#ifndef MYLOCAL
//# pragma GCC target("avx2")//yukiではNG
# pragma GCC optimize("O3")
# pragma GCC optimize("unroll-loops")
#endif
#if defined(NDEBUG)
#undef NDEBUG
#endif
#include "bits/stdc++.h"
using namespace std;
using ll=long long;
using dd=long double;
using pll=pair<ll,ll>;
using tll=tuple<ll,ll,ll>;
using qll=tuple<ll,ll,ll,ll>;
using namespace chrono;
constexpr ll INF = 1201001001001001001;
struct Fast{ Fast(){ cin.tie(0); ios::sync_with_stdio(false); cout<<fixed<<setprecision(numeric_limits<double>::max_digits10); } } fast;
#define EXPAND( x ) x//VS用おまじない
#define overload3(_1,_2,_3,name,...) name
#define overload4(_1,_2,_3,_4,name,...) name
#define overload5(_1,_2,_3,_4,_5,name,...) name
#define rep1(N)          for (ll dmyi = 0; dmyi < (N); dmyi++)
#define rep2(i, N)       for (ll i = 0; i < (N); i++)
#define rep3(i, S, E)    for (ll i = (S); i <= (E); i++)
#define rep4(i, S, E, t) for (ll i = (S); i <= (E); i+=(t))
#define rep(...) EXPAND(overload4(__VA_ARGS__,rep4,rep3,rep2,rep1)(__VA_ARGS__))
#define dep3(i, E, S)    for (ll i = (E); i >= (S); i--)
#define dep4(i, E, S, t) for (ll i = (E); i >= (S); i-=(t))
#define dep(...) EXPAND(overload4(__VA_ARGS__, dep4, dep3,_,_)(__VA_ARGS__))
#define ALL1(v)     (v).begin(),     (v).end()
#define ALL2(v,E)   (v).begin(),     (v).begin()+((E)+1)
#define ALL3(v,S,E) (v).begin()+(S), (v).begin()+((E)+1)
#define all(...) EXPAND(overload3(__VA_ARGS__, ALL3, ALL2, ALL1)(__VA_ARGS__))
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> [[nodiscard]] inline T limithi(T a,T b){ return min(a,b); }
template<class T> [[nodiscard]] inline T limitlo(T a,T b){ return max(a,b); }
template<class T> inline bool chlimithi(T &a,T b){ return chmin(a,b); }
template<class T> inline bool chlimitlo(T &a,T b){ return chmax(a,b); }
template<class T> inline auto maxe(T &&v,ll S,ll E){ return *max_element(all(v,S,E)); }
template<class T> inline auto maxe(T &&v){ return *max_element(all(v)); }
template<class T> inline auto mine(T &&v,ll S,ll E){ return *min_element(all(v,S,E)); }
template<class T> inline auto mine(T &&v){ return *min_element(all(v)); }
template<class T,class U=typename remove_reference<T>::type::value_type>
inline U sum(T &&v,ll S,ll E) {return accumulate(all(v,S,E),U());}
template<class T> inline auto sum(T &&v) {return sum(v,0,v.end()-v.begin()-1);}
template<class T> inline ll sz(T &&v){ return (ll)v.size(); }

//cin
struct cinutil{
    template<class T> static void cin1core(T &a){ cin>>a; }
    template<class T,class S> static void cin1core(pair<T,S> &a){
        cin1core(a.first),cin1core(a.second);
    }
    template<class... Args> static void cin1core(tuple<Args...> &a){
        cinTplRec<tuple<Args...>,sizeof...(Args)-1>()(a);
    }
    template<class T,size_t N>
    static void cin1core(array<T,N> &a){ for (int i=0; i<(int)N; ++i) cin>>a[i]; }
private:
    template<class Tpl,int i> struct cinTplRec{
        void operator()(Tpl &a){ cinTplRec<Tpl,i-1>()(a); cin1core(get<i>(a)); }
    };
    template<class Tpl> struct cinTplRec<Tpl,0>{
        void operator()(Tpl &a){ cin1core(get<0>(a)); }
    };
};
template<class T> T cin1(){ T a; cinutil::cin1core(a); return a; }
template<class... Args> tuple<Args...> cins(){ return cin1<tuple<Args...>>(); }

