#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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namespace V2Dspace{
using ll = long long;

template <typename T> //vector<string>,vector<vector<T>>等を許すconcept
concept VEC2Dconcept = requires{
    typename T::value_type;
    typename T::value_type::value_type;
};

template<VEC2Dconcept VEC2D> pair<ll,ll> GetHW(VEC2D &fd){
    ll H = (ll)fd.size();
    ll W = H==0 ? 0LL : (ll)fd[0].size();
    return {H,W};
}

template<VEC2Dconcept VEC2D> VEC2D Core(
    VEC2D &fd,
    const ll mode, //!<[in] 0:そのまま  1:90度回転 2:180度 3:270度
    //!<     4:transpose 5:上下反転 6:左右反転
    bool inplace, //!<[in] true:inplace, false:新規作成
    ll sx=-1,ll ex=-1,ll sy=-1,ll ey=-1//!<[in]範囲指定  省略時全体
){
    using VEC1D = typename VEC2D::value_type; //string or vector<T>
    auto is90=[](ll mode){ return mode==1 || mode==3 || mode==4; };
    //if (fd.empty()) return VEC2D{};
    //ll H=(ll)fd.size(),W=(ll)fd[0].size();
    auto [H,W]=GetHW(fd);
    if (sx==-1) sx=0,ex=H-1,sy=0,ey=W-1; //デフォルトの指定範囲=全体
    ll h=ex-sx+1,w=ey-sy+1;//指定範囲の高さと幅
    ll nh=is90(mode) ? w : h,nw=is90(mode) ? h : w; //新しい高さと幅

    //-- まず新規作成
    VEC2D ret(nh,VEC1D(nw,0));
    for (ll i=sx; i<=ex; ++i) for (ll j=sy; j<=ey; ++j){
        if (mode==0) ret[i-sx][j-sy]=fd[i][j];
        else if (mode==1) ret[nh-1-j+sy][i-sx]=fd[i][j];
        else if (mode==2) ret[nh-1-i+sx][nw-1-j+sy]=fd[i][j];
        else if (mode==3) ret[j-sy][nw-1-i+sx]=fd[i][j];
        else if (mode==4) ret[j-sy][i-sx]=fd[i][j];
        else if (mode==5) ret[nh-1-i+sx][j-sy]=fd[i][j];
        else if (mode==6) ret[i-sx][nw-1-j+sy]=fd[i][j];
        else assert(false);
    }
    //-- inplaceならfdにコピー
    if (inplace){
        assert(h==w || mode==0 || mode==2 || mode==5 || mode==6);
        for (ll i=0; i<nh; ++i) for (ll j=0; j<nw; ++j) {
            fd[i+sx][j+sy]=ret[i][j];
        }
    }
    return ret;
}
template<VEC2Dconcept VEC2D> VEC2D clip(VEC2D &fd,ll sx,ll ex,ll sy,ll ey){ return Core(fd,0,false,sx,ex,sy,ey); }
template<VEC2Dconcept VEC2D> VEC2D rot90    (VEC2D &fd){ return Core(fd,1,false); }
template<VEC2Dconcept VEC2D> VEC2D rot180   (VEC2D &fd){ return Core(fd,2,false); }
template<VEC2Dconcept VEC2D> VEC2D rot270   (VEC2D &fd){ return Core(fd,3,false); }
template<VEC2Dconcept VEC2D> VEC2D transpose(VEC2D &fd){ return Core(fd,4,false); }
template<VEC2Dconcept VEC2D> VEC2D flipTB   (VEC2D &fd){ return Core(fd,5,false); }
template<VEC2Dconcept VEC2D> VEC2D flipLR   (VEC2D &fd){ return Core(fd,6,false); }
template<VEC2Dconcept VEC2D> void inplaceRot90    (VEC2D &fd,ll sx,ll ex,ll sy,ll ey){ Core(fd,1,true,sx,ex,sy,ey); }
template<VEC2Dconcept VEC2D> void inplaceRot180   (VEC2D &fd,ll sx,ll ex,ll sy,ll ey){ Core(fd,2,true,sx,ex,sy,ey); }
template<VEC2Dconcept VEC2D> void inplaceRot270   (VEC2D &fd,ll sx,ll ex,ll sy,ll ey){ Core(fd,3,true,sx,ex,sy,ey); }
template<VEC2Dconcept VEC2D> void inplaceTranspose(VEC2D &fd,ll sx,ll ex,ll sy,ll ey){ Core(fd,4,true,sx,ex,sy,ey); }
template<VEC2Dconcept VEC2D> void inplaceFlipTB   (VEC2D &fd,ll sx,ll ex,ll sy,ll ey){ Core(fd,5,true,sx,ex,sy,ey); }
template<VEC2Dconcept VEC2D> void inplaceFlipLR   (VEC2D &fd,ll sx,ll ex,ll sy,ll ey){ Core(fd,6,true,sx,ex,sy,ey); }

