#997166 (C++17) No.705 ゴミ拾い Hard

提出ソース
結果

問題	No.705 ゴミ拾い Hard
ユーザー	hamamu
提出日時	2024-07-23 23:17:50
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	257 ms / 1,500 ms
コード長	65,037 bytes
コンパイル時間	6,111 ms
コンパイル使用メモリ	311,860 KB
実行使用メモリ	14,360 KB
最終ジャッジ日時	2024-07-23 23:18:04
合計ジャッジ時間	12,728 ms
ジャッジサーバーID （参考情報）	judge4 / judge1
このコードへのチャレンジ
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テストケース

テストケース表示
入力	結果	実行時間実行使用メモリ
testcase_00	AC	2 ms 6,812 KB
testcase_01	AC	3 ms 6,816 KB
testcase_02	AC	3 ms 6,812 KB
testcase_03	AC	3 ms 6,944 KB
testcase_04	AC	3 ms 6,940 KB
testcase_05	AC	3 ms 6,940 KB
testcase_06	AC	3 ms 6,940 KB
testcase_07	AC	3 ms 6,944 KB
testcase_08	AC	3 ms 6,940 KB
testcase_09	AC	3 ms 6,944 KB
testcase_10	AC	3 ms 6,944 KB
testcase_11	AC	3 ms 6,940 KB
testcase_12	AC	3 ms 6,944 KB
testcase_13	AC	3 ms 6,944 KB
testcase_14	AC	4 ms 6,940 KB
testcase_15	AC	4 ms 6,940 KB
testcase_16	AC	3 ms 6,940 KB
testcase_17	AC	4 ms 6,944 KB
testcase_18	AC	4 ms 6,940 KB
testcase_19	AC	4 ms 6,940 KB
testcase_20	AC	4 ms 6,940 KB
testcase_21	AC	4 ms 6,944 KB
testcase_22	AC	4 ms 6,940 KB
testcase_23	AC	4 ms 6,944 KB
testcase_24	AC	257 ms 14,236 KB
testcase_25	AC	232 ms 14,112 KB
testcase_26	AC	234 ms 14,232 KB
testcase_27	AC	234 ms 14,236 KB
testcase_28	AC	231 ms 14,232 KB
testcase_29	AC	230 ms 14,360 KB
testcase_30	AC	247 ms 14,108 KB
testcase_31	AC	227 ms 14,112 KB
testcase_32	AC	231 ms 14,156 KB
testcase_33	AC	209 ms 14,232 KB
testcase_34	AC	211 ms 14,236 KB
testcase_35	AC	218 ms 14,236 KB
testcase_36	AC	229 ms 14,232 KB
testcase_37	AC	217 ms 14,236 KB
testcase_38	AC	228 ms 14,232 KB
testcase_39	AC	223 ms 14,168 KB
testcase_40	AC	2 ms 6,944 KB
testcase_41	AC	2 ms 6,940 KB
testcase_42	AC	2 ms 6,948 KB
testcase_43	AC	241 ms 14,108 KB
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

raw source code
#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<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); }); }