//cout
template<class T,class S> inline ostream &operator<<(ostream &os,const pair<T,S> &a){ return os << a.first << ' ' << a.second; }
template<class T,class S,class R> inline ostream &operator<<(ostream &os,const tuple<T,S,R> &a){ return os << get<0>(a) << ' ' << get<1>(a) << ' ' << get<2>(a); }
template<class T,class S,class R,class Q> inline ostream &operator<<(ostream &os,const tuple<T,S,R,Q> &a){ return os << get<0>(a) << ' ' << get<1>(a) << ' ' << get<2>(a) << ' ' << get<3>(a); }
template<class T> inline ostream &operator<<(ostream &os,const vector<T> &a){ for (ll i=0; i<(ll)a.size(); i++) os<<(i>0?" ":"")<<a[i];  return os; }

inline struct{
  system_clock::time_point st = system_clock::now();
  ll operator()()const{return duration_cast<microseconds>(system_clock::now()-st).count()/1000;}
} timeget;


template<long long MOD> struct mll_{
    using Int = long long;
    using ll = long long;
    ll val_=0;
    /*---- utility ----*/
    mll_ &norm(){ return normR().normS(); }//正規化
    mll_ &normR(){ val_%=MOD; return *this; }//剰余正規化のみ
    mll_ &normS(){ if (val_<0) val_+=MOD; return *this; }//正負正規化のみ
    mll_ &normP(){ if (val_>=MOD) val_-=MOD; return *this; }//加算時正規化
    mll_ &invsg(){ val_=-val_; return normS(); }//正負反転
    ll modinv(int a){//a^-1 mod MOD
        int ypre=0,y=1,apre=MOD;
        while (a>1){
            int t=apre/a;
            apre-=a*t,swap(a,apre);
            ypre-=y*t,swap(y,ypre);
        }
        return y<0 ? y+MOD : y;
    }
    /*---- I/F ----*/
    mll_(){}
    mll_(ll v): val_(v){ norm(); }
    mll_(ll v,bool b): val_(v){} //正規化無のコンストラクタ
    Int val()const{ return (Int)val_; }
    bool isnone() const { return val_==-1; } //true:値なし
    mll_ &none() { val_=-1; return *this; } //値なしにする
    mll_ &inv(){ val_=modinv((int)val_); return *this; }
    mll_ &operator+=(mll_ b){ val_+=b.val_; return normP(); }
    mll_ &operator-=(mll_ b){ val_-=b.val_; return normS(); }
    mll_ &operator*=(mll_ b){ val_*=b.val_; return normR(); }
    mll_ &operator/=(mll_ b){ return *this*=b.inv(); }
    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); }
    mll_ operator-()const{ return mll_(*this).invsg(); }
    mll_ operator+(mll_ b)const{ return mll_(*this)+=b; }
    mll_ operator-(mll_ b)const{ return mll_(*this)-=b; }
    mll_ operator*(mll_ b)const{ return mll_(*this)*=b; }
    mll_ operator/(mll_ b)const{ return mll_(*this)/=b; }
    mll_ operator+(ll b)const{ return mll_(*this)+=b; }
    mll_ operator-(ll b)const{ return mll_(*this)-=b; }
    mll_ operator*(ll b)const{ return mll_(*this)*=b; }
    mll_ operator/(ll b)const{ return mll_(*this)/=b; }
    friend mll_ operator+(ll a,mll_ b){ return b+a; }
    friend mll_ operator-(ll a,mll_ b){ return -b+a; }
    friend mll_ operator*(ll a,mll_ b){ return b*a; }
    friend mll_ operator/(ll a,mll_ b){ return mll_(a)/b; }
    bool operator==(mll_ b)const{ return val_==b.val_; }
    bool operator!=(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,mll_ b){ return mll_(a)==b; }
    friend bool operator!=(ll a,mll_ b){ return mll_(a)!=b; }
    friend ostream &operator<<(ostream &os,mll_  a){ return os << a.val_; }
    friend istream &operator>>(istream &is,mll_ &a){ return is >> a.val_; }
    mll_ pow(ll k)const{
        mll_ ret(1,false),a(*this);
        for (; k>0; k>>=1,a*=a) if (k&1)ret*=a;
        return ret;
    }
    static constexpr int mod() { return MOD; }
    //enum{ modll=MOD };
};