template<VEC2Dconcept VEC2D> void paste2d(VEC2D &fd,VEC2D &gd,ll sx,ll sy){
    auto [H,W]=GetHW(fd);
    for (ll i=0; i<(ll)gd.size(); ++i){
        for (ll j=0; j<(ll)gd[i].size(); ++j){
            ll x=sx+i,y=sy+j;
            if (0<=x && x<H && 0<=y && y<W) fd[x][y]=gd[i][j];
        }
    }
}
template<VEC2Dconcept VEC2D,class T=VEC2D::value_type::value_type>
void assign2d(VEC2D &fd,ll sx,ll ex,ll sy,ll ey,T val){
    auto [H,W]=GetHW(fd);
    for (ll x=max(sx,0LL); x<=min(ex,H-1); ++x){
        for (ll y=max(sy,0LL); y<=min(ey,W-1); ++y){
            fd[x][y]=val;
        }
    }
}
}//namespace V2Dspace
using V2Dspace::clip;
using V2Dspace::rot90;    using V2Dspace::inplaceRot90;
using V2Dspace::rot180;   using V2Dspace::inplaceRot180;
using V2Dspace::rot270;   using V2Dspace::inplaceRot270;
using V2Dspace::transpose; using V2Dspace::inplaceTranspose;
using V2Dspace::flipTB;   using V2Dspace::inplaceFlipTB;
using V2Dspace::flipLR;   using V2Dspace::inplaceFlipLR;
using V2Dspace::paste2d;  using V2Dspace::assign2d;
/*
- vss,vvll等使用可能

- ---- 新規作成系 ----
auto gd=clip(fd,sx,ex,sy,ey);
auto gd=rot90    (fd);
auto gd=rot180   (fd);
auto gd=rot270   (fd);
auto gd=transpose(fd);
auto gd=flipTB   (fd);
auto gd=flipLR   (fd);

- ---- inplace系 ---- 変換後も同じ縦横サイズなら可(正方形 or Rot180,flip)
inplaceRot90    (fd,sx,ex,sy,ey);
inplaceRot180   (fd,sx,ex,sy,ey);
inplaceRot270   (fd,sx,ex,sy,ey);
inplaceTranspose(fd,sx,ex,sy,ey);
inplaceFlipTB   (fd,sx,ex,sy,ey);
inplaceFlipLR   (fd,sx,ex,sy,ey);
paste2d (fd,gd,sx,sy); //fdのsx,syにgdを貼り付け はみ出し可,gdは非長方形可
assign2d(fd,sx,ex,sy,ey,val); //fdの範囲[sx,ex][sy,ey]にvalを代入 はみ出し可

