結果

問題 No.2764 Warp Drive Spacecraft
ユーザー hamamu
提出日時 2024-07-25 21:36:16
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 424 ms / 3,000 ms
コード長 49,110 bytes
コンパイル時間 6,973 ms
コンパイル使用メモリ 309,528 KB
最終ジャッジ日時 2025-02-23 18:03:52
ジャッジサーバーID
（参考情報） 		judge1 / judge4
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 * 35
権限があれば一括ダウンロードができます

ソースコード

diff #
プレゼンテーションモードにする

#if !defined(MYLOCAL)//提出時用テンプレート
#pragma GCC optimize("Ofast")
#if defined(NDEBUG)
#undef NDEBUG
#endif
#include "bits/stdc++.h"
#if !defined(_MSC_VER) && __has_include(<atcoder/all>)
#include <atcoder/all>
using namespace atcoder;
#endif
using namespace std;
using     ll=long long;     using   dd=double;     
using    vll=vector<   ll>; using  vdd=vector< dd>;
using   vvll=vector<  vll>; using vvdd=vector<vdd>;
using  vvvll=vector< vvll>; using vvvdd=vector<vvdd>;
using vvvvll=vector<vvvll>;
using   pll=pair<ll,ll>;  using   tll=tuple<ll,ll,ll>; using   qll=tuple<ll,ll,ll,ll>;
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 namespace chrono;
constexpr ll INF = 1001001001001001001;
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 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 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,_,_)(__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 each2(e,v) for (auto && e:v)
#define each3(a,b,v) for (auto &&[a,b]:v)
#define each4(a,b,c,v) for (auto &&[a,b,c]:v)
#define each5(a,b,c,d,v) for (auto &&[a,b,c,d]:v)
#define each(...) EXPAND(overload5(__VA_ARGS__,each5,each4,each3,each2,_)(__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__))
#define all ALL
#define RALL1(v)     (v).rbegin(),     (v).rend()
#define RALL2(v,E)   (v).rbegin(),     (v).rbegin()+((E)+1)
#define RALL3(v,S,E) (v).rbegin()+(S), (v).rbegin()+((E)+1)
#define RALL(...) EXPAND(overload3(__VA_ARGS__, RALL3, RALL2, RALL1)(__VA_ARGS__))
#define rall RALL
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 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> 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,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(); }
inline ll CEIL(ll a,ll b){ return (a<0) ? -(-a/b) : (a+b-1)/b; } //負もOK
inline ll FLOOR(ll a,ll b){ return -CEIL(-a,b); } //負もOK
//pair用テンプレート
template<class T,class S> inline pair<T,S>& operator+=(pair<T,S> &a,const pair<T,S> &b){ a.first+=b.first; a.second+=b.second; return a; }
template<class T,class S> inline pair<T,S>& operator-=(pair<T,S> &a,const pair<T,S> &b){ a.first-=b.first; a.second-=b.second; return a; }
template<class T,class S> inline pair<T,S>& operator*=(pair<T,S> &a,const pair<T,S> &b){ a.first*=b.first; a.second*=b.second; return a; }
template<class T,class S> inline pair<T,S>& operator/=(pair<T,S> &a,const pair<T,S> &b){ a.first/=b.first; a.second/=b.second; return a; }
template<class T,class S> inline pair<T,S>& operator%=(pair<T,S> &a,const pair<T,S> &b){ a.first%=b.first; a.second%=b.second; return a; }
template<class T,class S,class R> inline pair<T,S>& operator+=(pair<T,S> &a,R b){ a.first+=b; a.second+=b; return a; }
template<class T,class S,class R> inline pair<T,S>& operator-=(pair<T,S> &a,R b){ a.first-=b; a.second-=b; return a; }
template<class T,class S,class R> inline pair<T,S>& operator*=(pair<T,S> &a,R b){ a.first*=b; a.second*=b; return a; }
template<class T,class S,class R> inline pair<T,S>& operator/=(pair<T,S> &a,R b){ a.first/=b; a.second/=b; return a; }
template<class T,class S,class R> inline pair<T,S>& operator%=(pair<T,S> &a,R b){ a.first%=b; a.second%=b; return a; }
template<class T,class S,class R> inline pair<T,S> operator+(const pair<T,S> &a,R b){ pair<T,S> c=a; return c+=b; }
template<class T,class S,class R> inline pair<T,S> operator-(const pair<T,S> &a,R b){ pair<T,S> c=a; return c-=b; }
template<class T,class S,class R> inline pair<T,S> operator*(const pair<T,S> &a,R b){ pair<T,S> c=a; return c*=b; }
template<class T,class S,class R> inline pair<T,S> operator/(const pair<T,S> &a,R b){ pair<T,S> c=a; return c/=b; }
template<class T,class S,class R> inline pair<T,S> operator%(const pair<T,S> &a,R b){ pair<T,S> c=a; return c%=b; }
template<class T,class S,class R> inline pair<T,S> operator-(R b,const pair<T,S> &a){ pair<T,S> c=-a; return c+=b; }
template<class T,class S> inline pair<T,S> operator-(const pair<T,S> &a,const pair<T,S> &b){ pair<T,S> c=a; return c-=b; }
template<class T,class S> inline pair<T,S> operator-(const pair<T,S> &a){ pair<T,S> c=a; return c*=(-1); }
template<class T,class S> inline ostream &operator<<(ostream &os,const pair<T,S> &a){ return os << a.first << ' ' << a.second; }
//tuple用テンプレート 出力用のみ
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); }
//vector用テンプレート
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; 
