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

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

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

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


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


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

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


#if 0
#define MODLL (1000000007LL)
#else
#define MODLL (998244353LL)
#endif
using mll = mll_<MODLL>;
//using mll = fraction;



namespace SolvingSpace{

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

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template<class T> struct cumulativesum{
    using Int = long long;
    using ll = long long;
    using pIT = pair<Int,T>;
    ll n=0;  vector<T> c;
    cumulativesum():c(1){}
    template<class S> cumulativesum(S &&v) : n((ll)v.size()),c(n+1) { Ini(v); }
    template<class S> void init(S &&v){ n=(ll)v.size(); c.resize(n+1); Ini(v); }
    void add(T x) { n++; c.push_back(c.back()+x); }
    T operator()(Int l,Int r){ return c[max(min(n,r+1),0LL)]-c[min(max(0LL,l),n)]; }

    pIT floorGroup(ll l,T x){
        l=clamp(l,0LL,(ll)c.size()-1);
        T th=x+c[l];
        ll r=upper_bound(c.begin(),c.end(),th)-c.begin()-2;
        T rem = r==-2 ? T() : th-c[r+1];
        return {r,rem};
    }

    pIT ceilGroup(ll l,T x){
        l=clamp(l,0LL,(ll)c.size()-1);
        T th=x+c[l];
        ll r=lower_bound(c.begin(),c.end(),th)-c.begin()-1;
        T rem = r==(ll)c.size()-1 ? T() : c[r+1]-th;
        return {r,rem};
    }

    pIT floorGroupRev(ll r,T x){
        // A0+…+A_{l-1} が (A0+…+Ar)-x以上に初めてなったときが答
        r=clamp(r,-1LL,(ll)c.size()-2);
        ll th=c[r+1]-x; //(A0+…+Ar)-x
        ll l=lower_bound(c.begin(),c.end(),th)-c.begin();
        T rem = l==(ll)c.size() ? T() : c[l]-th;
        return {l,rem};
    }

    pIT ceilGroupRev(ll r,T x){
        // A0+…+A_{l-1} が (A0+…+Ar)-x以下な最大のlが答
        r=clamp(r,-1LL,(ll)c.size()-2);
        ll th=c[r+1]-x; //(A0+…+Ar)-x
        ll l=upper_bound(c.begin(),c.end(),th)-c.begin()-1;
        T rem = l==-1 ? T() : th-c[l];
        return {l,rem};
    }

    pIT groupIdx(ll l,T x){
        auto [r,rem]=floorGroup(l,x);
        return (r+1==-1 || r+1==n) ? pIT{r+1,T()} : pIT{r+1,rem};
    }
    pIT groupIdxRev(ll r,T x){
        auto [l,rem]=floorGroupRev(r,x);
        return (l-1==-1 || l-1==n) ? pIT{l-1,T()} : pIT{l-1,c[l]-c[l-1]-1-rem};
    }

