#include "bits/stdc++.h"
using namespace std;
using     ll=long long;
using    vll=vector<   ll>;
using   vvll=vector<  vll>;
using  vvvll=vector< vvll>;
using vvvvll=vector<vvvll>;
using     dd=double;
using    vdd=vector<   dd>;
using   vvdd=vector<  vdd>;
using pll=pair<ll,ll>; using tll=tuple<ll,ll,ll>; using qll=tuple<ll,ll,ll,ll>;
using   vpll=vector<  pll>;

constexpr ll INF = 1LL << 60;
struct Fast{ Fast(){ cin.tie(0); ios::sync_with_stdio(false); cout<<fixed<<setprecision(numeric_limits<double>::max_digits10); } } fast;
#define REPS(i, S, E) for (ll i = (S); i <= (E); i++)
#define REP(i, N) REPS(i, 0, (N)-1)
#define DEPS(i, S, E) for (ll i = (E); i >= (S); i--)
#define DEP(i, N) DEPS(i, 0, (N)-1)
#define rep(i, S, E)  for (ll i = (S); i <= (E); i++)
#define dep(i, E, S)  for (ll i = (E); i >= (S); i--)
#define each(e, v) for (auto&& e : v)
#define ALL(v) (v).begin(), (v).end()
#define RALL(v) (v).rbegin(), (v).rend()
template<class T> inline bool chmax(T &a, T b) { if (a < b) { a = b; return true; }return false; }
template<class T> inline bool chmin(T &a, T b) { if (a > b) { a = b; return true; }return false; }
template<class T> inline T MaxE(vector<T>&v,ll S,ll E){ T m=v[S]; rep(i,S,E)chmax(m,v[i]); return m; }
template<class T> inline T MinE(vector<T>&v,ll S,ll E){ T m=v[S]; rep(i,S,E)chmin(m,v[i]); return m; }
template<class T> inline T MaxE(vector<T> &v) { return MaxE(v,0,(ll)v.size()-1); }
template<class T> inline T MinE(vector<T> &v) { return MinE(v,0,(ll)v.size()-1); }
template<class T> inline T Sum(vector<T> &v,ll S,ll E){ T s=T(); rep(i,S,E)s+=v[i]; return s; }
template<class T> inline T Sum(vector<T> &v) { return Sum(v,0,v.size()-1); }
template<class T> inline ll sz(T &v){ return (ll)v.size(); }
inline ll CEIL(ll a,ll b){ return (a<0) ? -(-a/b) : (a+b-1)/b; }
inline ll FLOOR(ll a,ll b){ return -CEIL(-a,b); }

template<ll MOD> struct mll_{
	ll val;
	mll_(ll v = 0): val(v % MOD){ if (val < 0) val += MOD; }
	mll_ operator - () const { return -val; }
	mll_ operator + (const mll_ &b) const { return val + b.val; }
	mll_ operator - (const mll_ &b) const { return val - b.val; }
	mll_ operator * (const mll_ &b) const { return val * b.val; }
	mll_ operator / (const mll_ &b) const { return mll_(*this) /= b; }
	mll_ operator + (ll b) const { return *this + mll_(b); }
	mll_ operator - (ll b) const { return *this - mll_(b); }
	mll_ operator * (ll b) const { return *this * mll_(b); }
	friend mll_ operator + (ll a,const mll_ &b) { return b + a; }
	friend mll_ operator - (ll a,const mll_ &b) { return -b + a; }
	friend mll_ operator * (ll a,const mll_ &b) { return b * a; }
	friend mll_ operator / (ll a,const mll_ &b) { return mll_(a)/b; }
	mll_ &operator += (const mll_ &b) { val=(val+b.val)%MOD; return *this; }
	mll_ &operator -= (const mll_ &b) { val=(val+MOD-b.val)%MOD; return *this; }
	mll_ &operator *= (const mll_ &b) { val=(val*b.val)%MOD; return *this; }
	mll_ &operator /= (const mll_ &b) {
		ll c=b.val,d=MOD,u=1,v=0;
		while (d){
			ll t = c / d;
			c -= t * d; swap(c,d);
			u -= t * v; swap(u,v);
		}
		val = val * u % MOD;
		if (val < 0) val += MOD;
		return *this;
	}
	mll_ &operator += (ll b) { return *this += mll_(b); }
	mll_ &operator -= (ll b) { return *this -= mll_(b); }
	mll_ &operator *= (ll b) { return *this *= mll_(b); }
	mll_ &operator /= (ll b) { return *this /= mll_(b); }
	bool operator == (const mll_ &b) const { return val == b.val; }
	bool operator != (const mll_ &b) const { return val != b.val; }
	bool operator == (ll b) const { return *this == mll_(b); }
	bool operator != (ll b) const { return *this != mll_(b); }
	friend bool operator == (ll a,const mll_ &b) { return mll_(a) == b.val; }
	friend bool operator != (ll a,const mll_ &b) { return mll_(a) != b.val; }
	friend ostream &operator << (ostream &os,const mll_ &a) { return os << a.val; }
	friend istream &operator >> (istream &is,mll_ &a) { return is >> a.val; }
	static mll_ Combination(ll a,ll b){
		chmin(b,a-b);
		if (b<0) return mll_(0);
		mll_ c = 1;
		rep(i,0,b-1) c *= a-i;
		rep(i,0,b-1) c /= i+1;
		return c;
	}
};
using mll = mll_<998244353LL>;
using vmll    = std::vector<mll>;
using vvmll   = std::vector<vmll>;
using vvvmll  = std::vector<vvmll>;
using vvvvmll = std::vector<vvvmll>;