namespace dumpstring{
using ll=long long;
using vss =vector<string>;
using vvss=vector<vss>;
template<class T> using V    = vector<T>;
template<class T> using VV   = V<V<T>>;
template<class T> using VVV  = V<VV<T>>;
template<class T> using VVVV = V<VVV<T>>;
/*---- dumpstring用転置関数 ----*/
template<class T> VV<T> transpose2d(const VV<T> &A){
  ll xl=A.size(),yl=A[0].size();
  VV<T> ret(yl,V<T>(xl));
  for(ll i=0;i<xl;++i) for(ll j=0;j<yl;++j) ret[j][i]=A[i][j];
  return ret;
}
template<class T> VVV<T> transpose3d(const VVV<T> &A,array<ll,3> axes){
  array<ll,3> shape={A.size(),A[0].size(),A[0][0].size()};
  auto [xl,yl,zl]=shape;
  auto [Xl,Yl,Zl]=array<ll,3>{shape[axes[0]],shape[axes[1]],shape[axes[2]]};
  VVV<T> ret(Xl,VV<T>(Yl,V<T>(Zl)));
  for(ll i=0;i<xl;++i) for(ll j=0;j<yl;++j) for(ll k=0;k<zl;++k){
    array<ll,3> co={i,j,k};
    auto [I,J,K]=array<ll,3>{co[axes[0]],co[axes[1]],co[axes[2]]};
    ret[I][J][K]=A[i][j][k];
  }
  return ret;
}
template<class T> VVVV<T> transpose4d(const VVVV<T> &A,array<ll,4> axes){
  array<ll,4> shape={A.size(),A[0].size(),A[0][0].size(),A[0][0][0].size()};
  auto [xl,yl,zl,wl]=shape;
  auto [Xl,Yl,Zl,Wl]=
    array<ll,4>{shape[axes[0]],shape[axes[1]],shape[axes[2]],shape[axes[3]]};
  VVVV<T> ret(Xl,VVV<T>(Yl,VV<T>(Zl,V<T>(Wl))));
  for(ll i=0;i<xl;++i) for(ll j=0;j<yl;++j) for(ll k=0;k<zl;++k){
    for(ll l=0;l<wl;++l){
      array<ll,4> co={i,j,k,l};
      auto [I,J,K,L]=array<ll,4>{co[axes[0]],co[axes[1]],co[axes[2]],co[axes[3]]};
      ret[I][J][K][L]=A[i][j][k][l];
    }
  }
  return ret;
}

struct DbgDump{
  using Int=long long;
  vector<vector<string>> field; //field[j][i]:j列のi行目文字列
  ostream &os;
  DbgDump(ostream &os_=cout):os(os_){}
  int W()const{ return (int)field.size(); }
  int H()const {
    int ret=0;
    for(const auto &ss:field) ret=max(ret,(int)ss.size());
    return ret;
  }
  void clear(){ field.clear(); }
  DbgDump &set(Int j,string &&str){ //j列に文字列追加
    if(j>=(int)field.size()) field.resize(j+1);
    field[j].push_back(move(str));
    return *this;
  }
  DbgDump &set(Int j,vector<string> &&strs){ //j列に文字列複数追加
    if(j>=(int)field.size()) field.resize(j+1);
    for(string &str:strs) field[j].push_back(move(str));
    return *this;
  }
  vector<string> flush2str(const string &sep=" ",bool clear_=true){
    vector<int> len(W());//len[j]:j列の文字列長max
    for(int j=0;j<W();++j){
      for(const auto &s:field[j]) len[j]=max(len[j],(int)s.size());
    }
    vector<string> ret;
    for(int i=0;i<H();++i){
      string line;
      for(int j=0;j<W();++j){
        int nSpace=len[j];
        if(i<field[j].size()){
          const string &s=field[j][i];
          line+=string(nSpace-(int)s.size(),' ');
          line+=s;
        }
        else line+=string(nSpace,' ');
        if(j<W()-1) line+=sep;
      }
      ret.push_back(move(line));
    }
    if(clear_) this->clear();
    return ret;
  }
  void flush(const string &sep=" ",bool clear_=true){
    for(auto&& s: flush2str(sep,clear_)) os<<s<<'\n';
  }
};

