結果
| 問題 |
No.2496 LCM between Permutations
|
| ユーザー |
 hamamu
|
| 提出日時 | 2023-10-06 23:10:36 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
TLE
|
| 実行時間 | - |
| コード長 | 45,611 bytes |
| コンパイル時間 | 5,145 ms |
| コンパイル使用メモリ | 284,620 KB |
| 最終ジャッジ日時 | 2025-02-17 05:32:05 |
|
ジャッジサーバーID （参考情報） |
judge3 / judge2 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | TLE * 1 |
| other | -- * 28 |
ソースコード
#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
struct{
system_clock::time_point st = system_clock::now();
ll operator()()const{return duration_cast<microseconds>(system_clock::now()-st).count()/1000;}
} timeget;
//////////////////////////////////////////
template<long long MOD> struct mll_{
using Int = long long;
using ll = long long;
ll val_=0;
/*---- utility ----*/
mll_ &norm(){ return normR().normS(); }//正規化
mll_ &normR(){ val_%=MOD; return *this; }//剰余正規化のみ
mll_ &normS(){ if (val_<0) val_+=MOD; return *this; }//正負正規化のみ
mll_ &normP(){ if (val_>=MOD) val_-=MOD; return *this; }//加算時正規化
mll_ &invsg(){ val_=-val_; return normS(); }//正負反転
ll modinv(int a){//a^-1 mod MOD
int ypre=0,y=1,apre=MOD;
while (a>1){
int t=apre/a;
apre-=a*t,swap(a,apre);
ypre-=y*t,swap(y,ypre);
}
return y<0 ? y+MOD: y;
}
/*---- I/F ----*/
mll_(){}
mll_(ll v): val_(v){ norm(); }
mll_(ll v,bool b): val_(v){} //正規化無のコンストラクタ
Int val()const{ return (Int)val_; }
bool isnone() const { return val_==-1; } //true:値なし
mll_ &none() { val_=-1; return *this; } //値なしにする
mll_ &inv(){ val_=modinv((int)val_); return *this; }
mll_ &operator+=(mll_ b){ val_+=b.val_; return normP(); }
mll_ &operator-=(mll_ b){ val_-=b.val_; return normS(); }
mll_ &operator*=(mll_ b){ val_*=b.val_; return normR(); }
mll_ &operator/=(mll_ b){ return *this*=b.inv(); }
mll_ &operator+=(ll b){ return *this+=mll_(b); }
mll_ &operator-=(ll b){ return *this-=mll_(b); }
mll_ &operator*=(ll b){ return *this*=mll_(b); }
mll_ &operator/=(ll b){ return *this/=mll_(b); }
mll_ operator-()const{ return mll_(*this).invsg(); }
mll_ operator+(mll_ b)const{ return mll_(*this)+=b; }
mll_ operator-(mll_ b)const{ return mll_(*this)-=b; }
mll_ operator*(mll_ b)const{ return mll_(*this)*=b; }
mll_ operator/(mll_ b)const{ return mll_(*this)/=b; }
mll_ operator+(ll b)const{ return mll_(*this)+=b; }
mll_ operator-(ll b)const{ return mll_(*this)-=b; }
mll_ operator*(ll b)const{ return mll_(*this)*=b; }
mll_ operator/(ll b)const{ return mll_(*this)/=b; }
friend mll_ operator+(ll a,mll_ b){ return b+a; }
friend mll_ operator-(ll a,mll_ b){ return -b+a; }
friend mll_ operator*(ll a,mll_ b){ return b*a; }
friend mll_ operator/(ll a,mll_ b){ return mll_(a)/b; }
bool operator==(mll_ b)const{ return val_==b.val_; }
bool operator!=(mll_ b)const{ return val_!=b.val_; }
bool operator==(ll b)const{ return *this==mll_(b); }
bool operator!=(ll b)const{ return *this!=mll_(b); }
friend bool operator==(ll a,mll_ b){ return mll_(a)==b; }
friend bool operator!=(ll a,mll_ b){ return mll_(a)!=b; }
friend ostream &operator<<(ostream &os,mll_ a){ return os << a.val_; }
friend istream &operator>>(istream &is,mll_ &a){ return is >> a.val_; }
mll_ pow(ll k)const{
mll_ ret(1,false),a(*this);
for (; k>0; k>>=1,a*=a) if (k&1)ret*=a;
return ret;
}
static constexpr int mod() { return MOD; }
//enum{ modll=MOD };
};
#if 0
template<long long MOD> struct mll_{
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
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;
}
enum{ modll=MOD };
};
#endif
#if 0
#define MODLL (1000000007LL)
#else
#define MODLL (998244353LL)
#endif
using mll = mll_<MODLL>;
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)){}
Vector(Int n,T s,T d){ iota(n,s,d); }
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; }
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>;
auto interactive_query(ll i,ll j){
//cout
cout << "? ";
cout << pll{i+1,j+1};
cout << endl;
//cin
ll x;
cin >> x;
return x;
}
void interactive_result(vll a,vll b){
cout << "! ";
cout << a;
cout << " ";
cout << b;
cout << endl;
}
void cin2solve()
{
ll n;
cin >> n;
if (n==1){
vll a={1};
vll b={1};
interactive_result(a,b);
return;
}
/////////////////////////
if (n==2){
vll a(n,-1);
vll b(n,-1);
vll c1;
rep(i,0,n-1){
c1.push_back(interactive_query(i,0));
}
//
if (c1[0]==2 and c1[1]==2){
b={2,1};
vll c2;
rep(i,0,n-1){
c2.push_back(interactive_query(i,1));
}
a=c2;
}
//
else{
a=c1;
b={1,2};
}
interactive_result(a,b);
return;
}
/////////////////////////
vll a(n,-1);
vll b(n,-1);
vll c1;
rep(i,0,n-1){
c1.push_back(interactive_query(i,0));
}
ll x=mine(c1);
ll ai=-1;
rep(i,0,n-1){
ll va=c1[i];
ll y=va/x;
if (y*2>n){
a[i]=y;
ai=i;
}
}
assert(ai!=-1);
ll p=a[ai];
/////////////////////////
vll c2;
rep(i,0,n-1){
c2.push_back(interactive_query(ai,i));
}
vll bjs;
rep(j,0,n-1){
ll va=c2[j];
ll y=va/p;
if (y==1){
bjs.push_back(j);
}
else b[j]=y;
}
/////////////////////////
vll c3;
rep(i,0,n-1){
c3.push_back(interactive_query(i,bjs[0]));
}
if (c3.count(1)>0){
b[bjs[0]]=1;
b[bjs[1]]=p;
a=c3;
}
else{
b[bjs[0]]=p;
b[bjs[1]]=1;
rep(i,0,n-1){
if (a[i]==-1) a[i]=c3[i]/p;
}
}
interactive_result(a,b);
return;
}
};//SolvingSpace
//////////////////////////////////////////
int main(){
#if 0
//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;
}