// 入力フォーマットチェック
#ifndef INCLUDE_MODE
  #define INCLUDE_MODE
  // #define REACTIVE
  #define USE_GETLINE
#endif

#ifdef INCLUDE_MAIN

inline void Solve()
{
  CEXPR( int , bound_N , 3e4 );
  GETLINE_COUNT( N_str , 1 , " " );
  STOI( N_str , N , bound_N );
  CEXPR( ll , bound_Ai , 1e18 );
  GETLINE_COUNT( A_str , N , " " );
  STOI_A( A_str , A , N , bound_Ai );
  CEXPR( int , bound_Q , 3e4 );
  GETLINE_COUNT( Q_str , 1 , " " );
  STOI( Q_str , Q , bound_Q );
  constexpr PrimeEnumeration<int,100> pe{};
  auto& C = pe.length();
  vector t( C , IntervalMultiplyLazySqrtDecomposition{ MultiplicativeMonoid( 1 ) , Module<int,int>() } );
  FOR( c , 0 , C ){
    vector<int> factor( N );
    FOR( i , 0 , N ){
      while( A[i] % pe[c] == 0 ){
	A[i] /= pe[c];
	factor[i]++;
      }
    }
    t[c].Reset( move( factor ) );
  }
  A.clear();
  FOR( q , 0 , Q ){
    GETLINE_COUNT( tlrx_str , 4 , " " );
    STOI( tlrx_str , type , 3 );
    STOI( tlrx_str , l , N );
    STOI( tlrx_str , r , N );
    assert( 1 <= l && l <= r && r <= N ); l--; r--;
    if( type == 1 ){
      CEXPR( ll , bound_x , 1e18 );
      STOI( tlrx_str , x , bound_x );
      FOR( c , 0 , C ){
	int e = 0;
	while( x % pe[c] == 0 ){
	  x /= pe[c];
	  e++;
	}
	t[c].IntervalSet( l , r , e );
      }
    } else if( type == 2 ){
      CEXPR( ll , bound_x , 1e18 );
      STOI( tlrx_str , x , bound_x );
      FOR( c , 0 , C ){
	int e = 0;
	while( x % pe[c] == 0 ){
	  x /= pe[c];
	  e++;
	}
	t[c].IntervalMultiply( l , r , e );
      }
    } else {
      assert( type == 3 );
      CEXPR( int , bound_x , 1e2 );
      STOI( tlrx_str , x , bound_x );
      ll answer = 1;
      FOR( c , 0 , C ){
	pe[c] <= x ? ( answer *= t[c].IntervalProduct( l , r ) + 1 ) %= 998244353 : answer;
      }
      COUT( answer );
    }
  }
}
REPEAT_MAIN(1);

#else // INCLUDE_MAIN

#ifdef INCLUDE_LIBRARY

// https://github.com/p-adic/cpp
// VVV ライブラリは以下に挿入する。

// Map (1KB)
// c:/Users/user/Documents/Programming/Mathematics/Function/Map/compress.txt
CL is_ordered{PU:is_ordered()= delete;TE <TY T> ST CE auto Check(CO T& t)-> decltype(t < t,true_type());ST CE false_type Check(...);TE <TY T> ST CE CO bool value = is_same_v< decltype(Check(declval<T>())),true_type >;};
TE <TY T , TY U>US Map = conditional_t<is_COructible_v<unordered_map<T,int>>,unordered_map<T,U>,conditional_t<is_ordered::value<T>,map<T,U>,VO>>;