    }
//array用テンプレート
template<class T,size_t S> inline array<T,S>& operator+=(array<T,S> &a,const array<T,S> &b){ for (ll i=0; i<(ll)S; i++) a[i]+=b[i];  return a; }
template<class T,size_t S> inline array<T,S>& operator-=(array<T,S> &a,const array<T,S> &b){ for (ll i=0; i<(ll)S; i++) a[i]-=b[i];  return a; }
template<class T,size_t S> inline array<T,S>& operator*=(array<T,S> &a,const array<T,S> &b){ for (ll i=0; i<(ll)S; i++) a[i]*=b[i];  return a; }
template<class T,size_t S> inline array<T,S>& operator/=(array<T,S> &a,const array<T,S> &b){ for (ll i=0; i<(ll)S; i++) a[i]/=b[i];  return a; }
template<class T,size_t S> inline array<T,S>& operator%=(array<T,S> &a,const array<T,S> &b){ for (ll i=0; i<(ll)S; i++) a[i]%=b[i];  return a; }
template<class T,size_t S,class R> inline array<T,S>& operator+=(array<T,S> &a,R b){ for (T &e: a) e+=b;  return a; }
template<class T,size_t S,class R> inline array<T,S>& operator-=(array<T,S> &a,R b){ for (T &e: a) e-=b;  return a; }
template<class T,size_t S,class R> inline array<T,S>& operator*=(array<T,S> &a,R b){ for (T &e: a) e*=b;  return a; }
template<class T,size_t S,class R> inline array<T,S>& operator/=(array<T,S> &a,R b){ for (T &e: a) e/=b;  return a; }
template<class T,size_t S,class R> inline array<T,S>& operator%=(array<T,S> &a,R b){ for (T &e: a) e%=b;  return a; }
template<class T,size_t S,class R> inline array<T,S> operator+(const array<T,S> &a,R b){ array<T,S> c=a; return c+=b; }
template<class T,size_t S,class R> inline array<T,S> operator-(const array<T,S> &a,R b){ array<T,S> c=a; return c-=b; }
template<class T,size_t S,class R> inline array<T,S> operator*(const array<T,S> &a,R b){ array<T,S> c=a; return c*=b; }
template<class T,size_t S,class R> inline array<T,S> operator/(const array<T,S> &a,R b){ array<T,S> c=a; return c/=b; }
template<class T,size_t S,class R> inline array<T,S> operator%(const array<T,S> &a,R b){ array<T,S> c=a; return c%=b; }
template<class T,size_t S,class R> inline array<T,S> operator-(R b,const array<T,S> &a){ array<T,S> c=-a; return c+=b; }
template<class T,size_t S> inline array<T,S> operator-(const array<T,S> &a,const array<T,S> &b){ array<T,S> c=a; return c-=b; }
template<class T,size_t S> inline array<T,S> operator-(const array<T,S> &a){ array<T,S> c=a; return c*=(-1); }
template<class T,size_t S> inline ostream &operator<<(ostream &os,const array<T,S> &a){ for (ll i=0; i<(ll)S; i++) os<<(i>0?" ":"")<<a[i];  return 
    os; }
template<class T,size_t S,class R> struct view1d;
template<class T,size_t S,class R> struct view1dIter{
  view1d<T,S,R> *vw=nullptr;
  ll idx=INF;
  view1dIter(){}
  view1dIter(view1d<T,S,R> *vw_,ll idx_):vw(vw_),idx(idx_){}
  view1dIter(const view1dIter<T,S,R> &it):vw(it.vw),idx(it.idx){}
  R &operator*()          { return (*vw)[idx]; }
  R &operator*()     const{ return (*vw)[idx]; }
  R &operator[](ll i)     { return (*vw)[idx+i]; }
  R &operator[](ll i)const{ return (*vw)[idx+i]; }
  auto &operator++(){ idx++; return *this; }
  auto &operator--(){ idx--; return *this; }
  auto operator++(int){ auto it=*this; idx++; return it; }
  auto operator--(int){ auto it=*this; idx--; return it; }
  auto &operator+=(ll n){ idx+=n; return *this; }
  auto &operator-=(ll n){ idx-=n; return *this; }
  auto operator+(ll n){ auto it=*this; return it+=n; }
  auto operator-(ll n){ auto it=*this; return it-=n; }
  ll   operator- (const view1dIter<T,S,R> &it)const{ return idx- it.idx; }
  bool operator< (const view1dIter<T,S,R> &it)const{ return idx< it.idx; }
  bool operator> (const view1dIter<T,S,R> &it)const{ return idx> it.idx; }
  bool operator<=(const view1dIter<T,S,R> &it)const{ return idx<=it.idx; }
  bool operator>=(const view1dIter<T,S,R> &it)const{ return idx>=it.idx; }
  bool operator!=(const view1dIter<T,S,R> &it)const{ return idx!=it.idx; }
  bool operator==(const view1dIter<T,S,R> &it)const{ return idx==it.idx; }
  using iterator_category = random_access_iterator_tag;
  using value_type = R;
  using difference_type = ll;
  using pointer = R*;
  using reference = R&;
};
template<class T,size_t S,class R> struct view1d{
  using Sll=array<ll,S>;
  T &data; //参照先データ
  Sll dsize; //参照先データ各軸のサイズ
  Sll s=Sll(); //view先頭
  Sll d=Sll(); //view方向
  ll len; //view長さ
  R &dummy; //範囲外の値参照
  R dummyj=R(); //範囲外の値実体
  /*---- コンストラクタ ----*/
  view1d(T &v): data(v),dummy(dummyj){
    SetDsize(v,dsize);
    d[S-1]=1;
    len=dsize[S-1];
  }
  //このコンストラクタは、マイナス座標指定を末尾にしない(暫定)
  //代入時Array<ll,2>{...}等と書くため、使い勝手悪い。将来廃止するかも。
  view1d(T &v,Sll s,Sll e,Sll d): data(v),s(s),d(d),len(Len(s,e,d)),dummy(dummyj){
    SetDsize(v,dsize);
  }
  view1d(T &v,Sll s,Sll d,ll len,R &dmy_): data(v),s(s),d(d),len(len),dummy(dmy_){
    SetDsize(v,dsize);
