\n";
    #else
    cout<<"Possible"<<"\n";
    #endif
    if(ex)exit(0);
    #ifdef LOCAL
    cout.flush();
    #endif
}
void impossible(bool ex=true){
    #ifdef CAPITAL
    cout<<"IMPOSSIBLE"<<"\n";
    #else
    cout<<"Impossible"<<"\n";
    #endif
    if(ex)exit(0);
    #ifdef LOCAL
    cout.flush();
    #endif
}
constexpr ll ten(int n){
    return n==0?1:ten(n-1)*10;
}
const ll infLL=LLONG_MAX/3;
#ifdef int
const int inf=infLL;
#else
const int inf=INT_MAX/2-100;
#endif
int topbit(signed t){
    return t==0?-1:31-__builtin_clz(t);
}
int topbit(ll t){
    return t==0?-1:63-__builtin_clzll(t);
}
int botbit(signed a){
    return a==0?32:__builtin_ctz(a);
}
int botbit(ll a){
    return a==0?64:__builtin_ctzll(a);
}
int popcount(signed t){
    return __builtin_popcount(t);
}
int popcount(ll t){
    return __builtin_popcountll(t);
}
bool ispow2(int i){
    return i&&(i&-i)==i;
}
ll mask(int i){
    return (ll(1)<<i)-1;
}
bool inc(int a,int b,int c){
    return a<=b&&b<=c;
}
template<class t> void mkuni(vc<t>&v){
    sort(all(v));
    v.erase(unique(all(v)),v.ed);
}
ll rand_int(ll l, ll r) { //[l, r]
    #ifdef LOCAL
    static mt19937_64 gen;
    #else
    static mt19937_64 gen(chrono::steady_clock::now().time_since_epoch().count());
    #endif
    return uniform_int_distribution<ll>(l, r)(gen);
}
template<class t>
void myshuffle(vc<t>&a){
    rep(i,si(a))swap(a[i],a[rand_int(0,i)]);
}
template<class t>
int lwb(const vc<t>&v,const t&a){
    return lower_bound(all(v),a)-v.bg;
}
vvc<int> readGraph(int n,int m){
    vvc<int> g(n);
    rep(i,m){
        int a,b;
        cin>>a>>b;
        //sc.read(a,b);
        a--;b--;
        g[a].pb(b);
        g[b].pb(a);
    }
    return g;
}
vvc<int> readTree(int n){
    return readGraph(n,n-1);
}
struct modinfo{uint mod,root;};
template<modinfo const&ref>
struct modular{
    static constexpr uint const &mod=ref.mod;
    static modular root(){return modular(ref.root);}
    uint v;
    //modular(initializer_list<uint>ls):v(*ls.bg){}
    modular(ll vv=0){s(vv%mod+mod);}
    modular& s(uint vv){
        v=vv<mod?vv:vv-mod;
        return *this;
    }
    modular operator-()const{return modular()-*this;}
    modular& operator+=(const modular&rhs){return s(v+rhs.v);}
    modular&operator-=(const modular&rhs){return s(v+mod-rhs.v);}
    modular&operator*=(const modular&rhs){
        v=ull(v)*rhs.v%mod;
        return *this;
    }
    modular&operator/=(const modular&rhs){return *this*=rhs.inv();}
    modular operator+(const modular&rhs)const{return modular(*this)+=rhs;}
    modular operator-(const modular&rhs)const{return modular(*this)-=rhs;}
    modular operator*(const modular&rhs)const{return modular(*this)*=rhs;}
    modular operator/(const modular&rhs)const{return modular(*this)/=rhs;}
    modular pow(int n)const{
        modular res(1),x(*this);
        while(n){
            if(n&1)res*=x;
            x*=x;
            n>>=1;
        }
        return res;
    }
    modular inv()const{return pow(mod-2);}
    /*modular inv()const{
        int x,y;
        int g=extgcd<ll>(v,mod,x,y);
        assert(g==1);
        if(x<0)x+=mod;
        return modular(x);
    }*/
    friend modular operator+(int x,const modular&y){
        return modular(x)+y;
    }
    friend modular operator-(int x,const modular&y){
        return modular(x)-y;
    }
    friend modular operator*(int x,const modular&y){
        return modular(x)*y;
    }
    friend modular operator/(int x,const modular&y){
        return modular(x)/y;
    }
    friend ostream& operator<<(ostream&os,const modular&m){
        return os<<m.v;
    }
    friend istream& operator>>(istream&is,modular&m){
        ll x;is>>x;
        m=modular(x);
        return is;
    }
    bool operator<(const modular&r)const{return v<r.v;}
    bool operator==(const modular&r)const{return v==r.v;}
    bool operator!=(const modular&r)const{return v!=r.v;}
    explicit operator bool()const{
        return v;
    }
};
extern constexpr modinfo base{998244353,3};
//extern constexpr modinfo base{1000000007,0};
//modinfo base{1,0};
using mint=modular<base>;
const int vmax=(1<<21)+10;
mint fact[vmax],finv[vmax],invs[vmax];
void initfact(){
    fact[0]=1;
    rng(i,1,vmax){
        fact[i]=fact[i-1]*i;
    }
    finv[vmax-1]=fact[vmax-1].inv();
    for(int i=vmax-2;i>=0;i--){
        finv[i]=finv[i+1]*(i+1);
    }
    for(int i=vmax-1;i>=1;i--){
        invs[i]=finv[i]*fact[i-1];
    }
}
mint choose(int n,int k){