// Algebra (4KB)
// c:/Users/user/Documents/Programming/Mathematics/Algebra/compress.txt
#define DC_OF_CPOINT(POINT)IN CO U& POINT()CO NE
#define DC_OF_POINT(POINT)IN U& POINT()NE
#define DF_OF_CPOINT(POINT)TE <TY U> IN CO U& VirtualPointedSet<U>::POINT()CO NE{RE Point();}
#define DF_OF_POINT(POINT)TE <TY U> IN U& VirtualPointedSet<U>::POINT()NE{RE Point();}
TE <TY U>CL UnderlyingSet{PU:US type = U;};TE <TY U>CL VirtualPointedSet:VI PU UnderlyingSet<U>{PU:VI CO U& Point()CO NE = 0;VI U& Point()NE = 0;DC_OF_CPOINT(Unit);DC_OF_CPOINT(Zero);DC_OF_CPOINT(One);DC_OF_CPOINT(Infty);DC_OF_POINT(init);DC_OF_POINT(root);};TE <TY U>CL PointedSet:VI PU VirtualPointedSet<U>{PU:U m_b_U;IN PointedSet(CO U& b_u = U());IN CO U& Point()CO NE;IN U& Point()NE;};TE <TY U>CL VirtualNSet:VI PU UnderlyingSet<U>{PU:VI U Transfer(CO U& u)= 0;IN U Inverse(CO U& u);};TE <TY U,TY F_U>CL AbstractNSet:VI PU VirtualNSet<U>{PU:F_U m_f_U;IN AbstractNSet(F_U f_U);IN U Transfer(CO U& u);};TE <TY U>CL VirtualMagma:VI PU UnderlyingSet<U>{PU:VI U Product(CO U& u0,CO U& u1)= 0;IN U Sum(CO U& u0,CO U& u1);};TE <TY U = ll>CL AdditiveMagma:VI PU VirtualMagma<U>{PU:IN U Product(CO U& u0,CO U& u1);};TE <TY U = ll>CL MultiplicativeMagma:VI PU VirtualMagma<U>{PU:IN U Product(CO U& u0,CO U& u1);};TE <TY U,TY M_U>CL AbstractMagma:VI PU VirtualMagma<U>{PU:M_U m_m_U;IN AbstractMagma(M_U m_U);IN U Product(CO U& u0,CO U& u1);};
TE <TY U> IN PointedSet<U>::PointedSet(CO U& b_U):m_b_U(b_U){}TE <TY U> IN CO U& PointedSet<U>::Point()CO NE{RE m_b_U;}TE <TY U> IN U& PointedSet<U>::Point()NE{RE m_b_U;}DF_OF_CPOINT(Unit);DF_OF_CPOINT(Zero);DF_OF_CPOINT(One);DF_OF_CPOINT(Infty);DF_OF_POINT(init);DF_OF_POINT(root);TE <TY U,TY F_U> IN AbstractNSet<U,F_U>::AbstractNSet(F_U f_U):m_f_U(MO(f_U)){ST_AS(is_invocable_r_v<U,F_U,U>);}TE <TY U,TY F_U> IN U AbstractNSet<U,F_U>::Transfer(CO U& u){RE m_f_U(u);}TE <TY U> IN U VirtualNSet<U>::Inverse(CO U& u){RE Transfer(u);}TE <TY U,TY M_U> IN AbstractMagma<U,M_U>::AbstractMagma(M_U m_U):m_m_U(MO(m_U)){ST_AS(is_invocable_r_v<U,M_U,U,U>);}TE <TY U> IN U AdditiveMagma<U>::Product(CO U& u0,CO U& u1){RE u0 + u1;}TE <TY U> IN U MultiplicativeMagma<U>::Product(CO U& u0,CO U& u1){RE u0 * u1;}TE <TY U,TY M_U> IN U AbstractMagma<U,M_U>::Product(CO U& u0,CO U& u1){RE m_m_U(u0,u1);}TE <TY U> IN U VirtualMagma<U>::Sum(CO U& u0,CO U& u1){RE Product(u0,u1);}

TE <TY U>CL VirtualMonoid:VI PU VirtualMagma<U>,VI PU VirtualPointedSet<U>{};TE <TY U = ll>CL AdditiveMonoid:VI PU VirtualMonoid<U>,PU AdditiveMagma<U>,PU PointedSet<U>{};TE <TY U = ll>CL MultiplicativeMonoid:VI PU VirtualMonoid<U>,PU MultiplicativeMagma<U>,PU PointedSet<U>{PU:IN MultiplicativeMonoid(CO U& e_U);};TE <TY U,TY M_U>CL AbstractMonoid:VI PU VirtualMonoid<U>,PU AbstractMagma<U,M_U>,PU PointedSet<U>{PU:IN AbstractMonoid(M_U m_U,CO U& e_U);};
TE <TY U> IN MultiplicativeMonoid<U>::MultiplicativeMonoid(CO U& e_U):PointedSet<U>(e_U){}TE <TY U,TY M_U> IN AbstractMonoid<U,M_U>::AbstractMonoid(M_U m_U,CO U& e_U):AbstractMagma<U,M_U>(MO(m_U)),PointedSet<U>(e_U){}