template<class T> struct Vector: vector<T>{
  using Int = long long;
  using vT=vector<T>;
  using cvT=const vector<T>;
  using cT=const T;
  using vT::vT; //親クラスのコンストラクタの隠蔽を回避
  using vT::begin,vT::end,vT::insert,vT::erase;
  auto it(Int i){ return begin()+i; }
  auto it(Int i)const{ return begin()+i; }
  Vector(cvT& b):vT(b){}
  Vector(vT&& b):vT(move(b)){}
  Vector(int n,cT& x):vT(n,x){}// ┬ 型推論のためラッパー
  Vector(long long n,cT& x):vT(n,x){}
  template<class S> Vector(const Vector<S>& b):vT(b.begin(),b.end()){}
  template<class S> Vector(const vector<S>& b):vT(b.begin(),b.end()){}
  Vector(Int n,T s,T d){ iota(n,s,d); }
  Vector(Int n,function<T(Int)> g):vT(n){ for(Int i=0;i<n;++i) (*this)[i]=g(i); }
  Vector &operator+=(cvT &b){ assert(size()==b.size()); for(Int i=0;i<size();++i) (*this)[i]+=b[i]; return *this; }
  Vector &operator-=(cvT &b){ assert(size()==b.size()); for(Int i=0;i<size();++i) (*this)[i]-=b[i]; return *this; }
  Vector &operator*=(cvT &b){ assert(size()==b.size()); for(Int i=0;i<size();++i) (*this)[i]*=b[i]; return *this; }
  Vector &operator/=(cvT &b){ assert(size()==b.size()); for(Int i=0;i<size();++i) (*this)[i]/=b[i]; return *this; }
  Vector &operator%=(cvT &b){ assert(size()==b.size()); for(Int i=0;i<size();++i) (*this)[i]%=b[i]; return *this; }
  Vector &operator+=(const Vector<T> &b){ return *this+=(cvT&)b; }
  Vector &operator-=(const Vector<T> &b){ return *this-=(cvT&)b; }
  Vector &operator*=(const Vector<T> &b){ return *this*=(cvT&)b; }
  Vector &operator/=(const Vector<T> &b){ return *this/=(cvT&)b; }
  Vector &operator%=(const Vector<T> &b){ return *this%=(cvT&)b; }
  Vector operator+(cvT &b){ return Vector(*this)+=b; }
  Vector operator-(cvT &b){ return Vector(*this)-=b; }
  Vector operator*(cvT &b){ return Vector(*this)*=b; }
  Vector operator/(cvT &b){ return Vector(*this)/=b; }
  Vector operator%(cvT &b){ return Vector(*this)%=b; }
  Vector operator+(const Vector<T> &b){ return Vector(*this)+=b; }
  Vector operator-(const Vector<T> &b){ return Vector(*this)-=b; }
  Vector operator*(const Vector<T> &b){ return Vector(*this)*=b; }
  Vector operator/(const Vector<T> &b){ return Vector(*this)/=b; }
  Vector operator%(const Vector<T> &b){ return Vector(*this)%=b; }
  template<class S> Vector &operator+=(S x){ for(T &e: *this) e+=x;  return *this; }
  template<class S> Vector &operator-=(S x){ for(T &e: *this) e-=x;  return *this; }
  template<class S> Vector &operator*=(S x){ for(T &e: *this) e*=x;  return *this; }
  template<class S> Vector &operator/=(S x){ for(T &e: *this) e/=x;  return *this; }
  template<class S> Vector &operator%=(S x){ for(T &e: *this) e%=x;  return *this; }
  template<class S> Vector operator+(S x)const{ return Vector(*this)+=x; }
  template<class S> Vector operator-(S x)const{ return Vector(*this)-=x; }
  template<class S> Vector operator*(S x)const{ return Vector(*this)*=x; }
  template<class S> Vector operator/(S x)const{ return Vector(*this)/=x; }
  template<class S> Vector operator%(S x)const{ return Vector(*this)%=x; }
  Vector &operator--(int){ return *this-=1; }
  Vector &operator++(int){ return *this+=1; }
  Vector operator-()const{ return Vector(*this)*=-1; }
  template<class S> friend Vector operator-(S x,const Vector &a){ return -a+=x; }
  T& at(Int i){ assert(i>=0); if(n()<=i)vT::resize(i+1); return vT::operator[](i); }
  Vector slice(Int l,Int r,Int d=1)const{
    Vector ret;
    for(Int i=l;(d>0&&i<=r)||(d<0&&r<=i);i+=d) ret.push_back((*this)[i]);
    return ret;
  }
  Int size()const{ return (Int)vT::size(); }
  Int n()const{ return size(); }
  Vector &push_back(cT& x,Int n=1){ for(Int i=0;i<n;++i){ vT::push_back(x); } return *this; }
  Vector &pop_back(Int n=1){ for(Int i=0;i<n;++i){ vT::pop_back(); } return *this; }
  Vector &push_front(cT& x,Int n=1){ this->insert(0,x,n); return *this; }
  Vector &pop_front(Int n=1){ erase(0,n-1); return *this; }
  T pull_back(){ T x=move(vT::back()); vT::pop_back(); return x; }
  T pull_front(){ T x=move(vT::front()); erase(0); return x; }
  Vector &insert(Int i,cT& x,Int n=1){ insert(it(i),n,x); return *this; }
  Vector &insert(Int i,cvT& b){ insert(it(i),b.begin(),b.end()); return *this; }
  Vector &erase(Int i){ erase(it(i)); return *this; }
  Vector &erase(Int l,Int r){ erase(it(l),it(r+1)); return *this; }
  Vector &erase(const Vector<Int> &idxs){