  }
  /*---- 演算 ----*/
  template<class Q> auto &operator =(const Q &b){ rep(i,0,len-1) (*this)[i] =b; return *this; }
  template<class Q> auto &operator+=(const Q &b){ rep(i,0,len-1) (*this)[i]+=b; return *this; }
  template<class Q> auto &operator-=(const Q &b){ rep(i,0,len-1) (*this)[i]-=b; return *this; }
  template<class Q> auto &operator*=(const Q &b){ rep(i,0,len-1) (*this)[i]*=b; return *this; }
  template<class Q> auto &operator/=(const Q &b){ rep(i,0,len-1) (*this)[i]/=b; return *this; }
  template<class Q> auto &operator%=(const Q &b){ rep(i,0,len-1) (*this)[i]%=b; return *this; }
  auto &operator =(const string &b){ return CpSeq(b); }
  template<size_t Q> auto &operator =(const char (&b)[Q]){ return *this=string(b); }
  template<class Q> auto &operator =(const vector<Q> &b){ return CpSeq(b); }
  template<class Q> auto &operator+=(const vector<Q> &b){ return PlSeq(b); }
  template<class Q> auto &operator-=(const vector<Q> &b){ return MnSeq(b); }
  template<class Q> auto &operator*=(const vector<Q> &b){ return PrSeq(b); }
  template<class Q> auto &operator/=(const vector<Q> &b){ return DvSeq(b); }
  template<class Q> auto &operator%=(const vector<Q> &b){ return RmSeq(b); }
  template<class Q,size_t P,class O> auto &operator =(const view1d<Q,P,O> &b){ return CpSeq(b); }
  template<class Q,size_t P,class O> auto &operator+=(const view1d<Q,P,O> &b){ return PlSeq(b); }
  template<class Q,size_t P,class O> auto &operator-=(const view1d<Q,P,O> &b){ return MnSeq(b); }
  template<class Q,size_t P,class O> auto &operator*=(const view1d<Q,P,O> &b){ return PrSeq(b); }
  template<class Q,size_t P,class O> auto &operator/=(const view1d<Q,P,O> &b){ return DvSeq(b); }
  template<class Q,size_t P,class O> auto &operator%=(const view1d<Q,P,O> &b){ return RmSeq(b); }
  template<class Q> auto &CpSeq(const Q &b){ rep(i,0,min(sz(b),len)-1) (*this)[i] =b[i]; return *this; }
  template<class Q> auto &PlSeq(const Q &b){ rep(i,0,min(sz(b),len)-1) (*this)[i]+=b[i]; return *this; }
  template<class Q> auto &MnSeq(const Q &b){ rep(i,0,min(sz(b),len)-1) (*this)[i]-=b[i]; return *this; }
  template<class Q> auto &PrSeq(const Q &b){ rep(i,0,min(sz(b),len)-1) (*this)[i]*=b[i]; return *this; }
  template<class Q> auto &DvSeq(const Q &b){ rep(i,0,min(sz(b),len)-1) (*this)[i]/=b[i]; return *this; }
  template<class Q> auto &RmSeq(const Q &b){ rep(i,0,min(sz(b),len)-1) (*this)[i]%=b[i]; return *this; }
  //template<class Q,class P> static bool eq(const Q &a,const P &b){
  //  return equals(ALL(a),ALL(b));
  //}
  template<class Q,class P> static bool eq(const Q &a,const P &b){
    if ((ll)a.size()!=(ll)b.size()) return false;
    rep(i,0,(ll)a.size()-1){
      if (a[i]!=b[i]) return false;
    }
    return true;
  }
  template<class Q,class P> static bool lt(const Q &a,const P &b){
    ll n=min((ll)a.size(),(ll)b.size());
    rep(i,0,n-1){
      if (a[i]<b[i])return true;
      if (a[i]>b[i])return false;
    }
    return (ll)a.size()<(ll)b.size();
  }
  template<class Q,size_t P,class O> bool operator==(           const view1d<Q,P,O> &b){ return eq(*this,b); }
  template<class Q>                  bool operator==(           const             Q &b){ return eq(*this,b); }
  template<class Q> friend           bool operator==(const Q &a,const view1d<T,S,R> &b){ return eq(    a,b); }
  template<size_t Q>                 bool operator==(           const     char (&b)[Q]){ return eq(*this,string(b)); }
  template<class Q,size_t P,class O> bool operator!=(           const view1d<Q,P,O> &b){ return !(*this==b); }
  template<class Q>                  bool operator!=(           const             Q &b){ return !(*this==b); }
  template<class Q> friend           bool operator!=(const Q &a,const view1d<T,S,R> &b){ return !(    a==b); }
  template<class Q,size_t P,class O> bool operator< (           const view1d<Q,P,O> &b){ return lt(*this,b); }
  template<class Q>                  bool operator< (           const             Q &b){ return lt(*this,b); }
  template<class Q> friend           bool operator< (const Q &a,const view1d<T,S,R> &b){ return lt(    a,b); }
  template<class Q,size_t P,class O> bool operator> (           const view1d<Q,P,O> &b){ return lt(b,*this); }
  template<class Q>                  bool operator> (           const             Q &b){ return lt(b,*this); }
  template<class Q> friend           bool operator> (const Q &a,const view1d<T,S,R> &b){ return lt(b,a    ); }
  template<class Q,size_t P,class O> bool operator<=(           const view1d<Q,P,O> &b){ return !(*this>b); }
  template<class Q>                  bool operator<=(           const             Q &b){ return !(*this>b); }
  template<class Q> friend           bool operator<=(const Q &a,const view1d<T,S,R> &b){ return !(    a>b); }