TE <TY U>CL VirtualGroup:VI PU VirtualMonoid<U>,VI PU VirtualPointedSet<U>,VI PU VirtualNSet<U>{};TE <TY U = ll>CL AdditiveGroup:VI PU VirtualGroup<U>,PU AdditiveMonoid<U>{PU:IN U Transfer(CO U& u);};TE <TY U,TY M_U,TY I_U>CL AbstractGroup:VI PU VirtualGroup<U>,PU AbstractMonoid<U,M_U>,PU AbstractNSet<U,I_U>{PU:IN AbstractGroup(M_U m_U,CO U& e_U,I_U i_U);};
TE <TY U,TY M_U,TY I_U> IN AbstractGroup<U,M_U,I_U>::AbstractGroup(M_U m_U,CO U& e_U,I_U i_U):AbstractMonoid<U,M_U>(MO(m_U),e_U),AbstractNSet<U,I_U>(MO(i_U)){}TE <TY U> IN U AdditiveGroup<U>::Transfer(CO U& u){RE -u;}

TE <TY INT,INT val_limit,int LE_max = val_limit>CL PrimeEnumeration{PU:bool m_is_composite[val_limit];INT m_val[LE_max];int m_LE;CE PrimeEnumeration();CE CO INT& OP[](CRI n) CO;CE CO INT& Get(CRI n) CO;CE CO bool& IsComposite(CRI i) CO;CE CRI LE() CO NE;};
TE <TY INT,INT val_limit,int LE_max>CE PrimeEnumeration<INT,val_limit,LE_max>::PrimeEnumeration():m_is_composite(),m_val(),m_LE(0){for(INT i = 2;i < val_limit;i++){if(! m_is_composite[i]){INT j = i;WH((j += i)< val_limit){m_is_composite[j] = true;}m_val[m_LE++] = i;if(m_LE >= LE_max){break;}}}}TE <TY INT,INT val_limit,int LE_max> CE CO INT& PrimeEnumeration<INT,val_limit,LE_max>::OP[](CRI n)CO{assert(n < m_LE);RE m_val[n];}TE <TY INT,INT val_limit,int LE_max> CE CO INT& PrimeEnumeration<INT,val_limit,LE_max>::Get(CRI n)CO{RE OP[](n);}TE <TY INT,INT val_limit,int LE_max> CE CO bool& PrimeEnumeration<INT,val_limit,LE_max>::IsComposite(CRI i)CO{assert(i < val_limit);RE m_is_composite[i];}TE <TY INT,INT val_limit,int LE_max> CE CRI PrimeEnumeration<INT,val_limit,LE_max>::LE()CO NE{RE m_LE;}
TE <TY INT,INT val_limit,int LE_max,TY INT1,TY INT2,TY INT3>VO SetPrimeFactorisation(CO PrimeEnumeration<INT,val_limit,LE_max>& prime,CO INT1& n,VE<INT2>& P,VE<INT3>& EX){INT1 n_copy = n;int i = 0;WH(i < prime.m_LE){CO INT2& p = prime[i];if(p * p > n_copy){break;}if(n_copy % p == 0){P.push_back(p);EX.push_back(1);INT3& EX_back = EX.back();n_copy /= p;WH(n_copy % p == 0){EX_back++;n_copy /= p;}}i++;}if(n_copy != 1){P.push_back(n_copy);EX.push_back(1);}RE;}