      for (Int I=0; I<idxs.n(); ++I){
          Int l=idxs[I]+1, r = (I<idxs.n()-1) ? idxs[I+1] : this->n();
          copy(it(l),it(r),it(l-I-1));//[l,r)を前にI+1個ずらす
      }
      vT::resize(this->n()-idxs.n());
      return *this;
  }
  Vector &eraseall(cT& x){ return eraseall(0,size()-1,x); }
  Vector &eraseall(Int l,Int r,cT& x){ erase(remove(it(l),it(r+1),x),it(r+1)); return *this; }
  template<class Pr> Vector &eraseif(Pr pr){ return eraseif(0,size()-1,pr); }
  template<class Pr> Vector &eraseif(Int l,Int r,Pr pr){ erase(remove_if(it(l),it(r+1),pr),it(r+1)); return *this; }
  Vector &concat(cvT &b,Int n=1){
    cvT B = (&b==this) ? *this : vT{};
    for(int i=0;i<n;++i) this->insert(size(),(&b==this)?B:b);
    return *this;
  }
  Vector repeat(Int n){ return Vector{}.concat(*this,n); }
  Vector &reverse(Int l=0,Int r=-1){ r+=r<0?size():0; std::reverse(it(l),it(r+1)); return *this; }
  Vector &rotate(Int m){ return rotate(0,size()-1,m); }
  Vector &rotate(Int l,Int r,Int m){ std::rotate(it(l),it(m),it(r+1)); return *this; }
  Vector &sort(Int l=0,Int r=-1){ r+=r<0?size():0; std::sort(it(l),it(r+1)); return *this; }
  Vector &rsort(Int l=0,Int r=-1){ return sort(l,r).reverse(l,r); }
  template<class Pr> Vector &sort(Pr pr){ return sort(0,size()-1,pr); }
  template<class Pr> Vector &sort(Int l,Int r,Pr pr){ std::sort(it(l),it(r+1),pr); return *this; }
  template<int key> Vector &sortbykey(Int l=0,Int r=-1){
    r+=r<0?size():0;
    sort(l,r,[](cT &x,cT &y){return get<key>(x)<get<key>(y);});
    return *this;
  }
  Vector &uniq(){ erase(unique(begin(),end()),end()); return *this; }
  Vector &sortq(){ return sort().uniq(); }
  Vector &fill(cT& x){ return fill(0,size()-1,x); }
  Vector &fill(Int l,Int r,cT& x){ std::fill(it(l),it(r+1),x); return *this; }
  Vector &copy(Int i,cvT &b,Int n=1){//A[i]スタートでbをn回分コピー
      for (int t=0; t<n; ++t) for (int j=0; j<(int)b.size(); ++j){
          if (i>=size()) return *this;
          if (i>=0) (*this)[i]=b[j];
          i++;
      }
      return *this;
  }
  template<class S=Int> Vector &iota(Int n,T s=0,S d=1){
    vT::resize(n);
    if(n==0) return *this;
    (*this)[0]=s;
    for(int i=1;i<n;++i) (*this)[i]=(*this)[i-1]+d;
    return *this;
  }
  Int count(cT& x)const{ return count(0,size()-1,x); }
  Int count(Int l,Int r,cT& x)const{ return Int(std::count(it(l),it(r+1),x)); }
  template<class Pr> Int countif(Pr pr)const{ return countif(0,size()-1,pr); }
  template<class Pr> Int countif(Int l,Int r,Pr pr)const{ return Int(count_if(it(l),it(r+1),pr)); }
  Int find(cT& x)const{ return find(0,size()-1,x); }
  Int find(Int l,Int r,cT& x)const{ return Int(std::find(it(l),it(r+1),x)-begin()); }
  Int rfind(cT& x)const{ return rfind(0,size()-1,x); }
  Int rfind(Int l,Int r,cT& x)const{
      for (int i=r;i>=l;--i) if ((*this)[i]==x) return i;
      return l-1;
  }
  template<class Pr> Int findif(Pr pr)const{ return findif(0,size()-1,pr); }
  template<class Pr> Int findif(Int l,Int r,Pr pr)const{ return Int(find_if(it(l),it(r+1),pr)-begin()); }
  Vector<Int> findall(cT& x)const{ return findall(0,size()-1,x); }
  Vector<Int> findall(Int l,Int r,cT& x)const{ return findallif(l,r,[&](cT& y){return y==x;}); }
  template<class Pr> Vector<Int> findallif(Pr pr)const{ return findallif(0,size()-1,pr); }
  template<class Pr> Vector<Int> findallif(Int l,Int r,Pr pr)const{
    Vector<Int> ret;
    for(Int i=l;i<=r;++i) if(pr((*this)[i])) ret.push_back(i);
    return ret;
  }
  Int  flooridx(cT& x)const{ return Int(upper_bound(begin(),end(),x)-begin()-1); }
  Int   ceilidx(cT& x)const{ return Int(lower_bound(begin(),end(),x)-begin()); }
  Int  leftnmof(cT& x)const{ return flooridx(x)+1; }
  Int rightnmof(cT& x)const{ return size()-ceilidx(x); }
  bool contains(cT& x)const{ Int i=flooridx(x); return i>=0 && (*this)[i]==x; }
  template<class Pr> Int  flooridx(cT& x,Pr pr)const{ return Int(upper_bound(begin(),end(),x,pr)-begin()-1); }
  template<class Pr> Int   ceilidx(cT& x,Pr pr)const{ return Int(lower_bound(begin(),end(),x,pr)-begin()); }
  template<class Pr> Int  leftnmof(cT& x,Pr pr)const{ return flooridx(x,pr)+1; }
  template<class Pr> Int rightnmof(cT& x,Pr pr)const{ return size()-ceilidx(x,pr); }
  template<class Pr> bool contains(cT& x,Pr pr)const{ Int i=flooridx(x,pr); return i>=0 && (*this)[i]==x; }