  template<class Q,size_t P,class O> bool operator>=(           const view1d<Q,P,O> &b){ return !(*this<b); }
  template<class Q>                  bool operator>=(           const             Q &b){ return !(*this<b); }
  template<class Q> friend           bool operator>=(const Q &a,const view1d<T,S,R> &b){ return !(    a<b); }
  /*---- getter ----*/
  ll size() const { return len; }
  R &operator[](ll i){ return const_cast<R&>(OrgAt(s+d*i)); }
  const R &operator[](ll i) const { return OrgAt(s+d*i); }
  R &at(ll i){ if(i<0)i+=len; return (*this)[i]; }
  //vector<R> tov(){ vector<R> vvv(len);  rep(i,0,len-1) vvv[i]=(*this)[i];  return vvv; }
  operator vector<R>(){ vector<R> v(len);  rep(i,0,len-1) v[i]=(*this)[i];  return v; }
  bool contains(R a){ rep(i,0,len-1) if((*this)[i]==a)return true;  return false; }
  auto begin(){ return view1dIter<T,S,R>(this,0); }
  auto end(){ return view1dIter<T,S,R>(this,len); }
  /*---- view設定 ----*/
  view1d<T,S,R> &dmy(R dmy_) { dummy=dmy_; return *this; }//ダミー値セット
  template<class...Q> view1d<T,S,R> &st(Q... s_){//始点set 負は末尾からの位置
    this->s=RevIfNeg(SllD(s_...));
    this->len=AutoLen(this->s,this->d,this->dsize);
    return *this;
  }
  template<class...Q> view1d<T,S,R> &en(Q... e_){//終了条件再設定 負は末尾から
    this->len=Len(s, RevIfNeg(SllD(e_...)), d);
    return *this;
  }
  template<class...Q> view1d<T,S,R> &dir(Q... d_){//方向set、長さはdata端まで
    this->d=SllD(d_...);
    this->len=AutoLen(this->s,this->d,this->dsize);
    return *this;
  }
  template<class...Q>
  view1d<T,S,R> &mv(Q... s_){ this->s+=SllD(s_...); return *this; }//平行移動
  view1d<T,S,R> &size(ll len_) { len=len_; return *this; }//長さset
  template<class Q> view1d<T,S,R> &size(Q &v){ len=(ll)v.size(); return *this; }//長さset
  view1d<T,S,R> &rev() { s+=d*(len-1); d*=-1; return *this; }//反転
  /*---- utility ----*/
  template<class Q> inline static ll sz(Q &v){ return (ll)v.size(); }
  Sll RevIfNeg(Sll pos){//!< 負なら末尾からの位置に変換
    rep(i,0,S-1)  if (pos[i]<0) pos[i]+=dsize[i];
    return pos;
  }
  static ll AutoLen(Sll s_,Sll d_,Sll dsz){//位置s_から方向d_ではみ出すまでの長さ
    Sll e=dsz-1;
    rep(i,0,S-1) e[i] *= (d_[i]>=0);//方向が負の軸を0にする
    return Len(s_,e,d_);
  }
  /*---- 先頭位置s、方向d、終了条件eから長さlen計算 ----*/
  //template<size_t Q> static ll Len(array<ll,Q> s,array<ll,Q> e,array<ll,Q> d){
  //  ll ret=INF;
  //  rep(i,0,Q-1) chmin(ret, Len1(s[i],e[i],d[i]));
  //  return ret;
  //}
  static ll Len(Sll s,Sll e,Sll d){
    ll ret=INF;
    rep(i,0,S-1) chmin(ret, Len1(s[i],e[i],d[i]));
    return ret;
  }
  static ll Len1(ll s,ll e,ll d){
    if (d==0) return INF;
    if (d<0){ s=-s; e=-e; d=-d; }
    if (s>e) return 0;
    return (e-s)/d+1;
  }
  /*---- 可変長引数をSllに変換 ----*/
  template<class...Q> static Sll SllD(Q... args){ return SllRec(0,args...); }
  template<class...Q> static Sll SllRec(ll i,ll first,Q... rest) {
    Sll sll = (i==S-1) ? Sll() : SllRec(i+1,rest...);
    sll[i]=first;
    return sll;
  }
  static Sll SllRec(ll i){ return Sll(); }
  /*---- dataの位置posの値取得 ----*/
  const R &OrgAt(Sll pos) const {
    rep(i,0,S-1){
      if (pos[i]<0 || dsize[i]<=pos[i]) return dummy;
    }
    return OrgAt_(data,pos);
  }
  template<class Q> using V   = vector<Q>;
  template<class Q> using VV  = V<V<Q>>;
  template<class Q> using VVV = V<V<V<Q>>>;
  using Vs  = V<string>;
  using VVs = VV<string>;
  using ll1 = array<ll,1>;
  using ll2 = array<ll,2>;
  using ll3 = array<ll,3>;
  auto &OrgAt_(V<R>   &dat,ll1 pos)const{ auto [i]    =pos; return dat[i]; }
  auto &OrgAt_(string &dat,ll1 pos)const{ auto [i]    =pos; return dat[i]; }
  auto &OrgAt_(VV<R>  &dat,ll2 pos)const{ auto [i,j]  =pos; return dat[i][j]; }
  auto &OrgAt_(Vs     &dat,ll2 pos)const{ auto [i,j]  =pos; return dat[i][j]; }
  auto &OrgAt_(VVV<R> &dat,ll3 pos)const{ auto [i,j,k]=pos; return dat[i][j][k]; }
  auto &OrgAt_(VVs    &dat,ll3 pos)const{ auto [i,j,k]=pos; return dat[i][j][k]; }
  /*---- dataの各軸size取得 ----*/
  static void SetDsize(V<R>   &dat,ll1 &dsz){ dsz={sz(dat)}; }
  static void SetDsize(string &dat,ll1 &dsz){ dsz={sz(dat)}; }
  static void SetDsize(VV<R>  &dat,ll2 &dsz){ dsz={sz(dat),sz(dat[0])}; }
  static void SetDsize(Vs     &dat,ll2 &dsz){ dsz={sz(dat),sz(dat[0])}; }
  static void SetDsize(VVV<R> &dat,ll3 &dsz){ dsz={sz(dat),sz(dat[0]),sz(dat[0][0])}; }
  static void SetDsize(VVs    &dat,ll3 &dsz){ dsz={sz(dat),sz(dat[0]),sz(dat[0][0])}; }
  typedef view1dIter<T,S,R> iterator;
  using value_type = R;
};
template<class Q> using V   = vector<Q>;
template<class Q> using VV  = V<V<Q>>;
template<class Q> using VVV = V<V<V<Q>>>;
template<class T>         view1d(    VVV<T>      ) -> view1d<    VVV<T>,3,T>;
template<class T>         view1d(     VV<T>      ) -> view1d<     VV<T>,2,T>;