TE <TY R,TY U>CL VirtualModule{PU:VI U Action(CO R& r,CO U& u)= 0;IN U PW(CO U& u,CO R& r);IN U ScalarProduct(CO R& r,CO U& u);};TE <TY R,TY U,TY O_U,TY GROUP>CL AbstractModule:VI PU VirtualModule<R,U>,PU GROUP{PU:O_U m_o_U;IN AbstractModule(CO R& dummy,O_U o_U,GROUP M);IN U Action(CO R& r,CO U& u);};TE <TY R,TY O_U,TY GROUP> AbstractModule(CO R& dummy,O_U o_U,GROUP M)-> AbstractModule<R,inner_t<GROUP>,O_U,GROUP>;TE <TY R,TY U>CL Module:VI PU VirtualModule<R,U>,PU AdditiveGroup<U>{PU:IN U Action(CO R& r,CO U& u);};
TE <TY R,TY U,TY O_U,TY GROUP> IN AbstractModule<R,U,O_U,GROUP>::AbstractModule(CO R& dummy,O_U o_U,GROUP M):GROUP(MO(M)),m_o_U(MO(o_U)){ST_AS(is_same_v<U,inner_t<GROUP>> && is_invocable_r_v<U,O_U,R,U>);}TE <TY R,TY U,TY O_U,TY GROUP> IN U AbstractModule<R,U,O_U,GROUP>::Action(CO R& r,CO U& u){RE m_o_U(r,u);}TE <TY R,TY U> IN U Module<R,U>::Action(CO R& r,CO U& u){RE r * u;}TE <TY R,TY U> IN U VirtualModule<R,U>::PW(CO U& u,CO R& r){RE Action(r,u);}TE <TY R,TY U> IN U VirtualModule<R,U>::ScalarProduct(CO R& r,CO U& u){RE Action(r,u);}

IN CE int Sqrt(CRI N)NE{if(N <= 1){RE 1;}int left = 0;int right = N;WH(left + 1 < right){int m =(left + right)/ 2;(m <=(N - 1)/ m?left:right)= m;}RE right;}