  template<class S> using VV    = Vector<Vector<S>>; template<class S> using sVV    = vector<vector<S>>;
  template<class S> using VVV   = Vector<VV<S>>;     template<class S> using sVVV   = vector<sVV<S>>;
  template<class S> using VVVV  = Vector<VVV<S>>;    template<class S> using sVVVV  = vector<sVVV<S>>;
  template<class S> using VVVVV = Vector<VVVV<S>>;   template<class S> using sVVVVV = vector<sVVVV<S>>;
  auto tostd()const{ return tov(*this); }
  template <class S> static vector<S> tov(const Vector<S>&v){ return v; }
  template <class S> static sVV<S>    tov(const VV<S>    &v){ sVV<S>    ret; for(auto&& e:v) ret.push_back(e);         return ret; }
  template <class S> static sVVV<S>   tov(const VVV<S>   &v){ sVVV<S>   ret; for(auto&& e:v) ret.push_back(e.tostd()); return ret; }
  template <class S> static sVVVV<S>  tov(const VVVV<S>  &v){ sVVVV<S>  ret; for(auto&& e:v) ret.push_back(e.tostd()); return ret; }
  template <class S> static sVVVVV<S> tov(const VVVVV<S> &v){ sVVVVV<S> ret; for(auto&& e:v) ret.push_back(e.tostd()); return ret; }
};