template<class T>         view1d(      V<T>      ) -> view1d<      V<T>,1,T>;
;                         view1d(VV<string>      ) -> view1d<VV<string>,3,char>;
;                         view1d( V<string>      ) -> view1d< V<string>,2,char>;
;                         view1d(   string       ) -> view1d<   string ,1,char>;
template<class T,class S> view1d(    VVV<T>,S,S,S) -> view1d<    VVV<T>,3,T>;
template<class T,class S> view1d(     VV<T>,S,S,S) -> view1d<     VV<T>,2,T>;
template<class T,class S> view1d(      V<T>,S,S,S) -> view1d<      V<T>,1,T>;
template<class S>         view1d(VV<string>,S,S,S) -> view1d<VV<string>,3,char>;
template<class S>         view1d( V<string>,S,S,S) -> view1d< V<string>,2,char>;
template<class S>         view1d(   string ,S,S,S) -> view1d<   string ,1,char>;
template<class VIEW2D> struct view2dIter{
  VIEW2D *vw=nullptr;
  ll idx=INF;
  view2dIter(){}
  view2dIter(VIEW2D *vw_,ll idx_):vw(vw_),idx(idx_){}
  view2dIter(const view2dIter &it):vw(it.vw),idx(it.idx){}
  auto &operator*()          { return (*vw)[x(idx)][y(idx)]; }
  auto &operator*()     const{ return (*vw)[x(idx)][y(idx)]; }
  auto &operator[](ll i)     { return (*vw)[x(idx+i)][y(idx+i)]; }
  auto &operator[](ll i)const{ return (*vw)[x(idx+i)][y(idx+i)]; }
  auto &operator++(){ idx++; return *this; }
  auto &operator--(){ idx--; return *this; }
  auto operator++(int){ auto it=*this; idx++; return it; }
  auto operator--(int){ auto it=*this; idx--; return it; }
  auto &operator+=(ll n){ idx+=n; return *this; }
  auto &operator-=(ll n){ idx-=n; return *this; }
  auto operator+(ll n){ auto it=*this; return it+=n; }
  auto operator-(ll n){ auto it=*this; return it-=n; }
  ll   operator- (const view2dIter &it)const{ return idx- it.idx; }
  bool operator< (const view2dIter &it)const{ return idx< it.idx; }
  bool operator> (const view2dIter &it)const{ return idx> it.idx; }
  bool operator<=(const view2dIter &it)const{ return idx<=it.idx; }
  bool operator>=(const view2dIter &it)const{ return idx>=it.idx; }
  bool operator!=(const view2dIter &it)const{ return idx!=it.idx; }
  bool operator==(const view2dIter &it)const{ return idx==it.idx; }
  ll x(ll i)const{ return i/vw->leny(); }
  ll y(ll i)const{ return i%vw->leny(); }
  using iterator_category = random_access_iterator_tag;
  using value_type = typename VIEW2D::value_type;
  using difference_type = ll;
  using pointer = value_type*;
  using reference = value_type&;
};
template<class T,size_t S,class R> struct view2d{
  using Sll=array<ll,S>;
  T &data; //参照先データ
  Sll dsize; //参照先データ各軸のサイズ
  Sll s=Sll(); //view始点
  Sll dx=Sll(); //view x軸方向
  Sll dy=Sll(); //view y軸方向
  ll xl; //view x軸長さ
  ll yl; //view y軸長さ
  R dummy=R(); //範囲外の値
  /*---- コンストラクタ ----*/
  view2d(T &v): data(v){
    view1d<T,S,R>::SetDsize(v,dsize);
    dx[S-2]=1;
    dy[S-1]=1;
    xl=dsize[S-2];
    yl=dsize[S-1];
  }
  /*---- 演算 ----*/
  //template<class Q> auto &operator =(const Q &b){ rep(i,0,xl-1) (*this)[i] =b; return *this; }
  //template<class Q,size_t P,class O> auto &operator+=(const view2d<Q,P,O> &b){
  //  rep(i,0,xl-1) (*this)[i]
  //  return PlSeq(b); }
  /*---- getter ----*/
  ll size() const { return xl; }
  array<ll,2> shape() const { return {xl,yl}; }
  ll lenx() const { return xl; }
  ll leny() const { return yl; }
  ///pll shape() const { return {xl,yl}; }
  view1d<T,S,R> operator[](ll i){ return view1d(data,s+dx*i,dy,yl,dummy); }
  const view1d<T,S,R> operator[](ll i) const { return view1d(data,s+dx*i,dy,yl,dummy); }
  R &at(ll i,ll j){ if(i<0)i+=xl;  if(j<0)j+=yl;  return (*this)[i][j]; }
  //vector<vector<R>> tovv(){
  //  vector<vector<R>> vvv(xl);
  //  ///rep(i,0,xl-1) vvv[i]=(*this)[i].tov();  return vvv;
  //  rep(i,0,xl-1) vvv[i]=(*this)[i];  return vvv;
  //}
  operator vector<vector<R>>(){
    vector<vector<R>> v(xl);
    rep(i,0,xl-1){ v[i]=(*this)[i]; }  return v;
  }
  auto begin(){ return view2dIter(this,0); }
  auto end(){ return view2dIter(this,xl*yl); }
  #if defined(_DEBUG)
  void dump(){ ::dump(tovv()); }
  #endif
  /*---- view設定 ----*/
  view2d<T,S,R> &dmy(R dmy_) { dummy=dmy_; return *this; }//ダミー値セット
  template<class...Q> view2d<T,S,R> &st(Q... s_){//始点set 負は末尾からの位置
    this->s=RevIfNeg(view1d<T,S,R>::SllD(s_...));
    this->xl=view1d<T,S,R>::AutoLen(this->s,this->dx,this->dsize);
    this->yl=view1d<T,S,R>::AutoLen(this->s,this->dy,this->dsize);
    return *this;
  }
  template<class...Q> view2d<T,S,R> &dirx(Q... d_){//x軸set、長さはdata端まで
    this->dx=view1d<T,S,R>::SllD(d_...);
    this->xl=view1d<T,S,R>::AutoLen(this->s,this->dx,this->dsize);
    return *this;
  }
  template<class...Q> view2d<T,S,R> &diry(Q... d_){//y軸set、長さはdata端まで
    this->dy=view1d<T,S,R>::SllD(d_...);