string stringf(const char *format,...){
  char bf[1000];
  va_list ap;
  va_start(ap,format);
  vsprintf(bf,format,ap);
  va_end(ap);
  return string(bf);
}
string stringfx(int x,int wd=1){
  return stringf("%*d",wd,x);
}
string stringfx(ll x,int wd=1){
  if(x==INF)   return stringf("%*s",wd,"OO");
  if(x>INF/2)  return stringf("%*s",wd,"oo");
  if(x==-INF)  return stringf("%*s",wd,"-OO");
  if(x<-INF/2) return stringf("%*s",wd,"-oo");
  return stringf("%*lld",wd,x);
}
string stringfx(double x,int wd=1,int fr=4){
  return stringf("%*.*f",wd,fr,x);
}
template <int MOD> string stringfx(mll_<MOD> x,int wd=1){
  return stringfx(x.val(),wd);
}
template <int m> string stringfx(static_modint<m> x,int wd=1){
  return stringfx((ll)x.val(),wd);
}
template <int id> string stringfx(dynamic_modint<id> x,int wd=1){
  return stringfx((ll)x.val(),wd);
}
template<class T,class S> string stringfx(pair<T,S> x,int wd=1){
  return stringfx(x.first,wd)+","+stringfx(x.second,wd);
}
template<class T,size_t N> string stringfx(const array<T,N> &x,int wd=1){
  string ret;
  for(int i=0;i<(int)N;++i) ret+=stringfx(x[i],wd)+(i<N-1?",":"");
  return ret;
}
template <class T> string stringfx(T x,int wd=1){
  return stringf("%*s",wd,x.to_string().c_str());
}
template<class T> string stringf1d(const vector<T> &v,ll wd){
  string ret;
  for(int i=0; i<(int)v.size(); ++i) ret+=stringfx(v[i],(int)wd);
  return ret;
}
struct args{
  using Int = long long;
  Int wd_=1,sx_=0,sy_=0,sz_=0,sw_=0,dx_=1,dy_=1,dz_=1,dw_=1;
  vector<Int> tr_;
  vector<string> labels_;
  bool xrev_=false,yrev_=false,zrev_=false,wrev_=false;
  args():tr_({0,1,2,3,4,5}){}
  args &wd(Int wd__){ wd_=wd__; return *this; }
  args &sx(Int s){ sx_=s; return *this; }
  args &sy(Int s){ sy_=s; return *this; }
  args &sz(Int s){ sz_=s; return *this; }
  args &sw(Int s){ sw_=s; return *this; }
  args &dx(Int d){ dx_=d; return *this; }
  args &dy(Int d){ dy_=d; return *this; }
  args &dz(Int d){ dz_=d; return *this; }
  args &dw(Int d){ dw_=d; return *this; }
  template<size_t DIM> args &rngs(array<array<Int,DIM>,2> rngs){
    if(DIM>=1) sx_=rngs[0][0],dx_=rngs[1][0];
    if(DIM>=2) sy_=rngs[0][1],dy_=rngs[1][1];
    if(DIM>=3) sz_=rngs[0][2],dz_=rngs[1][2];
    if(DIM>=4) sw_=rngs[0][3],dw_=rngs[1][3];
    return *this;
  }
  args &tr(vector<Int> tr__){ tr_=tr__; return *this; }
  args &tr(){ tr_={1,0}; return *this; }
  args &labels(vector<string> labels__){ labels_=labels__; return *this; }
  args &xrev(){ xrev_=true; return *this; }
  args &yrev(){ yrev_=true; return *this; }
  args &zrev(){ zrev_=true; return *this; }
  args &wrev(){ wrev_=true; return *this; }
  tuple<Int,Int,Int,bool> getargs1d()const{ return {wd_,sx_,dx_,xrev_}; }
  tuple<Int,Int,Int,Int,Int,bool,bool,bool> getargs2d()const{
    return {wd_,sx_,sy_,dx_,dy_,tr_[0]==1&&tr_[1]==0,xrev_,yrev_};
  }
  tuple<Int,Int,Int,Int,Int,Int,Int,array<Int,3>,bool,bool,bool> getargs3d()const{
    return {wd_,sx_,sy_,sz_,dx_,dy_,dz_,
      {tr_[0],tr_[1],tr_[2]},xrev_,yrev_,zrev_};
  }
  tuple<Int,Int,Int,Int,Int,Int,Int,Int,Int,array<Int,4>,bool,bool,bool,bool>
    getargs4d()const
  {
    return {wd_,sx_,sy_,sz_,sw_,dx_,dy_,dz_,dw_,
      {tr_[0],tr_[1],tr_[2],tr_[3]},xrev_,yrev_,zrev_,wrev_};
  }
  const char *label(Int i)const{//転置後第i軸(0-origin)のラベル
    return tr_[i]<(Int)labels_.size() ? labels_[tr_[i]].c_str() : "";
  }
};
template<class T> vector<string> sdumpNd(
  const string &header,const vector<T> &v_,const args &p=args())
{
  //-- パラメータ取り出し
  ll N=(ll)v_.size();
  auto [wd,sx,dx,xrv]=p.getargs1d();
  //-- 反転を吸収
  vector<T> v=v_;
  if(xrv) sx+=dx*(N-1),dx*=-1,reverse(v.begin(),v.end());
  //-- 文字列化
  DbgDump dbgd;
  for(ll j=0;j<N;++j) dbgd.set(j,stringf("%s%lld",p.label(0),sx+j*dx));//上目盛
  for(ll j=0;j<N;++j) dbgd.set(j,stringfx(v[j],(int)wd));//中身
  vss ret=dbgd.flush2str();
  ret.insert(ret.begin(),header);//ヘッダを上に挿入
  ret.insert(ret.begin()+2,string(ret[1].size(),'-'));//横線を上目盛の下に挿入
  return ret;
}
template<class T> vss sdumpNd(
  const string &header,const vector<vector<T>> &fd_,const args &p=args())
{
  //-- パラメータ取り出し
  ll h=(ll)fd_.size(),w=(ll)fd_[0].size();
  auto [wd,sx,sy,dx,dy,tr,xrv,yrv]=p.getargs2d();
  //-- fdで反転・transを吸収(反転は未実装)