template<class T> struct MatG{
	ll h=0, w=0; //h行w列
	vector<vector<T>> mat;
	MatG(){}
	MatG(ll h_, ll w_, T x) { init(h_, w_, x); }
	MatG(ll h_, ll w_) { init(h_, w_); }
	MatG(ll h_, ll w_, string c) { init(h_, w_, c); }
	void init(ll h_, ll w_, T x){ h=h_; w=w_; mat.assign(h, vector<T>(w,x)); }
	void init(ll h_, ll w_){ init(h_,w_,T()); }
	void init(ll h_, ll w_, string c){ init(h_, w_); if(c=="E")E(); }
	ll H() const { return h; }
	ll W() const { return w; }
	bool invalid() const { mat.empty(); }
	vector<T> &operator[](ll i) { return mat[i]; }
	const vector<T> &operator[](ll i) const { return mat[i]; }
	MatG<T> &operator+=(const MatG<T> &B) {REP(i,h)REP(j,w) mat[i][j]+=B[i][j];return *this;}
	MatG<T> operator+(const MatG<T> &B) const {return MatG<T>(*this) += B;}
	MatG<T> operator*(const MatG<T> &B) const {
		MatG<T> ret(h, B.W());
		REP(i, h) REP(j, B.W()) REP(k, w) ret[i][j] += mat[i][k] * B[k][j];
		return move(ret);
	}
	vector<T> operator*(const vector<T> &v) const {
		vector<T> ret(v.size());
		REP(i, this->h) REP(j, this->w) ret[i] += this->mat[i][j] * v[j];
		return move(ret);
	}
	MatG<T> Pow(ll N) const {
		MatG<T> ret(*this), a(*this);
		for (ll n=N-1; n>0; n>>=1, a=a*a){ if (n&1) ret=ret*a; }
		return move(ret);
	}
	MatG<T> t() const {
		MatG<T> ret(this->w, this->h);
		REP(i, this->w) REP(j, this->h) ret[i][j] = this->mat[j][i];
		return move(ret);
	}
	void E(){ rep(i, 0, min(h,w)-1) mat[i][i]=1; }
#if defined(_DEBUG)
	void dump() { ::dump(mat); }
#endif
	MatG(MatG<T> &&B){ *this=move(B); } //以下、ムーブ対応
	MatG(MatG<T> const &B){ *this=B; }
	MatG<T> &operator=(MatG<T> &&B){ h=B.h; w=B.w; mat.swap(B.mat); return *this; }
	MatG<T> &operator=(MatG<T> const &B){ h=B.h; w=B.w; mat=B.mat; return *this; }
};
using Mat = MatG<mll>;