    this->yl=view1d<T,S,R>::AutoLen(this->s,this->dy,this->dsize);
    return *this;
  }
  template<class...Q> view2d<T,S,R> &mv(Q... s_){//平行移動
    this->s += view1d<T,S,R>::SllD(s_...);
    return *this;
  }
  view2d<T,S,R> &lenx(ll xl_) { xl=xl_; return *this; }
  view2d<T,S,R> &leny(ll yl_) { yl=yl_; return *this; }
  view2d<T,S,R> &shape(ll xl_,ll yl_) { xl=xl_; yl=yl_; return *this; }
  template<class Q> view2d<T,S,R> &shape(Q &v) { xl=v.lenx(); yl=v.leny(); return *this; }
  view2d<T,S,R> &rot90 () { s+=dx*(xl-1); swap(xl,yl); swap(dx,dy); dy*=-1; return *this; }
  view2d<T,S,R> &rot270() { s+=dy*(yl-1); swap(xl,yl); swap(dx,dy); dx*=-1; return *this; }
  view2d<T,S,R> &rot180() { s+=dx*(xl-1)+dy*(yl-1); dx*=-1; dy*=-1; return *this; }
  view2d<T,S,R> &revx() { s+=dx*(xl-1); dx*=-1; return *this; }
  view2d<T,S,R> &revy() { s+=dy*(yl-1); dy*=-1; return *this; }
  view2d<T,S,R> &swapxy() { swap(xl,yl); swap(dx,dy); return *this; }//xy軸入替
  /*---- utility ----*/
  Sll RevIfNeg(Sll pos){//!< 負なら末尾からの位置に変換
    rep(i,0,S-1)  if (pos[i]<0) pos[i]+=dsize[i];
    return pos;
  }
  using value_type = R;
};
template<class T> view2d(    VVV<T>) -> view2d<    VVV<T>,3,T>;
template<class T> view2d(     VV<T>) -> view2d<     VV<T>,2,T>;
;                 view2d(VV<string>) -> view2d<VV<string>,3,char>;
;                 view2d( V<string>) -> view2d< V<string>,2,char>;
/*
zipは参照のpairを返す。それをさらに参照するのはまずいので、コピーする。
*/
template<class ZIP> struct zipIter{
  ZIP *z=nullptr;
  ll idx=INF;
  zipIter(){}
  zipIter(ZIP *z_,ll idx_):z(z_),idx(idx_){}
  zipIter(const zipIter<ZIP> &it):z(it.z),idx(it.idx){}
  auto operator*()          { return (*z)[idx]; }//参照ではなく値戻し
  auto operator*()     const{ return (*z)[idx]; }//同上
  auto operator[](ll i)     { return (*z)[idx+i]; }//同上
  auto operator[](ll i)const{ return (*z)[idx+i]; }//同上
  auto &operator++(){ idx++; return *this; }
  auto &operator--(){ idx--; return *this; }
  auto operator++(int){ auto it=*this; idx++; return it; }
  auto operator--(int){ auto it=*this; idx--; return it; }
  auto &operator+=(ll n){ idx+=n; return *this; }
  auto &operator-=(ll n){ idx-=n; return *this; }
  auto operator+(ll n){ auto it=*this; return it+=n; }
  auto operator-(ll n){ auto it=*this; return it-=n; }
  ll   operator- (const zipIter<ZIP> &it)const{ return idx- it.idx; }
  bool operator< (const zipIter<ZIP> &it)const{ return idx< it.idx; }
  bool operator> (const zipIter<ZIP> &it)const{ return idx> it.idx; }
  bool operator<=(const zipIter<ZIP> &it)const{ return idx<=it.idx; }
  bool operator>=(const zipIter<ZIP> &it)const{ return idx>=it.idx; }
  bool operator!=(const zipIter<ZIP> &it)const{ return idx!=it.idx; }
  bool operator==(const zipIter<ZIP> &it)const{ return idx==it.idx; }
  using iterator_category = random_access_iterator_tag;
  using value_type = typename ZIP::value_type;
  using difference_type = ll;
  using pointer = value_type*;
  using reference = value_type&;
};
template<class T,class S> struct zip2{
  T &t; S &s;
  zip2(T &t_,S &s_):t(t_),s(s_){}
  ll size() const { return t.end()-t.begin(); }
  auto operator[](ll i)     { return make_pair(ref(t.begin()[i]),ref(s.begin()[i])); }
  auto operator[](ll i)const{ return make_pair(ref(t.begin()[i]),ref(s.begin()[i])); }
  auto begin(){ return zipIter(this,0); }
  auto end(){ return zipIter(this,size()); }
  using value_type = pair<typename T::value_type,typename S::value_type>;
};
template<class T,class S,class R> struct zip3{
  T &t; S &s; R &r;
  zip3(T &t_,S &s_,R &r_):t(t_),s(s_),r(r_){}
  ll size() const { return t.end()-t.begin(); }
  auto operator[](ll i)     { return make_tuple(ref(t.begin()[i]),ref(s.begin()[i]),ref(r.begin()[i])); }
  auto operator[](ll i)const{ return make_tuple(ref(t.begin()[i]),ref(s.begin()[i]),ref(r.begin()[i])); }
  auto begin(){ return zipIter(this,0); }
  auto end(){ return zipIter(this,size()); }
  using value_type = tuple<typename T::value_type,typename S::value_type,typename R::value_type>;
};
#endif//テンプレートend
#if defined(_MSC_VER) && __has_include(<atcoder/all>)
#include <atcoder/all>
using namespace atcoder;
#endif
#if defined(_MSC_VER)
#pragma warning( disable : 4996 )
#endif
struct{
  system_clock::time_point st = system_clock::now();
  ll operator()()const{return duration_cast<microseconds>(system_clock::now()-st).count()/1000;}
} timeget;
//////////////////////////////////////////
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...>>(); }
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 };
};
#if 0
#define MODLL (1000000007LL)
#else
#define MODLL (998244353LL)
#endif
using mll = mll_<MODLL>;
//using mll = fraction;
using vmll    = std::vector<mll>;
using vvmll   = std::vector<vmll>;
using vvvmll  = std::vector<vvmll>;