  vector<vector<T>> fd = tr ? transpose2d(fd_) : fd_;
  if(tr) swap(sx,sy),swap(dx,dy),swap(h,w);
  //-- 文字列化
  DbgDump dbgd;
  dbgd.set(0,"|");
  for(ll i=0;i<h;++i) dbgd.set(0,stringf("%s%lld |",p.label(0),sx+i*dx));//左目盛
  for(ll j=0;j<w;++j) dbgd.set(j+1,stringf("%s%lld",p.label(1),sy+j*dy));//上目盛
  for(ll i=0;i<h;++i) for(ll j=0;j<w;++j){//中身
    dbgd.set(j+1,stringfx(fd[i][j],(int)wd));
  }
  vss ret=dbgd.flush2str();
  ret.insert(ret.begin()+1,string(ret[0].size(),'-'));//横線を上目盛の下に挿入
  if(!header.empty()) ret.insert(ret.begin(),header);//ヘッダを上に挿入
  return ret;
}
template<class T> vss sdumpNd(const string &header,
  const vector<vector<vector<T>>> &fd_,const args &p=args())
{
  //-- パラメータ取り出し
  auto [wd,sx,sy,sz,dx,dy,dz,tr,xrv,yrv,zrv]=p.getargs3d();
  //-- fdで反転・transを吸収(反転は未実装)
  vector<vector<vector<T>>> fd=transpose3d(fd_,tr);
  array<ll,3> sxyz={sx,sy,sz},dxyz={dx,dy,dz};
  sx=sxyz[tr[0]]; sy=sxyz[tr[1]]; sz=sxyz[tr[2]];
  dx=dxyz[tr[0]]; dy=dxyz[tr[1]]; dz=dxyz[tr[2]];
  //-- 文字列化
  DbgDump dbgd;
  for(ll i=0;i<(ll)fd.size();++i){
    vss s2d=sdumpNd(string(),fd[i],
      args().sx(sy).dx(dy).sy(sz).dy(dz).labels({p.label(1),p.label(2)}));
    string header=stringf("<%s%d>",p.label(0),sx+i*dx);
    header.resize(s2d[0].size(),' ');
    dbgd.set(i*2,move(header));
    dbgd.set(i*2,move(s2d));
    if(i>0){
      for(ll t=0;t<(ll)s2d.size()+1;++t) dbgd.set(i*2-1,"||");
    }
  }
  vss ret=dbgd.flush2str();
  if(!header.empty()) ret.insert(ret.begin(),header);//ヘッダを上に挿入
  return ret;
}
template<class T> vss sdumpNd(const string &header,
  const vector<vector<vector<vector<T>>>> &fd_,const args &p=args()
){
  //-- パラメータ取り出し
  auto [wd,sx,sy,sz,sw,dx,dy,dz,dw,tr,xrv,yrv,zrv,wrv]=p.getargs4d();
  //-- fdで反転・transを吸収(反転は未実装)
  vector<vector<vector<vector<T>>>> fd=transpose4d(fd_,tr);
  array<ll,4> sxyzw={sx,sy,sz,sw},dxyzw={dx,dy,dz,dw};
  sx=sxyzw[tr[0]]; sy=sxyzw[tr[1]]; sz=sxyzw[tr[2]]; sw=sxyzw[tr[3]];
  dx=dxyzw[tr[0]]; dy=dxyzw[tr[1]]; dz=dxyzw[tr[2]]; dw=dxyzw[tr[3]];
  //-- 文字列化
  vss ret;
  if(!header.empty()) ret.push_back(header);
  for(ll i=0;i<(ll)fd.size();++i){
    if(i>0) ret.push_back("");
    ret.push_back(stringf("---<%s%lld>---",p.label(0),sx+i*dx));
    vss s3d=sdumpNd(string(),fd[i],args().sx(sy).dx(dy).sy(sz).dy(dz)
      .sz(sw).dz(dw).labels({p.label(1),p.label(2),p.label(3)}));
    ret.insert(ret.end(),s3d.begin(),s3d.end());
  }
  return ret;
}
#if defined(_DEBUG)
template<class NdT> void dumpNd(const string &h,const NdT &fd,const args &p=args(),ostream &os=cerr){ for(auto&&e: sdumpNd(h,fd,p)) os<<e<<endl; }
#else
template<class NdT> void dumpNd(const string &h,const NdT &fd,const args &p=args(),ostream &os=cerr){}
#endif
};
using dumpstring::stringf; using dumpstring::stringfx; using dumpstring::stringf1d;
using dumpstring::args;    using dumpstring::sdumpNd;  using dumpstring::dumpNd;
/*
- -------- printfと同じ書式でstringを生成 --------
string s=stringf("(%2lld,%2lld) E:%5.3f",x,y,E*100)
- -------- 幅wdの整数で値xをstring化 --------
string s=stringfx(x,wd);
- -------- 幅wdの整数で配列vをstring化 --------  ll,int,dd,mll,fraction,pair,array対応
string s=stringf1d(v,wd);
- -------- 1D配列ダンプ --------  ll,int,dd,mll,fraction,pair,array対応
vector<string> ss=sdumpNd("タイトル",v);
dumpNd("タイトル",v);
dumpNd("タイトル",v,args().sx(N).dx(-1).xrev().wd(5));
.                        ↑パラメータ wd:表示幅
- -------- 2D配列ダンプ --------  ll,int,dd,mll,fraction,pair,array対応
vector<string> ss=sdumpNd("タイトル",fd);
dumpNd("タイトル",fd);
dumpNd("タイトル",fd,args().sx(N).dx(-1).sy(-5).dy(1).wd(5).tr().labels({"i","s"}));
.                        ↑パラメータ wd:表示幅 tr:転置 xrev,yrevは未実装
- -------- 3D配列ダンプ --------  ll,int,dd,mll,fraction,pair,array対応
vector<string> ss=sdumpNd("タイトル",fd);
dumpNd("タイトル",fd);
dumpNd("タイトル",fd,args().sx(2).dx(-1).sy(5).dy(1).sz(-3).dz(-1).tr({2,1,0}).labels({"i","s","u"}));
.                        ↑パラメータ wd:表示幅 tr:軸順指定 反転(xrev等)は未実装
- -------- 4D配列ダンプ --------  ll,int,dd,mll,fraction,pair,array対応
vector<string> ss=sdumpNd("タイトル",fd);
dumpNd("タイトル",fd);
dumpNd("タイトル",fd,args().sx(2).dx(-1).sy(5).dy(1).sz(-3).dz(-1).sw(-1).dw(1).tr({2,1,3,0}).labels({"t","u","i","s"}));
.                        ↑パラメータ wd:表示幅 tr:軸順指定 反転(xrev等)は未実装
*/