#if 1
#define MODLL (1000000007LL)
#else
#define MODLL (998244353LL)
#endif
using mll = mll_<MODLL>;
//using mll = fraction;



namespace SolvingSpace{

template<class T> using vector = Vector<T>;
using    vll=vector<   ll>; using    vmll=vector<   mll>; using    vdd=vector<   dd>;
using   vvll=vector<  vll>; using   vvmll=vector<  vmll>; using   vvdd=vector<  vdd>;
using  vvvll=vector< vvll>; using  vvvmll=vector< vvmll>; using  vvvdd=vector< vvdd>;
using vvvvll=vector<vvvll>; using vvvvmll=vector<vvvmll>; using vvvvdd=vector<vvvdd>;
using   vpll=vector<  pll>; using    vtll=vector<   tll>; using   vqll=vector<  qll>;
using  vvpll=vector< vpll>; using   vvtll=vector<  vtll>; using  vvqll=vector< vqll>;
using vss=vector<string>;
template<class T> vector<T> cinv(ll nm){ return vector<T>(nm,[](ll i){ (void)i; return cin1<T>(); }); }
template<class T> vector<vector<T>> cinvv(ll H,ll W){ return vector<vector<T>>(H,[&](ll i){ (void)i; return cinv<T>(W); }); }

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namespace graphSpace{
using Int=long long;
using ll=long long;

//FirstType<T> Tがpair,tupleのとき第一要素の型、それ以外のときT
template <class T> concept IsTpl=requires{ typename tuple_size<T>::type; };
template <class T> struct FirstTypeSub { using type=T; };
template <IsTpl T> struct FirstTypeSub<T> { using type=tuple_element_t<0,T>; };
template <class T> using FirstType = typename FirstTypeSub<T>::type;

template<class T> struct edge{
    using CostType=FirstType<T>;
    int to=-1;
    int idx_=-1;//辺の通し番号
    T data_=T(); //long long, pair<int,int>, tuple<int,int,char>等 第1要素がcost
    edge(){}
    edge(Int to,T data,Int idx=-1): to((int)to),idx_((int)idx),data_(data){}
    operator Int()const{ return (Int)to; }
    Int operator=(Int v){ this->to=(int)v; return v; }
    int &idx(){ return idx_; }
    Int idx()const{ return (Int)idx_; }
    CostType &cost(){
        if constexpr (IsTpl<T>){ return std::get<0>(data_); }
        else return data_;
    }
    const CostType &cost()const{ return const_cast<edge*>(this)->cost(); }
    template<int i> auto &val(){ return std::get<i>(data_); }
    template<int i> const auto &val()const{ return std::get<i>(data_); }
    T &data(){ return data_; }
    const T &data()const{ return data_; }
    bool operator<(const edge &e)const{ return to==e.to ? idx_<e.idx_ : to<e.to; }
};

template<class T=Int> struct graphHelper{
    vector<vector<edge<T>>> to;
    ll edgeIdxLast=-1;//最後に追加した辺の通し番号
    bool edgeSorted=false;
    /*---- 準備関連I/F ----*/
    graphHelper(){}
    graphHelper(Int N):to(N){}
    graphHelper(Int N,const vector<tuple<Int,Int,T>> &uvc,bool isDirected)
        : to(N){
        build(uvc,isDirected);
    }
    graphHelper(Int N,const vector<pair<Int,Int>> &uv,bool isDirected,T cost=T(1))
        : to(N){
        build(uv,isDirected,cost);
    }
    void build(const vector<tuple<Int,Int,T>> &uvc,bool isDirected){
        for (auto [u,v,c]:uvc){
            ll ei=newEdgeIdx();
            to[u].emplace_back(v,c,ei);
            if (!isDirected) to[v].emplace_back(u,c,ei);
        }
    }
    void build(const vector<pair<Int,Int>> &uv,bool isDirected,T cost=T(1)){
        for (auto [u,v]:uv){
            ll ei=newEdgeIdx();
            to[u].emplace_back(v,cost,ei);
            if (!isDirected) to[v].emplace_back(u,cost,ei);
        }
    }
    void sortedge(){
        for (auto &v:to) sort(v.begin(),v.end());
        edgeSorted=true;
    }
    /*---- 操作・アクセスI/F ----*/
    vector<vector<edge<T>>> &get(){ return to; }
    Int size()const{ return (Int)to.size(); }

    bool existarc(Int u,Int v){
        for (const auto &eg:to[u]) if (Int(eg)==v) return true;
        return false;
    }
    bool existarcS(Int u,Int v){
        assert(edgeSorted);
        auto it=lower_bound(to[u].begin(),to[u].end(),edge(v,T(),-1));
        return !(it==to[u].end() || Int(*it)!=v);
    }

    edge<T> &getarc(Int u,Int v){
        vector<edge<T>> &vec=to[u];
        auto it=find_if(vec.begin(),vec.end(),[&](auto &eg){return eg==v; });
        assert(it!=vec.end());
        return *it;
    }
    edge<T> &getarcS(Int u,Int v){
        assert(edgeSorted);
        auto it=lower_bound(to[u].begin(),to[u].end(),edge(v,T(),-1));
        assert(!(it==to[u].end() || Int(*it)!=v));
        return *it;
    }