using vvvvmll = std::vector<vvvmll>;
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)){}
  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); }
  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-()const{ return Vector(*this)*=-1; }
  template<class S> friend Vector operator-(S x,const Vector &a){ return -a+=x; }
  Int size()const{ return (Int)vT::size(); }
  Vector &push_back(cT& x){ vT::push_back(x); return *this; }
  Vector &pop_back(){ vT::pop_back(); return *this; }
  Vector &push_front(cT& x){ insert(begin(),x); return *this; }
  Vector &pop_front(){ erase(0); 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){ insert(it(i),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 &concat(cvT &b){ insert(end(),b.begin(),b.end()); return *this; }
  Vector &concat(cvT &b,Int n){ for (int i=0;i<n;++i) concat(b); return *this; }
  Vector &repeat(Int n){ concat(vT(*this),n-1); return *this; }
  Vector &reverse(){ std::reverse(begin(),end()); return *this; }
  Vector &sort(){ std::sort(begin(),end()); return *this; }
  Vector &rsort(){ std::sort(vT::rbegin(),vT::rend()); return *this; }
  template<class Pr> Vector &sort(Pr pr){ std::sort(begin(),end(),pr); return *this; }
  Vector &uniq(){ erase(unique(begin(),end()),end()); return *this; }
  Vector &sortq(){ return sort().uniq(); }
  Vector &fill(Int l,Int r,cT& x){ std::fill(it(l),it(r+1),x); 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 Int(std::count(begin(),end(),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 Int(count_if(begin(),end(),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 Int(std::find(begin(),end(),x)-begin()); }
  Int find(Int l,Int r,cT& x)const{ return Int(std::find(it(l),it(r+1),x)-begin()); }
  template<class Pr> Int findif(Pr pr)const{ return Int(find_if(begin(),end(),pr)-begin()); }
  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; }
};
/*
vll a={9,8,7},b={1,2,3};
vpll p={{5,3},{7,8},{0,2},};
- -------- 操作系 --------
a+=x a-=x a*=x a/=x a%=x a+x a-x a*x a/x a%x -a x-a  //∀i a[i]にxを演算
a.push_front(x);
a.push_back(x);
a.pop_front();
a.pop_back();
a.insert(i,x); //a[i]にx挿入
a.insert(i,b); //a[i]にvll b挿入
a.erase(i);    //a[i]削除
a.erase(l,r);  //区間[l,r]削除
a.concat(b);   //aにbを結合
a.concat(b,n); //aにbをn回結合
a.repeat(n);   //aをn回繰り返す
a.reverse(); //反転
a.sort();    //ソート
a.rsort();   //逆順ソート
p.sort([&](pll x,pll y){return x.second<y.second;});//比較関数指定ソート
a.uniq();      //連続同値を1つにする
a.sortq();     //ソートしてユニーク
a.fill(l,r,x); //[l,r]にx代入
a.iota(n,s,d); //aを等差数列にする 長さn,初項s,公差d
vll a(n,s,d);  //コンストラクタ版iota
- -------- 検索系 --------
auto pr=[&](auto &x){ return x>0; };  //検索条件
ll m=a.count(x);     //xの個数
ll m=a.count(l,r,x); //xの個数in[l,r]
ll m=a.countif(pr);     //条件満たす個数
ll m=a.countif(l,r,pr); //条件満たす個数in[l,r]
ll i=a.find(x);         //xの最左位置i         ない時N(配列長)
ll i=a.find(l,r,x);     //xの最左位置i in[l,r] ない時r+1
ll i=a.findif(pr);      //条件満たす最左位置i         ない時N(配列長)
ll i=a.findif(l,r,pr);  //条件満たす最左位置i in[l,r] ない時r+1
vll is=a.findall(x);        //xの位置i列挙
vll is=a.findall(l,r,x);    //xの位置i列挙in[l,r]
vll is=a.findallif(pr);     //条件満たす位置i列挙
vll is=a.findallif(l,r,pr); //条件満たす位置i列挙in[l,r]
- -------- 昇順sort済み配列用 --------
ll i=a.flooridx(x);   //x以下の最近傍位置i ない時-1
ll i=a.ceilidx(x);    //x以上の最近傍位置i ない時N(配列長)
ll m=a.leftnmof(x);   //x以下の個数
ll m=a.rightnmof(x);  //x以上の個数
bool b=a.contains(x); //xを含む
- -------- 比較関数prでsort済みの配列用 --------
auto pr=[&](auto &x,auto &y){ return x>y; }; //降順ソート時
ll i=a.flooridx(x,pr);   //x以左の最近傍位置i ない時-1
ll i=a.ceilidx(x,pr);    //x以右の最近傍位置i ない時N(配列長)
ll m=a.leftnmof(x,pr);   //x以左の個数
ll m=a.rightnmof(x,pr);  //x以右の個数
bool b=a.contains(x,pr); //xを含む
a.concat(b,n).pop_back().rsort().uniq();  //連続適用できる
*/
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   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>;
using    ll2=array<ll,2>;   using    ll3=array<ll,3>;   using    ll4=array<ll,4>;
using   vll2=vector<  ll2>; using   vll3=vector<  ll3>; using   vll4=vector<  ll4>;
using  vvll2=vector< vll2>; using  vvll3=vector< vll3>; using  vvll4=vector< vll4>;
using vvvll2=vector<vvll2>; using vvvll3=vector<vvll3>; using vvvll4=vector<vvll4>;
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); }); }
struct edge{
  using Int = long long;
  Int to=-1;
  Int cost=0;
  edge(){}
  template<class TLL> edge(const TLL &eg){
    auto [u,v,c]=eg;
    this->to=v;
    this->cost=c;
  }
  operator Int()const{ return to; }
};
struct convexhulltrick{
  using Int=long long;
  using ll=long long;
  ll n=0;
  deque<pll> d; //{a1,b1},{a2,b2},… aiの降順
  bool isMin=true;
  bool isxDesc=false;
  convexhulltrick(bool isMin_,bool isxDesc_=false){ Ini(isMin_,isxDesc_); }
  void Ini(bool isMin_,bool isxDesc_=false){ isMin=isMin_,isxDesc=isxDesc_; }