- ---- 90度回転の向き ----
★・      ・・●
★・  →  ★★◇
◇●
*/


namespace baseNspace {
using Int = long long;
using ll = long long;
vector<Int> to_vector(ll x,bool rev = false,ll d = 10,ll k = 0) {
    vector<Int> dgs;
    for (; x > 0; x /= d) dgs.push_back(Int(x % d));
    if ((ll)dgs.size() < k) dgs.resize(k,0);       // 上位桁側を 0 埋め
    if (!rev) reverse(dgs.begin(),dgs.end());      // rev=false のときだけ反転
    return dgs;
}
ll vtoll(const vector<Int>& v,ll d = 10) {
    ll x = 0;
    for (Int dg : v) x = x * d + dg;
    return x;
};
string v_to_string(const vector<Int>& v,bool empty_0=true) {
    if (empty_0 && v.empty()) return "0";
    string s;
    for (auto&& e : v) s += e < 10 ? char(e + '0') : char(e - 10 + 'A');
    return s;
}
vector<Int> s_to_vector(const string& s) {
    vector<Int> dgs;
    if (s == "0") return dgs;
    for (auto&& c : s) dgs.push_back(c <= '9' ? Int(c - '0') : Int(c - 'A') + 10);
    return dgs;
}
string to_string(ll x,bool rev,ll d,ll k = 1) { // overload
    return v_to_string(to_vector(x,rev,d,k),false);
}

template<ll d> struct basen {
    ll x = 0;
    basen() {}
    basen(ll x): x(x) {}
    basen(int x): x(x) {}
    basen(const char* s) { fromString(s); }
    basen(const string& s) { fromString(s); }
    Int operator[](Int i)const {
        ll y = valid(i + 1) ? x % bases[i + 1] : x;
        return valid(i) ? Int(y / bases[i]) : Int(0);
    }
    operator Int()const { return Int(x); }
    basen operator++(int) { basen b(*this); x++; return b; }
    basen operator--(int) { basen b(*this); x--; return b; }
    basen& operator+=(Int b) { x += b; return *this; }
    basen& operator-=(Int b) { x -= b; return *this; }
    basen operator+(ll b)const { return x + b; }
    basen operator-(ll b)const { return x - b; }
    basen operator+(int b)const { return x + b; }
    basen operator-(int b)const { return x - b; }
    basen operator+(const basen& b)const { return x + b.x; }
    basen operator-(const basen& b)const { return x - b.x; }
    basen& seteq(Int i,Int dg) { assert(valid(i)); return addeq(i,dg - (*this)[i]); }
    basen& addeq(Int i,Int dg) { assert(valid(i)); x += dg * bases[i]; return *this; }
    [[nodiscard]] basen set(Int i,Int dg)const { return basen(*this).seteq(i,dg); }
    [[nodiscard]] basen add(Int i,Int dg)const { return basen(*this).addeq(i,dg); }
    static void setbase(const vector<Int>& v) {
        bases = {1};
        for (auto&& x : v) bases.push_back(bases.back() * x);
    }
    static Int size() { return (Int)bases.back(); }
    static Int size(ll n) { return (Int)bases[n]; }
    Int ndigits()const {//桁数
        for (Int ng = -1,ok = (Int)bases.size();;) {
            Int m = (ng + ok) / 2;
            if (bases[m] > x) ok = m; else ng = m;
            if (ok - ng == 1) return ok;
        }
    }
    string to_string(Int wd = -1)const {
        wd = max({wd,ndigits(),1LL});
        string ret;
        for (ll i = wd - 1; i >= 0; --i) ret += '0' + char((*this)[i]);
        return ret;
    }
private:
    static vector<ll> setbaseD() {
        vector<ll> ret{1};
        if (d >= 2) while (ret.back() <= LLONG_MAX / d) ret.push_back(ret.back() * d);
        return ret;
    }
    bool valid(Int i)const { return i < (Int)bases.size(); }
    void fromString(const string& s) {
        ll N = (ll)s.size();
        for (ll i = 0; i < N; ++i) addeq(i,s[N - 1 - i] - '0');
    }
    static inline vector<ll> bases = setbaseD();
};
}
using baseNspace::to_vector; using baseNspace::v_to_string; using baseNspace::vtoll;
using baseNspace::to_string; using baseNspace::s_to_vector;
using std::to_string;
using baseNspace::basen;
/*
- ******************** ll・vll・string d進法変換ライブラリ ********************
ll:常に10進、string,vll:d進法 として変換
ll 3041 ⇔ vll {3,0,4,1} ⇔ string "3041" (10進法)
ll 0    ⇔ vll {}        ⇔ string "0"    (10進法)
ll 12   ⇔ vll {1,1,0,0} ⇔ string "1100" (2進法)
ll 46   ⇔ vll {2,14}    ⇔ string "2E"   (16進法)