    T mx(){//区間和max
        T mn=T(),samx=0;
        for (ll i=1; i<=n; ++i){
            chmax(samx,c[i]-mn);
            chmin(mn,c[i]);
        }
        return samx;
    }
    template<class S> void Ini(S &&v) { for (ll i=0; i<n; ++i) c[i+1]=c[i]+v[i]; }
};
template<class S> cumulativesum(S) -> cumulativesum<typename remove_reference<S>::type::value_type>;
/*
- ===================== 定義 =====================
cumulativesum cm(v);
- =================== 逐次追加 ===================  複数定義する例
vector<cumulativesum<ll>> vc(n); //定義
vc[i].add(x);                    //末尾に追加
- ================== 区間和取得 ==================
ll sm=cm(l,r); //v[l]～v[r]の和
ll sm=cm(4,2); //定義外は0埋めと見なす＆逆順は正負反転するだけで落ちない
- =================== 二分探索 ===================  全要素≧0  x負でr<lにも拡張
auto[r,rem]=cm.floorGroup(l,x);   //Al+A_{l+1}+…+Ar+rem=x なる最大のr r=-2:解無
auto[r,rem]=cm.ceilGroup(l,x);    //Al+A_{l+1}+…+Ar=x+rem なる最小のr r=N :解無
auto[l,rem]=cm.floorGroupRev(r,x);//Ar+A_{r-1}+…+Al+rem=x なる最小のl l=N+1:解無
auto[l,rem]=cm.ceilGroupRev(r,x); //Ar+A_{r-1}+…+Al=x+rem なる最大のl l=-1 :解無
- ============= 二分探索(群数列用I/F) ============  全要素≧0  x負でr<lにも拡張
vll A={0,3,1,4,0,1,5}; //A[g]:グループgの個数
0|    1   | 2|     3     |4| 5|       6        グループ番号g
.| 0  1  2| 0| 0  1  2  3| | 0| 0  1  2  3  4  グループ内位置rem
.|● ● ●|●|● ● ● ●| |●|● ● ● ● ●
.| 0  1  2| 3| 4  5  6  7| | 8| 9 10 11 12 13  i
cumulativesum cm(A);
auto [g,rem]=cm.groupIdx(l,x);   //グループl先頭から右へx番目(0-origin)のg,rem
auto [g,rem]=cm.groupIdxRev(r,x);//グループr末尾から左へx番目(0-origin)のg,rem
.                                  いずれも g=-1:左に範囲外、g=N:右に範囲外
- ================ 区間和の最大値 ================ 空集合は0とする
ll s=cm.mx();
*/



struct IndexSort{
    using Int=long long;
    vector<Int> is;
    template<class T> IndexSort(const vector<T> &A,bool desc=false):is(A.size()){
        iota(is.begin(),is.end(),0);
        if (!desc) sort(is.begin(),is.end(),[&](Int i,Int j){return A[i]<A[j]; });
        else      sort(is.begin(),is.end(),[&](Int i,Int j){return A[i]>A[j]; });
    }
    template<class Comp> IndexSort(Int N,Comp comp) : is(N){
        iota(is.begin(),is.end(),0);
        sort(is.begin(),is.end(),comp);
    }
    vector<Int> get(){ return move(is); }
    vector<Int> Rankof(){
        vector<Int> rankof(is.size());
        for (int r=0; r<(int)is.size(); ++r) rankof[is[r]]=r;
        return rankof;
    }
    pair<vector<Int>,vector<Int>> is_rankof(){
        vector<Int> rankof=Rankof();
        return {move(is),move(rankof)};
    }
};
/*
vll is=IndexSort(A).get();
.   ↑           ↑Ai昇順にソート Aの型は何でもOK(比較できれば)
.   is[k]:昇順k番目のindex (k:0-origin)

vll is=IndexSort(A,true).get();
.                   ↑true:降順ソート

vll is=IndexSort(N, [&](ll i,ll j){return A[i].second < A[j].second;}).get();
.               ↑要素数                             ↑比較するラムダ式

vll rankof=IndexSort(A).Rankof();
.    ↑rankof[i]:Aiの順位r (r:0-origin) 重複時順不同

auto[is,rankof]=IndexSort(A).is_rankof(); //is,rankof同時取得
*/


void cin2solve()
{
    auto N=cin1<ll>();
    auto A=cinv<ll>(N);
    auto B=cinv<ll>(N);
    vll AA=A;
    AA.sort();
    cumulativesum cma(AA);
    cumulativesum cmb(B);

    ll mxval=sum(A);
    ll mxn=0;
    rep(i,0,N-1){
        ll va=cma(i+1,N-1)+cmb(0,i);
        if (chmax(mxval,va))
            mxn=i+1;
    }

    vll is=IndexSort(A).get();
    string ans(N,'0');
    rep(I,0,mxn-1){
        ll i=is[I];
        ans[i]='1';
    }
    cout << ans << '\n';


    return;
}

}//SolvingSpace

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

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