template<int DIM> struct rangeNd{
  using Int = long long;
  using NInt = array<Int,DIM>;
  NInt sv,ev,lv,dv; //各変数の初期値,終了値,項数,公差(通常±1)
  Int size_=1;
  NInt cyclemask;
  rangeNd(const NInt &sv_,const NInt &ev_,Int cycle=-1): sv(sv_),ev(ev_){
    for(ll i=0;i<DIM;++i) lv[i]=abs(sv[i]-ev[i])+1;
    for(ll i=0;i<DIM;++i) dv[i]=sign(ev[i]-sv[i]);
    for(ll i=0;i<DIM;++i) size_*=lv[i];
    for(ll i=0;i<DIM;++i) cyclemask[i]=~0;
    if(cycle!=-1) cyclemask[0]=cycle-1;
  }
  Int size()const{ return size_; }
  Int csize()const{ return size_/lv[0]; }
  bool isCycle()const{ return cyclemask[0]!=~0; }
  Int cycle()const{ return isCycle() ? cyclemask[0]+1 : -1; }
  tuple<Int,Int,Int,Int> SELDx()const{ return SELDof(0); }
  tuple<Int,Int,Int,Int> SELDy()const{ return SELDof(1); }
  tuple<Int,Int,Int,Int> SELDz()const{ return SELDof(2); }
  tuple<Int,Int,Int,Int> SELDw()const{ return SELDof(3); }
  array<NInt,2> rngs()const{ return {sv,dv}; }
  NInt ls()const{ return lv; }
  NInt v2i(const NInt &vx)const{
    NInt ret;
    for(Int i=0;i<DIM;++i) ret[i]=(vx[i]-sv[i])*dv[i];
    return ret;
  }
  auto toID(){
    return [this](const NInt &vx)->Int{
      Int id=0;
      for(Int i=0;i<DIM;++i){
        Int x=vx[i],s=sv[i],l=lv[i],d=dv[i],xx=(x-s)*d;
        if(xx<0 || l<=xx) return -1;
        id=id*l+(xx&cyclemask[i]);
      }
      return id;
    };
  }
  auto fromID(){
    return [this](Int id)->NInt{
      NInt ret;
      for(Int i=DIM-1;i>=0;--i){
        Int s=sv[i],l=lv[i],d=dv[i],nid=id/l,xx=id-nid*l;
        ret[i]=s+xx*d;
        id=nid;
      }
      return ret;
    };
  }
  bool out(const NInt &vx){
    for(Int i=0;i<DIM;++i){
      Int x=vx[i],s=sv[i],l=lv[i],d=dv[i];
      Int xx=(x-s)*d;
      if(xx<0 || l<=xx) return true;
    }
    return false;
  }
  NInt start(Int xx=0)const{
    NInt ret=sv;
    ret[0]=sv[0]+dv[0]*xx;
    return ret;
  }
  bool next(NInt &vx,Int dMn=0)const{ //次へ進める 対象:第dMn以降 @return true:次有
    for(int d=DIM-1;d>=dMn;--d){
      if(vx[d]==ev[d]) vx[d]=sv[d];
      else{ vx[d]+=dv[d]; return true; }
    }
    return false;
  }
private:
  tuple<Int,Int,Int,Int> SELDof(Int i)const{
    if(i>=DIM) return {-1,-1,-1,-1};
    return {sv[i],ev[i],lv[i],dv[i]};
  }
  static Int sign(Int x){ return x==0 ? 0 : x>0 ? 1 : -1; }
};