- ===========================
- ======== ll ⇔ vll ========

- ---- ll → vll ----
vll dgs=to_vector(x);
vll dgs=to_vector(x,true,d,k);
.       true:reverse ┘ ↑ └ k桁未満なら上位桁0埋め 省略時0
.       省略時false     └ d進法 省略時10
- ---- vll → ll ----
ll x=vtoll(dgs);
ll x=vtoll(dgs,d);
.              ↑d進法 省略時10

- ===============================
- ======== string ⇔ vll ========

- ---- string → vll ----
vll dgs=s_to_vector(s);

- ---- vll → string ----
string s=v_to_string(dgs);

- ==============================
- ======== ll ⇔ string ========

- ---- ll → string ----   std::to_stringのoverload
string s=to_string(x);
string s=to_string(x,true,d,k);
.        true:reverse ┘ ↑ └ k桁未満なら上位桁0埋め 省略時0
.             省略NG     └ d進法 省略NG
.※引数1つならstd::to_stringが呼ばれ、3つ以上ならオーバーロードが呼ばれる

- ---- string → ll ----   std::stoll使う
ll x=stoll(s);
ll x=stoll(s,nullptr,d);
.                    ↑d進法

- ******************* llのままd進法各桁を操作するライブラリ *******************
- -------- 定義 --------
using base=basen<d>;   //d進法のとき
using base=basen<-1>;  //┬各桁別進法のとき
base::setbase(v);      //┘    第i桁の範囲が[0,v[i])になる
base b=x;     //整数から
base b="101"; //文字列から
- -------- 操作 --------
ll dg=base(x)[i];  //xの第i桁
ll u=base::size(); //取り得る値の上限 [0,n)  v={2,3,2}ならu=2*3*2=12 各桁別進法のみ
ll u=base::size(N);//N桁の上限 [0,u)  d進法,各桁別進法両用
base b=x;
ll n=b.ndigits(); //桁数 201(3)なら3
b.seteq(i,dg); //第i桁dgに変更
b.addeq(i,dg); //第i桁にdg加算
base bb=b.set(i,dg);    //第i桁dgに変更したもの返す
base bb=b.add(i,dg);    //第i桁にdg加算したもの返す
ll y=base(x).set(i,dg); //llのまま扱うことも可能(キャストで実現)
b+=x b-=x b++ b--
b+x b-x      //base型を返す
(b==x b!=x)  //llへのcastを経由し可能
string s=b.to_string();  //文字列出力
string s=b.to_string(6); //文字列出力 桁数指定(0埋め)
*/





using  vvss=vector< vss>;
using vvvss=vector<vvss>;

void cin2solve()
{
    auto [N,M]=cins<ll,ll>();
    vvvss S(N,vvss(4));
    rep(i,0,N-1){
        auto s=cinv<string>(M);
        S[i][0]=move(s);
        rep(j,1,3){
            auto T=rot90(S[i][j-1]);
            S[i][j]=move(T);
        }
    }

    using base=basen<4>;   //d進法のとき

    ll u=base::size(N);

    ll ans=INF;
    rep(b,0,u-1){

        vss t(M,string(M,'.'));
        rep(i,0,N-1){
            ll x=base(b)[i];//0~3
            vss &s=S[i][x];
            rep(I,0,M-1) rep(J,0,M-1){
                if (s[I][J]=='#')
                    t[I][J]='#';
            }
        }
        ll ct=0;
        rep(I,0,M-1) rep(J,0,M-1){
            ct+=t[I][J]=='#';
        }
        chmin(ans,ct);
    }
    cout << ans << '\n';

    return;
}

}//SolvingSpace

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


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