#if 0
#include <atcoder/all>
using namespace atcoder;
#endif

vvll cinGraph(ll nodeNum,ll edgeNum,bool isDirected){//無向false、有向true
	vvll to(nodeNum);
	rep(i,0,edgeNum-1){
		ll v,u; cin >> v >> u;
		v--; u--;
		to[v].push_back(u);
		if (!isDirected) to[u].push_back(v);
	}
	return move(to);
}

struct ConnectedComponents{
	vvll &to; ll n; vll ccids;
	ConnectedComponents(vvll &to):to(to),n((ll)to.size()),ccids(n,-1){}
	void dfs(ll v){
		each(u,to[v]){
			if (ccids[u]!=-1)continue;
			ccids[u]=ccids[v];
			dfs(u);
		}
	}
	pair<ll,vll> get(){
		ll nm=0;
		rep(v,0,n-1){
			if (ccids[v]!=-1)continue;
			ccids[v]=nm++;
			dfs(v);
		}
		return {nm,move(ccids)};
	}
};


pair<ll,mll> GaussJordan(Mat &mat, bool isExtended, bool isTriangle){
	ll H=mat.H(), W=mat.W();
	mll det=1;
	ll rank=0;
	rep(j,0,W-1-isExtended){
		ll pivot=-1;
		rep(i,rank,H-1){
			if (mat[i][j]!=0){
				pivot=i; break;
			}
		}
		if (pivot==-1){
			det=0; continue;
		}
		if (rank<pivot){
			swap(mat[rank],mat[pivot]);
			det=-det;
		}
		det*=mat[rank][j];
		mll inv=mll(1)/mat[rank][j];
		rep(jj,j,W-1) mat[rank][jj]*=inv;

		rep(i,isTriangle?rank+1:0,H-1){
			mll tim=mat[i][j];
			if (i==rank || tim==0) continue;
			rep(jj,j,W-1) mat[i][jj]-=mat[rank][jj]*tim;
		}
		if (H==++rank) break;
	}
	return {rank,det};
}

pair<Mat,mll> MatInverse(Mat &A){//正方行列限定
	ll N=A.H();
	Mat B(N,2*N);
	rep(i,0,N-1)rep(j,0,N-1) B[i][j]=A[i][j];
	rep(i,0,N-1) B[i][N+i]=1;
	mll det; tie(ignore,det)=GaussJordan(B,false,false);
	if (det==0) return {Mat(),det};
	Mat ret(N,N);
	rep(i,0,N-1)rep(j,0,N-1) ret[i][j]=B[i][N+j];
	return {move(ret),det};
}

mll countST(ll N,vvll &to,ll id,vll &cids){
	unordered_map<ll,ll> mp;
	vll tr;
	ll idx=0;
	rep(v,0,N-1){
		if (cids[v]!=id) continue;
		mp[v]=idx++;
		tr.push_back(v);
	}
	ll mm=(ll)tr.size();
	if (mm==1)return mll(1);
	
	Mat L(mm-1,mm-1);//ラプラシアン行列の端を削ったもの
	rep(i,0,mm-2){
		ll v=tr[i];
		each(u,to[v]){
			ll idx=mp[u];
			if (idx==mm-1)continue;
			L[i][idx]=-1;
		}
		L[i][i]=(ll)to[v].size();
	}
	return GaussJordan(L,false,true).second;
}

mll calc(ll N,vvll &to){
	Mat L(N,N);
	rep(v,0,N-1){
		each(u,to[v]) L[v][u]=-1;
		L[v][v]=(ll)to[v].size();
	}
	mll ans=0;
	rep(v,1,N-1){
		Mat B=L;
		B.mat.erase(B.mat.begin()+v);
		each(e,B.mat) e.erase(e.begin()+v);
		B.h--; B.w--;
		Mat C; mll det; tie(C,det)=MatInverse(B);
		if (v==1) ans+=det; //任意道路不使用分のカウント

		rep(u,0,v-1){
			if (L[u][v]!=0) continue;
			ans+=C[u][u]*det;
		}
	}
	return ans;
}

pll solve(ll N,ll M,vvll &to)
{
	ll cnm; vll cids; tie(cnm,cids)=ConnectedComponents(to).get();
	if (cnm==1){
		mll ans = calc(N,to);
		return {0,ans.val};
	}