  bool empty() const { return n==0; }
  ll size() const { return n; }
  void add(Int a,Int b){
    if(!isMin) a=-a,b=-b;
    if(isxDesc) a=-a;
    if(d.empty() || d.back().first>=a) AddBack((ll)a,(ll)b);
    else if(a>=d.front().first) AddFront((ll)a,(ll)b);
    else assert(false);
    n++;
  }
  template<class PLL> void add(vector<PLL> &abs){
    sort(abs.begin(),abs.end());
    for(auto [a,b]: abs) add(a,b);
  }
  ll get(Int x){
    if(isxDesc) x=-x;
    auto y=[&](Int x,ll i){
      auto [a,b]=d[i];
      return a*x+b;
    };
    while(d.size()>=2U && y(x,0)>=y(x,1)) d.pop_front();
    return isMin ? y(x,0) : -y(x,0);
  }
private:
  void AddFront(ll a,ll b){
    while(d.size()>=2U){
      auto [a2,b2]=d[0];
      auto [a3,b3]=d[1];
      if((a2-a)*(b3-b2)<(b2-b)*(a3-a2)) break;
      d.pop_front();
    }
    d.emplace_front(a,b);
  }
  void AddBack(ll a,ll b){
    while(d.size()>=2U){
      auto [a1,b1]=d[d.size()-2];
      auto [a2,b2]=d[d.size()-1];
      if((a2-a1)*(b-b2)<(b2-b1)*(a-a2)) break;
      d.pop_back();
    }
    d.emplace_back(a,b);
  }
};
/*
- ------------------- 定義 -------------------
convexhulltrick cht(true);
.                   ↑true:min, false:max
convexhulltrick cht(true,true);
.                         ↑true:xを降順に与える, 省略:x昇順
- ------------ 直線f(x)=ax+b 追加 ------------ 追加済aのmin以下かmax以上のみ可
cht.add(a,b);
- ----------- min_{a,b} f(x) 取得 ------------ xの指定順は昇順or降順のみ可
ll mn=cht.get(x);
- ------------------ その他 ------------------
ll m=cht.size(); //追加した直線の個数
ll m=cht.empty(); //true:追加した直線の個数0
*/
namespace Dijkstra{
using Int=long long;
using ll=long long;
template<class T> vector<T> dijkstra(vector<vector<edge>> &to,Int s,T inf){
  ll N = (ll)to.size();
  vector<T> dist(N,inf);
  priority_queue<pair<T,Int>,vector<pair<T,Int>>,greater<pair<T,Int>>> Q;
  Q.emplace(T(0),s);
  dist[s]=T(0);
  while(!Q.empty()){
    auto[d,v]=Q.top();  Q.pop();
    if(d>dist[v]) continue;
    for(const edge &eg:to[v]){
      Int u=eg;
      T c=eg.cost;
      if(chmin(dist[u],dist[v]+c)) Q.emplace(dist[u],u);
    }
  }
  return dist;
}
}
using Dijkstra::dijkstra;
/*
vll dist=dijkstra(to,s,INF);
vdd dist=dijkstra<dd>(to,s,1e100);
.    ↑dist[v]:sからvまでの距離
*/
struct IndexSort{
  using Int=long long;
  vector<Int> is;
  template<class T> IndexSort(const vector<T> &A,bool desc=false):is(A.size()){
    iota(is.begin(),is.end(),0);
    if(!desc) sort(is.begin(),is.end(),[&](Int i,Int j){return A[i]<A[j];});
    else      sort(is.begin(),is.end(),[&](Int i,Int j){return A[i]>A[j];});
  }
  template<class Comp> IndexSort(Int N,Comp comp):is(N){
    iota(is.begin(),is.end(),0);
    sort(is.begin(),is.end(),comp);
  }
  vector<Int> get(){ return move(is); }
  vector<Int> Rankof(){
    vector<Int> rankof(is.size());
    for(int r=0;r<(int)is.size();++r) rankof[is[r]]=r;
    return rankof;
  }
  pair<vector<Int>,vector<Int>> is_rankof(){
    vector<Int> rankof=Rankof();
    return {move(is),move(rankof)};
  }
};
/*
vll is=IndexSort(A).get();
.   ↑           ↑Ai昇順にソート Aの型は何でもOK(比較できれば)
.   is[k]:昇順k番目のindex (k:0-origin)
vll is=IndexSort(A,true).get();
.                   ↑true:降順ソート
vll is=IndexSort(N, [&](ll i,ll j){return A[i].second < A[j].second;}).get();
.               ↑要素数                             ↑比較するラムダ式
vll rankof=IndexSort(A).Rankof();
.    ↑rankof[i]:Aiの順位r (r:0-origin) 重複時順不同
auto[is,rankof]=IndexSort(A).is_rankof(); //is,rankof同時取得
*/
void cin2solve()
{
  auto [N,M]=cins<ll,ll>();
  auto W=cinv<ll>(N);
  auto uvt=cinv<tuple<ll,ll,ll>>(M);
  for(auto&&[u,v,t]:uvt) u--,v--;
  using vve=vector<vector<edge>>;
  auto makeWGraph=[](ll n,const auto &edges,bool isDirected){
    vve to(n);
    for(auto eg:edges){
      ll &u=get<0>(eg);
      ll &v=get<1>(eg);
      to[u].emplace_back(eg);
      if(!isDirected) swap(u,v),to[u].emplace_back(eg);
    }
    return to;
  };
  vve to=makeWGraph(N,uvt,false);
  vll ds=dijkstra(to,0,INF);
  vll de=dijkstra(to,N-1,INF);
  convexhulltrick cht(true);
  {
    vll2 abs;
    rep(j,0,N-1){
      abs.push_back(ll2{W[j],de[j]});
    }
    cht.add(abs);
  }
  vll is=IndexSort(W).get();
  //vll is(N,0,1);
  //is.sort([&](ll i,ll j){return W[i]<W[j];});
  //vll ansv(N);
  ll ans=ds[N-1];
  for(auto&& i: is){
    ll mnva=cht.get(W[i]);
    chmin(ans,ds[i]+mnva);
    //ansv[i]=ds[i]+mnva;
  }
  cout << ans << '\n';
  return;
}
};//SolvingSpace
//////////////////////////////////////////
int main(){
  #if 1
  //SolvingSpace::labo();
  SolvingSpace::cin2solve();
  //SolvingSpace::generand();
  #else
  ll t;  cin >> t;
  rep(i,0,t-1){
    SolvingSpace::cin2solve();
    //SolvingSpace::generand();
  } 
  #endif
  cerr << timeget() <<"ms"<< '\n';
  return 0;
}
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