template<class STATE,class VAL,class Ope,class Tran,class ToID,class FromID>
struct PushBasedDP{
  using Int = long long;
  using ll = long long;
  Ope ope; //配るときの演算
  Tran tran;
  ToID toID;
  FromID fromID;
  VAL ini,dmy; //ini:dpテーブルの初期値
  vector<VAL> dp_;
  bool autoResize = true;
  bool nextdp = false; //true:nextDP
  //-------- コンストラクタ --------
  PushBasedDP(STATE,VAL,Ope ope_,Tran tran_,ToID toID_,FromID fromID_,VAL ini_)
    : ope(ope_),tran(tran_),toID(toID_),fromID(fromID_),ini(ini_),dmy(ini_){}
  //事前メモリ確保用コンストラクタ
  template<class RNG> PushBasedDP(STATE,VAL,Ope ope_,Tran tran_,ToID toID_,
    FromID fromID_,VAL ini_,const RNG &rng)
    : ope(ope_),tran(tran_),toID(toID_),fromID(fromID_),ini(ini_),dmy(ini_),
    dp_(rng.isCycle() ? rng.csize()*rng.cycle() : rng.size(),ini),
    autoResize(false),nextdp(rng.isCycle()){}
  //-------- アクセス・計算実行 --------
  template<class... Args> VAL &operator()(Args&&... args){ return Dp(STATE{args...}); }
  template<class... Args> void calc(Args&&... args){ calcSt({args...}); }
  template<class RNG> void calcall(const RNG &rng){
    if(nextdp) calcallNextDp(rng);
    else        calcallNormal(rng);
  }
  using   vVAL = vector<  VAL>;  using   vvVAL = vector<  vVAL>;
  using vvvVAL = vector<vvVAL>;  using vvvvVAL = vector<vvvVAL>;
  vVAL    tov(array<Int,1> ls){ return tov(ls[0]); }
  vvVAL   tov(array<Int,2> ls){ return tov(ls[0],ls[1]); }
  vvvVAL  tov(array<Int,3> ls){ return tov(ls[0],ls[1],ls[2]); }
  vvvvVAL tov(array<Int,4> ls){ return tov(ls[0],ls[1],ls[2],ls[3]); }
  vVAL tov(Int xl){
    dp_.resize(xl,ini);  return vVAL(dp_);
  }
  vvVAL tov(Int xl,Int yl){
    dp_.resize(xl*yl,ini);
    vvVAL ret(xl,vVAL(yl));
    for(ll i=0;i<xl;++i) for(ll j=0;j<yl;++j) ret[i][j]=dp_[i*yl+j];
    return ret;
  }
  vvvVAL tov(Int xl,Int yl,Int zl){
    dp_.resize(xl*yl*zl,ini);
    vvvVAL ret(xl,vvVAL(yl,vVAL(zl)));
    for(ll i=0;i<xl;++i) for(ll j=0;j<yl;++j) for(ll k=0;k<zl;++k){
      ret[i][j][k]=dp_[i*yl*zl+j*zl+k];
    }
    return ret;
  }
  vvvvVAL tov(Int xl,Int yl,Int zl,Int wl){
    dp_.resize(xl*yl*zl*wl,ini);
    vvvvVAL ret(xl,vvvVAL(yl,vvVAL(zl,vVAL(wl))));
    for(ll i=0;i<xl;++i) for(ll j=0;j<yl;++j) for(ll k=0;k<zl;++k){
      for(ll l=0;l<wl;++l) ret[i][j][k][l]=dp_[i*yl*zl*wl+j*zl*wl+k*wl+l];
    }
    return ret;
  }
private:
  VAL &Dp(const STATE &vx){
    ll id=toID(vx);
    if(autoResize && (ll)dp_.size()<=id) dp_.resize(id+1,ini);
    return id<0 ? (dmy=ini) : dp_[id];
  }
  void calcSt(const STATE &vx){
    auto dstVal=[&](const STATE &nvx,VAL val){
      VAL &DpNvx=Dp(nvx);
      VAL nval=ope(DpNvx,val);
      if(DpNvx!=nval) DpNvx=nval,preRenew(nvx,vx);
    };
    tran(vx,Dp(vx),dstVal);
  }
  template<class RNG> void calcallNormal(const RNG &rng){
    STATE vx=rng.start();
    do calcSt(vx); while(rng.next(vx));
  }
  template<class RNG> void calcallNextDp(const RNG &rng){
    auto [sx,ex,xl,dx]=rng.SELDx();
    for(ll xx=0;xx<xl;++xx){
      //1つ前を消去
      if(xx>0){
        ll id=toID(rng.start(xx-1));
        auto it=dp_.begin()+id;
        fill(it,it+rng.csize(),ini);//dp_[id～id+csize-1]を消去
      }
      //現在位置xxを処理
      STATE vx=rng.start(xx);
      do calcSt(vx); while(rng.next(vx,1));
    }
  }
  //-------- ダンプ --------
public:
  #if 1
  template<int N>
  void dump(rangeNd<N> &rng,vector<string> labels={},const vector<ll> axes={0,1,2,3}){
    auto ls=rng.ls();
    if(nextdp) ls[0]=rng.cycle();
    dumpstring::dumpNd("",tov(ls),args().rngs(rng.rngs()).labels(labels).tr(axes));
  }
  #endif
  //-------- 最適パス --------
  #if 0
private:
  vector<ll> pre;
  ll preini=-1,predmy=-1;
  ll &Pre(const STATE &vx){
    ll id=toID(vx);
    if((ll)pre.size()<=id) pre.resize(id+1,preini);
    return id<0 ? (predmy=preini) : pre[id];
  }
  void preRenew(const STATE &vx,const STATE &src){ Pre(vx)=toID(src); }
public:
  template<class... Args> vector<STATE> pathget(Args&&... endargs){
    vector<ll> ids{toID({endargs...})};
    while(ids.back()<(ll)pre.size() && pre[ids.back()]!=preini) ids.push_back(pre[ids.back()]);
    reverse(ids.begin(),ids.end());
    vector<STATE> path;
    for(auto&& id: ids) path.push_back(fromID(id));
    return path;
  }
  #else
  void preRenew(const STATE &vx,const STATE &src)const{ (void)vx,(void)src; }
  #endif
};