    return fact[n]*finv[n-k]*finv[k];
}
mint binom(int a,int b){
    return fact[a+b]*finv[a]*finv[b];
}
mint catalan(int n){
    return binom(n,n)-(n-1>=0?binom(n-1,n+1):0);
}
/*
const int vmax=110;
mint binbuf[vmax][vmax];
mint choose(int n,int k){
    return binbuf[n-k][k];
}
mint binom(int a,int b){
    return binbuf[a][b];
}
void initfact(){
    binbuf[0][0]=1;
    rep(i,vmax)rep(j,vmax){
        if(i)binbuf[i][j]+=binbuf[i-1][j];
        if(j)binbuf[i][j]+=binbuf[i][j-1];
    }
}
*/
//VERIFY: yosupo
mint det(vvc<mint> a){
    const int n=a.size();
    mint ans(1);
    rep(i,n){
        rng(j,i+1,n)if(a[j][i].v){
            ans=-ans;
            swap(a[j],a[i]);
            break;
        }
        if(!a[i][i].v)return 0;
        ans*=a[i][i];
        rng(j,i+1,n){
            mint w=-a[j][i]/a[i][i];
            rng(k,i,n)
                a[j][k]+=a[i][k]*w;
        }
    }
    return ans;
}
//CF459D
mint eval(const vc<mint>&f,mint x){
    mint a=0;
    per(i,si(f)){
        a*=x;
        a+=f[i];
    }
    return a;
}
vc<mint> mult_poly(const vc<mint>&a,const vc<mint>&b){
    int n=si(a),m=si(b);
    vc<mint> c(n+m-1);
    rep(i,n)rep(j,m)c[i+j]+=a[i]*b[j];
    return c;
}
vc<mint> pow_poly(vc<mint> a,int n){
    vc<mint> res{1};
    while(n){
        if(n&1)res=mult_poly(res,a);
        n>>=1;
        if(n)a=mult_poly(a,a);
    }
    return res;
}
vc<mint> integrate(const vc<mint>&a){
    int n=si(a);
    vc<mint> c(n+1);
    rep(i,n)c[i+1]=invs[i+1]*a[i];
    return c;
}
//CF459D
vc<mint> interpolate_f(const vc<mint>&x,const vc<mint>&y){
    int n=si(x);
    assert(si(y)==n);
    vc<mint> res(n);
    vc<mint> cur(n+1);
    cur[0]=1;
    rep(i,n){
        per(j,i+1){
            cur[j+1]+=cur[j];
            cur[j]*=-x[i];
        }
    }
    vc<mint> tmp(n);
    rep(i,n){
        mint pre=0;
        per(j,n)pre=tmp[j]=cur[j+1]+pre*x[i];
        mint w=y[i]/eval(tmp,x[i]);
        rep(j,n)res[j]+=tmp[j]*w;
    }
    return res;
}
//SRM551H
struct matrix_tree{
    vvc<mint> w;
    matrix_tree(int n):w(n-1,vc<mint>(n-1)){}
    void ae(int a,int b){
        if(a>b)swap(a,b);
        if(a<si(w))w[a][a]+=1;
        if(b<si(w)){
            w[a][b]-=1;
            w[b][a]-=1;
            w[b][b]+=1;
        }
    }
    mint calc(){
        return det(w);
    }
};
//VERIFY: yosupo
//KUPC2017J
//AOJDSL1A
//without rank
struct unionfind{
    vi p,s;
    int c;
    unionfind(int n):p(n,-1),s(n,1),c(n){}
    int find(int a){
        return p[a]==-1?a:(p[a]=find(p[a]));
    }
    //set b to a child of a
    bool unite(int a,int b){
        a=find(a);
        b=find(b);
        if(a==b)return false;
        p[b]=a;
        s[a]+=s[b];
        c--;
        return true;
    }
    bool same(int a,int b){
        return find(a)==find(b);
    }
    int sz(int a){
        return s[find(a)];
    }
};
void slv(){
    int n,m;cin>>n>>m;
    unionfind uf(n);
    vvc<bool> adj(n,vc<bool>(n));
    rep(_,m){
        int a,b;cin>>a>>b;
        a--;b--;
        adj[a][b]=true;
        uf.unite(a,b);
    }
    if(uf.c==1){
        vc<mint> xs(n);rep(i,n)xs[i]=i;
        vc<mint> ys(n);
        rep(x,n){
            vvc<mint> mat(n-1,vc<mint>(n-1));
            rep(i,n)rng(j,i+1,n){
                int val=adj[i][j]?1:x;
                mat[i][i]+=val;
                if(j<n-1){
                    mat[j][j]+=val;
                    mat[i][j]-=val;
                    mat[j][i]-=val;
                }
            }
            ys[x]=det(mat);
        }
        auto f=interpolate_f(xs,ys);
        print(0);
        print(f[0]+f[1]);
    }else{
        vvc<int> idx(n);
        rep(i,n)idx[uf.find(i)].pb(i);
        int ans=n*n;
        vi ls;
        mint way=1;
        rep(r,n)if(uf.find(r)==r){
            int s=uf.sz(r);
            ls.pb(s);
            ans-=s*s;
            matrix_tree mt(s);
            rep(i,s)rep(j,s)if(adj[idx[r][i]][idx[r][j]])
                mt.ae(i,j);
            way*=mt.calc();
        }
        sort(all(ls),greater<int>());
        int a=ls[0],b=ls[1];
        ans-=a*b*2;
        if(a==b){
            int num=count(all(ls),a);
            way*=num*(num-1)/2*a*a;
        }else{
            int num=count(all(ls),b);
            way*=num*a*b;
        }
        print(ans);
        print(way);
    }
}
signed main(){
    cin.tie(0);
    ios::sync_with_stdio(0);
    cout<<fixed<<setprecision(20);
    
    //int t;cin>>t;rep(_,t)
    slv();
}
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