    Int addnode(){ to.resize(size()+1); return size()-1; }
    void addnode(Int num){ to.resize((Int)to.size()+num); }

    void addarc(Int u,Int v,T cost=T(1)){
        to[u].emplace_back(v,cost,newEdgeIdx());
    }
    void addedge(Int u,Int v,T cost=T(1)){
        ll ei=newEdgeIdx();
        to[u].emplace_back(v,cost,ei);
        to[v].emplace_back(u,cost,ei);
    }

    void erasenode(Int v,bool isDir){
        if (isDir){
            to[v].clear(); //出辺全削除
            for (ll u=0; u<size(); ++u) eraseArcAll(u,v); //入辺全削除
        }
        else{//無向グラフのとき
            vector<ll> us;
            for (auto&& eg: to[v]) us.push_back(ll(eg)); //隣接頂点列挙
            sort(us.begin(),us.end());
            us.erase(unique(us.begin(),us.end()),us.end()); //重複削除
            for (auto&& u: us) eraseArcAll(u,v); //入辺全削除
            to[v].clear(); //出辺全削除
        }
    }
    void eraseedge(Int u,Int v,bool isall=true){
        if (isall){
            eraseArcAll(u,v);
            eraseArcAll(v,u);
        }
        else{
            int idx=eraseArc1(u,v);
            eraseArcIdx(v,u,idx);
        }
    }
    void erasearc(Int u,Int v,bool isall=true){
        if (isall) eraseArcAll(u,v);
        else       eraseArc1  (u,v);
    }

    void dump(bool isDirected,bool withCost,bool zeroIndexed=false){
        multiset<tuple<ll,ll,ll,T>> egs;//<idx,v,u,T>
        for (ll v=0; v<(ll)to.size(); ++v) for (auto&& eg: to[v]){
            egs.emplace(eg.idx(),v,ll(eg),eg.data());
        }
        vector<tuple<ll,ll,T>> abw;
        while (egs.size()){
            auto it=egs.begin();
            auto [idx,v,u,data]=*it;
            abw.emplace_back(v,u,data);
            egs.erase(it);
            if (!isDirected){ //無向辺の場合、反対向きの辺を消す
                auto itrev=egs.find({idx,u,v,data});
                assert(itrev!=egs.end());
                egs.erase(itrev);
            }
        }
        cout << to.size() << ' ' << abw.size() << '\n';
        for (auto&&[a,b,w]:abw){
            cout << a+1-zeroIndexed << ' ' << b+1-zeroIndexed;
            if (withCost) cout << ' ' << w;
            cout << '\n';
        }
    }
private:
    ll newEdgeIdx(){ return ++edgeIdxLast; }

    void eraseArcAll(Int u,Int v){//有向辺u→vを全削除  to[u]内のvを全削除
        vector<edge<T>> &vec=to[u];
        auto it=remove_if(vec.begin(),vec.end(),[&](auto &eg){return eg==v; });
        vec.erase(it,vec.end());
    }
    int eraseArc1(Int u,Int v){//有向辺u→vを1つ削除  @return 削除した辺のidx
        vector<edge<T>> &vec=to[u];
        auto it=find_if(vec.begin(),vec.end(),[&](auto &eg){return eg==v; });
        assert(it!=vec.end());
        int idx=it->idx();
        vec.erase(it);
        return idx;
    }
    void eraseArcIdx(Int u,Int v,int idx){//辺のidxを指定して削除
        vector<edge<T>> &vec=to[u];
        auto it=find_if(vec.begin(),vec.end(),[&](auto &eg){
            return eg==v && eg.idx()==idx;
        });
        assert(it!=vec.end());
        vec.erase(it);
    }
};
}
using graphSpace::edge;
using graphSpace::graphHelper;
/*
重み無しグラフは重み1の重み付きグラフとして扱う
- ---- N頂点0辺グラフ ----
graphHelper     G(N);
graphHelper<dd> G(N);
graphHelper<pair<ll,char>> G(N);
.            ↑辺に乗せる値(重み等)の型  省略時ll

- ---- N頂点辺指定 ----
.     {<u,v>,…}↓   ↓true:有向、false:無向
graphHelper G(N,uv,false);     //重み無しグラフ(重みall1)
graphHelper G(N,uv,false,5ll); //↑の重みをall5に指定
graphHelper G(N,uvc,false);    //重み付きグラフ
.               ↑{<u,v,コスト>,…}
- ---- 操作 ----
ll v=G.addnode();               //頂点1つ追加 v:追加された頂点番号
G.addnode(n);                   //頂点n個追加
G.addarc(u,v);         //有向辺u→vを張る
G.addedge(u,v);        //無向辺u→vを張る
G.addedge(u,v,c);      //重みcで張る
G.addedge(u,v,{c,a});  //辺に複数の値を乗せる例
G.erasenode(v,false);  //vにつながる辺を全削除 無向グラフ
G.erasenode(v,true);   //vにつながる辺を全削除 有向グラフ O(N)
G.erasearc(u,v);        //有向辺u→vを全て削除
G.erasearc(u,v,false);  //有向辺u→vを1つ削除
G.eraseedge(u,v);       //無向辺u-vを全て削除
G.eraseedge(u,v,false); //無向辺u-vを1つ削除
G.existarc(u,v);        //true:辺uv有
auto &eg=G.getarc(u,v); //辺uv取得 ないときは落ちる
G.dump(false,false);
.true:有向↑    ↑true:重み有