namespace MonotoneMinima{
using Int=long long;
using ll=long long;
template<class F,class Comp> vector<Int> monotoneMinima(F f,Int H,Int W,Comp comp){
  vector<Int> ret(H);
  auto dfs=[&](auto dfs,ll si,ll ei,ll sj,ll ej){
    if(si>ei) return;
    ll mi=(si+ei)/2;
    ll minj=sj;
    for(ll j=sj+1;j<=ej;++j){
      if(comp(f(mi,j),f(mi,minj))) minj=j;
    }
    ret[mi]=minj;
    dfs(dfs,si,mi-1,sj,minj);
    dfs(dfs,mi+1,ei,minj,ej);
  };
  dfs(dfs,0,H-1,0,W-1);
  return ret;
}
template<class DP,class Tran,class Comp>
void onlineMonotoneMinima(DP dp,Int st,Int en,Tran F,Comp comp){
  auto Chmin=[&](auto &a,const auto &b){if(comp(b,a)) a=b;};
  auto induce=[&](ll l,ll m,ll r){//[l,m]→[m+1,r]
    auto f=[&](ll i,ll j){ return F(i+m+1,j+l,dp(j+l)); };
    vector<ll> minjs=monotoneMinima(f,r-m,m-l+1,comp);
    for(ll i=0;i<r-m;++i){
      Chmin(dp(i+m+1),f(i,minjs[i]));
    }
  };
  auto dfs=[&](auto dfs,ll l,ll r){
    if(l==r) return;
    ll m=(l+r+1)/2-1; //[l,m]と[m+1,r]に分割
    dfs(dfs,l,m);
    induce(l,m,r);
    dfs(dfs,m+1,r);
  };
  dfs(dfs,st,en);
}
};
using MonotoneMinima::monotoneMinima;
using MonotoneMinima::onlineMonotoneMinima;