	vll csz(cnm);
	each(e,cids) csz[e]++;
	sort(ALL(csz));

	ll fuben=0;
	{
		ll tmp=csz[cnm-1]+csz[cnm-2];
		fuben+=(N-tmp)*tmp;
		dep(i,cnm-3,0) fuben+=(N-csz[i])*csz[i];
	}
	ll x=-1,y=-1;
	ll p=0,q=0;
	while (!csz.empty()){
		ll s=csz.back();  csz.pop_back();
		if (x==-1) x=s;
		if (x==s){
			p++; continue;
		}
		if (y==-1) y=s;
		if (y==s){
			q++; continue;
		}
		break;
	}

	mll ans=1;
	rep(id,0,cnm-1) ans*=countST(N,to,id,cids);
	if (p>=2){
		ans*=x*x*p*(p-1)/2;
	}
	else{
		ans*=x*y*q;
	}
	return {fuben,ans.val};
}

pll solv2(ll N,ll M,vvll &to){//愚直解
	vvll w(N,vll(N));
	rep(v,0,N-1)each(u,to[v]) w[u][v]=1;

	vpll idxes;
	map<pll,ll> mp;
	rep(v,0,N-1)rep(u,v+1,N-1){
		mp[{v,u}]=(ll)idxes.size();
		idxes.emplace_back(v,u);
	}
	ll mm=(ll)idxes.size();

	pll fubenRdMin{INF,INF};
	ll cnt=0;
	rep(s,0,(1LL<<mm)-1){
		ll ck=0;
		dep(i,mm-1,0){
			if (!(s&(1LL<<i)))continue;
			ll v,u;  tie(v,u) = idxes[i];
			if (w[v][u]==0) ck++;
			if (ck==2){
				s+=(1LL<<i)-1;
				break;
			}
		}
		if (ck==2) continue;

		vvll t2(N);
		rep(i,0,mm-1){
			if (!(s&(1LL<<i)))continue;
			ll v,u;  tie(v,u) = idxes[i];
			t2[v].push_back(u);
			t2[u].push_back(v);
		}
		ll cnm; vll cids; tie(cnm,cids)=ConnectedComponents(t2).get();
		vll csz(cnm);
		each(e,cids) csz[e]++;
		ll fuben=0;
		rep(i,0,cnm-1) fuben+=(N-csz[i])*csz[i];

		pll fubenRd{fuben,bitset<64>(s).count()};
		if (chmin(fubenRdMin,fubenRd)) cnt=1;
		else if (fubenRdMin==fubenRd) cnt++;
	}
	return {fubenRdMin.first, cnt};
}

void solvecomp(ll N,ll M,vvll &to){
	pll ret=solve(N,M,to);
#if 1
	cout << ret.first << '\n';
	cout << ret.second << '\n';
#else
	pll re2=solv2(N,M,to);
	if (ret!=re2){
		cout << "\n======= diff ========\n";
		cout << ret.first << ' ' << ret.second << '\n';
		cout << re2.first << ' ' << re2.second << '\n';
	}
#endif
}

void cin2solve(){
	ll N,M;  cin >> N >> M;
	vvll to = cinGraph(N,M,false);
	solvecomp(N,M,to);
}

void gene(){
	ll N=7;
	vpll idxes;
	map<pll,ll> mp;
	rep(v,0,N-1)rep(u,v+1,N-1){
		mp[{v,u}]=(ll)idxes.size();
		idxes.emplace_back(v,u);
	}
	ll mm=(ll)idxes.size();

	rep(s,0,(1LL<<mm)-1){
		vvll to(N);
		rep(i,0,mm-1){
			if (!(s&(1LL<<i)))continue;
			ll v,u;  tie(v,u) = idxes[i];
			to[v].push_back(u);
			to[u].push_back(v);
		}
		ll M=bitset<64>(s).count();
		printf("\b\b\b\b\b\b\b\b\b\b%10lld",s);
		solvecomp(N,M,to);
	}
}

int main(){
#if 1
	//solve();
	cin2solve();
	//gene();
#else
	ll t;  cin >> t;
	rep(i, 0, t-1){
		solve();
	}
#endif
	return 0;
}