- ---- 辺クラス内部のアクセス ----
auto &to=G.to; //グラフ
auto &eg=to[v][i]; //辺取得
auto [c,va]=eg.data();  //辺に乗せた値全て
ll cost    =eg.cost();  //コスト(＝辺に乗せた値の第1要素)
ll val     =eg.val<1>();//辺に乗せた値の第2要素
ll ei      =eg.idx();   //辺index 追加した順に振られる
eg.cost()=c, eg.val<1>()=va, eg.idx()=i, eg.data()={c,va}; //代入も可能

- ---- 辺ソート時のみの処理 ----
G.sortedge(); //辺を頂点番号順にソート
auto &eg=G.getarcS(u,v); //辺uv取得 ないときは落ちる
bool b=G.existarcS(u,v); //true:辺uv有
G.getarcS(u,v).cost()=cost;                       //有向辺uvのコスト変更
G.getarcS(u,v).cost()=G.getarcS(v,u).cost()=cost; //無向辺uvの   〃
*/


namespace BFSspace{
using Int=long long;
using  ll=long long;

template<class E> vector<Int> bfs(vector<vector<E>> &to,ll s,Int inf){
    vector<Int> dist(to.size(),inf);
    queue<ll> Q;
    dist[s] = 0;
    Q.push(s);
    while (!Q.empty()){
        ll v = Q.front();  Q.pop();
        for (ll u : to[v]) if (chmin(dist[u],dist[v]+1)) Q.push(u);
    }
    return dist;
}

template<class E>
vector<Int> getpath(vector<Int> &dist,ll g,vector<vector<E>> &rto){
    vector<Int> path={(Int)g};
    ll v=g;
    while (dist[v]!=0){
        for (ll u : rto[v]){
            if (dist[u]==dist[v]-1){
                v=u;
                break;
            }
        }
        path.push_back(v);
    }
    reverse(path.begin(),path.end());
    return path;
}
}
using BFSspace::bfs;
using BFSspace::getpath;
/*
- ---- bfs ----
vll dist = bfs(to,s,INF);
.    ↑dist[v]:sからvまでの距離  到達できないノードはINF

- ---- sからgまでの最短パス ----
vll path=getpath(dist,g,to);
vll path=getpath(dist,g,rto); //有向グラフのときはrtoを指定
.    ↑path[0]=s, path.back()=g
*/


void cin2solve()
{
    auto [N,M]=cins<ll,ll>();
    auto abc=cinv<tuple<ll,ll,ll>>(M);
    for (auto&&[a,b,c]:abc) a--,b--;

    /*
    ≠を1つ以下使って、最短でNまでいく
    */

    graphHelper     Geq(N);
    for (auto&&[a,b,c]:abc){
        if (c==1)
            Geq.addedge(a,b);
    }
    auto &toeq=Geq.to;

    vll dist1 = bfs(toeq,0,INF);
    vll distN = bfs(toeq,N-1,INF);

    if (dist1[N-1]<INF/2){
        ll ans=dist1[N-1];
        cout << "Same" << '\n';
        cout << ans << '\n'; return;
    }
    
    {
        ll ans=INF;
        for (auto&&[a,b,c]:abc){
            if (c==1)continue;
            ll dz= dist1[a]+distN[b]+1;
            ll dy= dist1[b]+distN[a]+1;
            chmin(ans,min(dz,dy));
        }
        if (ans>INF/2){
            cout << "Unknown" << '\n';
        }
        else{
            cout << "Different" << '\n';
            cout << ans << '\n';
        }
    }

    return;
}

}//SolvingSpace

//////////////////////////////////////////


int main(){
#if defined(RANDOM_TEST)
    SolvingSpace::cin2solve();
    SolvingSpace::generand();
#else
  #if 0
    //SolvingSpace::labo();'
    SolvingSpace::cin2solve();
  #else
    ll t;  cin >> t;
    rep(i,0,t-1){
        SolvingSpace::cin2solve();
    }
  #endif
#endif
    cerr << timeget() <<"ms"<< '\n';
    return 0;
}