void cin2solve()
{
  auto N=cin1<ll>();
  auto A=cinv<ll>(N);
  auto X=cinv<ll>(N);
  auto Y=cinv<ll>(N);

  /*
  dp(i) 人iが回収した後のコストmin
  */
  #if 0
  using STATE=array<ll,1>; //i
  using VAL=ll;
  auto operation=[&](VAL a,VAL b){return min(a,b);};  VAL ini=INF;
  auto transition=[&](const STATE &vx,VAL va,auto dstVal){};

  auto [s1,e1]=pll{-1,N-1}; //1つ目の変数の範囲
  rangeNd<1> rng({s1,},{e1,});
  PushBasedDP dp(STATE(),VAL(),operation,transition,rng.toID(),rng.fromID(),ini,rng);

  dp(-1)=0;
  #endif

  vll dp(N+1,INF);
  using VAL=ll;

  auto comp=less<VAL>(); //最小化
  auto F=[&](ll i,ll j,const VAL &dpj){ //j→i遷移で配られる値
    ll ax=A[i],ay=0;
    ll bx=X[j+1],by=Y[j+1];
    ll sax=abs(ax-bx);
    ll say=abs(ay-by);
    return dpj+sax*sax*sax+say*say*say;
  };
  auto Dp=[&](ll i)->VAL& { return dp[i+1]; };
  Dp(-1)=0;
  onlineMonotoneMinima(Dp,-1,N-1,F,comp);

  ll ans=Dp(N-1);
  cout << ans << '\n';

  //dp.dump(rng,{"i"});

  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;
}
yukicoder

結果

テストケース

ソースコード