TE <TY R,TY PT_MAGMA,TY U,TY R_MODULE>CL IntervalMultiplyLazySqrtDecomposition{PU:PT_MAGMA m_L;R_MODULE m_M;int m_N;int m_N_sqrt;int m_N_d;int m_N_m;VE<U> m_a;VE<U> m_b;VE<U> m_lazy_substitution;VE<bool> m_suspENed;VE<R> m_lazy_action;VE<U> m_lazy_MU;IN IntervalMultiplyLazySqrtDecomposition(PT_MAGMA L,R_MODULE M,CRI N = 0);IN IntervalMultiplyLazySqrtDecomposition(PT_MAGMA L,R_MODULE M,CRI N,CRI N_sqrt);IN IntervalMultiplyLazySqrtDecomposition(PT_MAGMA L,R_MODULE M,VE<U> a);IN IntervalMultiplyLazySqrtDecomposition(PT_MAGMA L,R_MODULE M,VE<U> a,CRI N_sqrt);TE <TY...Args> IN VO Reset(Args&&... args);IN VO Set(CRI i,CO U& u);IN VO IntervalSet(CRI i_start,CRI i_final,CO U& u);IN VO IntervalAct(CRI i_start,CRI i_final,CO R& r);IN VO IntervalMultiply(CRI i_start,CRI i_final,CO U& u);IN U OP[](CRI i);IN U Get(CRI i);IN U IntervalProduct(CRI i_start,CRI i_final);IN VO Initialise();IN VO SetProduct(CRI i);IN VO SolveSuspENedSubstitution(CRI d,CO U& u);IN VO IntervalSet_Body(CRI i_min,CRI i_ulim,CO U& u);IN VO SolveSuspENedAction(CRI d);IN VO IntervalAct_Body(CRI i_min,CRI i_ulim,CO R& r);IN VO IntervalMultiply_Body(CRI i_min,CRI i_ulim,CO U& u);IN U IntervalProduct_Body(CRI i_min,CRI i_ulim);};TE <TY PT_MAGMA,TY R_MODULE,TY...Args> IntervalMultiplyLazySqrtDecomposition(PT_MAGMA L,R_MODULE M,CO Args&... args)-> IntervalMultiplyLazySqrtDecomposition<inner_t<PT_MAGMA>,PT_MAGMA,inner_t<R_MODULE>,R_MODULE>;
TE <TY R,TY PT_MAGMA,TY U,TY R_MODULE> IN IntervalMultiplyLazySqrtDecomposition<R,PT_MAGMA,U,R_MODULE>::IntervalMultiplyLazySqrtDecomposition(PT_MAGMA L,R_MODULE M,CRI N):IntervalMultiplyLazySqrtDecomposition(MO(L),MO(M),N,Sqrt(N)){}TE <TY R,TY PT_MAGMA,TY U,TY R_MODULE> IN IntervalMultiplyLazySqrtDecomposition<R,PT_MAGMA,U,R_MODULE>::IntervalMultiplyLazySqrtDecomposition(PT_MAGMA L,R_MODULE M,CRI N,CRI N_sqrt):m_L(MO(L)),m_M(MO(M)),m_N(N),m_N_sqrt(N_sqrt),m_N_d((m_N + m_N_sqrt - 1)/ m_N_sqrt),m_N_m(m_N_d * m_N_sqrt),m_a(N,m_M.One()),m_b(m_N_d,m_M.One()),m_lazy_substitution(m_b),m_suspENed(m_N_d),m_lazy_action(m_N_d,m_L.Point()),m_lazy_MU(m_b){Initialise();}TE <TY R,TY PT_MAGMA,TY U,TY R_MODULE> IN IntervalMultiplyLazySqrtDecomposition<R,PT_MAGMA,U,R_MODULE>::IntervalMultiplyLazySqrtDecomposition(PT_MAGMA L,R_MODULE M,VE<U> a):m_L(MO(L)),m_M(MO(M)),m_N(a.SZ()),m_N_sqrt(Sqrt(m_N)),m_N_d((m_N + m_N_sqrt - 1)/ m_N_sqrt),m_N_m(m_N_d * m_N_sqrt),m_a(MO(a)),m_b(m_N_d,m_M.One()),m_lazy_substitution(m_b),m_suspENed(m_N_d),m_lazy_action(m_N_d,m_L.Point()),m_lazy_MU(m_b){Initialise();}TE <TY R,TY PT_MAGMA,TY U,TY R_MODULE> IN IntervalMultiplyLazySqrtDecomposition<R,PT_MAGMA,U,R_MODULE>::IntervalMultiplyLazySqrtDecomposition(PT_MAGMA L,R_MODULE M,VE<U> a,CRI N_sqrt):m_L(MO(L)),m_M(MO(M)),m_N(a.SZ()),m_N_sqrt(N_sqrt),m_N_d((m_N + m_N_sqrt - 1)/ m_N_sqrt),m_N_m(m_N_d * m_N_sqrt),m_a(MO(a)),m_b(m_N_d,m_M.One()),m_lazy_substitution(m_b),m_suspENed(m_N_d),m_lazy_action(m_N_d,m_L.Point()),m_lazy_MU(m_b){Initialise();}TE <TY R,TY PT_MAGMA,TY U,TY R_MODULE> IN VO IntervalMultiplyLazySqrtDecomposition<R,PT_MAGMA,U,R_MODULE>::Initialise(){ST_AS(is_same_v<R,inner_t<PT_MAGMA>> && is_same_v<U,inner_t<R_MODULE>>);m_a.reSZ(m_N_m,m_M.One());int i_min = 0;int i_ulim = m_N_sqrt;for(int d = 0;d < m_N_d;d++){U& m_bd = m_b[d];for(int i = i_min;i < i_ulim;i++){m_bd = m_M.Product(m_bd,m_a[i]);}i_min = i_ulim;i_ulim += m_N_sqrt;}}TE <TY R,TY PT_MAGMA,TY U,TY R_MODULE> TE <TY...Args> IN VO IntervalMultiplyLazySqrtDecomposition<R,PT_MAGMA,U,R_MODULE>::Reset(Args&&...args){*TH = IntervalMultiplyLazySqrtDecomposition<R,PT_MAGMA,U,R_MODULE>(MO(m_L),MO(m_M),forward<Args>(args)...);}TE <TY R,TY PT_MAGMA,TY U,TY R_MODULE> IN VO IntervalMultiplyLazySqrtDecomposition<R,PT_MAGMA,U,R_MODULE>::Set(CRI i,CO U& u){CO int d = i / m_N_sqrt;CO int i_min = d * m_N_sqrt;CO int i_ulim = i_min + m_N_sqrt;U& m_ai = m_a[i];U& m_bd = m_b[d];if(m_suspENed[d]){U& m_lazy_substitution_d = m_lazy_substitution[d];if(m_lazy_substitution_d != u){SolveSuspENedSubstitution(d,m_lazy_substitution_d);m_ai = u;m_bd = m_M.Product(m_M.PW(m_lazy_substitution_d,m_N_sqrt - 1),u);}}else{SolveSuspENedAction(d);if(m_ai != u){m_ai = u;SetProduct(d);}}RE;}TE <TY R,TY PT_MAGMA,TY U,TY R_MODULE> IN VO IntervalMultiplyLazySqrtDecomposition<R,PT_MAGMA,U,R_MODULE>::IntervalSet(CRI i_start,CRI i_final,CO U& u){CO int i_min = max(i_start,0);CO int i_ulim = min(i_final + 1,m_N);CO int d_0 =(i_min + m_N_sqrt - 1)/ m_N_sqrt;CO int d_1 = max(d_0,i_ulim / m_N_sqrt);CO int d_0_N_sqrt = d_0 * m_N_sqrt;CO int d_1_N_sqrt = d_1 * m_N_sqrt;CO int i_0 = min(d_0_N_sqrt,i_ulim);CO int i_1 = max(i_0,d_1_N_sqrt);if(i_min < i_0){CO int d_0_minus = d_0 - 1;CO int d_0_N_sqrt_minus = d_0_N_sqrt - m_N_sqrt;U& m_bd = m_b[d_0_minus];VE<bool>::reference m_suspENed_d = m_suspENed[d_0_minus];if(m_suspENed_d){U& m_lazy_substitution_d = m_lazy_substitution[d_0_minus];IntervalSet_Body(d_0_N_sqrt_minus,i_min,m_lazy_substitution_d);IntervalSet_Body(i_min,i_0,u);IntervalSet_Body(i_0,d_0_N_sqrt,m_lazy_substitution_d);m_suspENed_d = false;m_bd = m_M.Product(m_M.PW(m_lazy_substitution_d,m_N_sqrt -(i_0 - i_min)),m_M.PW(u,i_0 - i_min));}else{SolveSuspENedAction(d_0_minus);IntervalSet_Body(i_min,i_0,u);m_bd = m_M.Product(m_M.Product(IntervalProduct_Body(d_0_N_sqrt_minus,i_min),m_M.PW(u,i_0 - i_min)),IntervalProduct_Body(i_0,d_0_N_sqrt));}}CO U PW = m_M.PW(u,m_N_sqrt);CO U& one = m_M.One();CO R& point = m_L.Point();for(int d = d_0;d < d_1;d++){m_b[d]= PW;m_lazy_substitution[d]= u;m_suspENed[d]= true;m_lazy_MU[d]= one;m_lazy_action[d]= point;}if(i_1 < i_ulim){CO int d_1_N_sqrt_plus = d_1_N_sqrt + m_N_sqrt;U& m_bd = m_b[d_1];VE<bool>::reference m_suspENed_d = m_suspENed[d_1];if(m_suspENed_d){U& m_lazy_substitution_d = m_lazy_substitution[d_1];IntervalSet_Body(d_1_N_sqrt,i_1,m_lazy_substitution_d);IntervalSet_Body(i_1,i_ulim,u);IntervalSet_Body(i_ulim,d_1_N_sqrt_plus,m_lazy_substitution_d);m_suspENed_d = false;m_bd = m_M.Product(m_M.Product(m_M.PW(m_lazy_substitution_d,i_1 - d_1_N_sqrt),m_M.PW(u,i_ulim - i_1)),m_M.PW(m_lazy_substitution_d,d_1_N_sqrt_plus - i_ulim));}else{SolveSuspENedAction(d_1);IntervalSet_Body(i_1,i_ulim,u);m_bd = m_M.Product(m_M.Product(IntervalProduct_Body(d_1_N_sqrt,i_1),m_M.PW(u,i_ulim - i_1)),IntervalProduct_Body(i_ulim,d_1_N_sqrt_plus));}}RE;}TE <TY R,TY PT_MAGMA,TY U,TY R_MODULE> IN VO IntervalMultiplyLazySqrtDecomposition<R,PT_MAGMA,U,R_MODULE>::IntervalAct(CRI i_start,CRI i_final,CO R& r){CO R& point = m_L.Point();if(r != point){CO U& one = m_M.One();CO int i_min = max(i_start,0);CO int i_ulim = min(i_final + 1,m_N);CO int d_0 =(i_min + m_N_sqrt - 1)/ m_N_sqrt;CO int d_1 = max(d_0,i_ulim / m_N_sqrt);CO int d_0_N_sqrt = d_0 * m_N_sqrt;CO int d_1_N_sqrt = d_1 * m_N_sqrt;CO int i_0 = min(d_0_N_sqrt,i_ulim);CO int i_1 = max(i_0,d_1_N_sqrt);if(i_min < i_0){CO int d_0_minus = d_0 - 1;CO int d_0_N_sqrt_minus = d_0_N_sqrt - m_N_sqrt;VE<bool>::reference m_suspENed_d = m_suspENed[d_0_minus];if(m_suspENed_d){U& m_lazy_substitution_d = m_lazy_substitution[d_0_minus];U& m_bd = m_b[d_0_minus];CO U u = m_M.Action(r,m_lazy_substitution_d);IntervalSet_Body(d_0_N_sqrt_minus,i_min,m_lazy_substitution_d);IntervalSet_Body(i_min,i_0,u);IntervalSet_Body(i_0,d_0_N_sqrt,m_lazy_substitution_d);m_suspENed_d = false;m_bd = m_M.Product(m_M.PW(m_lazy_substitution_d,m_N_sqrt -(i_0 - i_min)),m_M.PW(u,i_0 - i_min));}else{R& m_lazy_action_d = m_lazy_action[d_0_minus];if(m_lazy_action_d == point){IntervalAct_Body(i_min,i_0,r);}else{IntervalAct_Body(d_0_N_sqrt_minus,i_min,m_lazy_action_d);IntervalAct_Body(i_min,i_0,m_L.Product(r,m_lazy_action_d));IntervalAct_Body(i_0,d_0_N_sqrt,m_lazy_action_d);m_lazy_action_d = point;}U& m_lazy_MU_d = m_lazy_MU[d_0_minus];if(m_lazy_MU_d != one){IntervalMultiply_Body(d_0_N_sqrt_minus,i_min,m_lazy_MU_d);IntervalMultiply_Body(i_min,i_0,m_M.Action(r,m_lazy_MU_d));IntervalMultiply_Body(i_0,d_0_N_sqrt,m_lazy_MU_d);m_lazy_MU_d = one;}SetProduct(d_0_minus);}}for(int d = d_0;d < d_1;d++){U& m_bd = m_b[d];m_bd = m_M.Action(r,m_bd);if(m_suspENed[d]){U& m_lazy_substitution_d = m_lazy_substitution[d];m_lazy_substitution_d = m_M.Action(r,m_lazy_substitution_d);}else{R& m_lazy_action_d = m_lazy_action[d];m_lazy_action_d = m_L.Product(r,m_lazy_action_d);U& m_lazy_MU_d = m_lazy_MU[d];m_lazy_MU_d = m_M.Action(r,m_lazy_MU_d);}}if(i_1 < i_ulim){CO int d_1_N_sqrt_plus = d_1_N_sqrt + m_N_sqrt;VE<bool>::reference m_suspENed_d = m_suspENed[d_1];if(m_suspENed_d){U& m_lazy_substitution_d = m_lazy_substitution[d_1];U& m_bd = m_b[d_1];CO U u = m_M.Action(r,m_lazy_substitution_d);IntervalSet_Body(d_1_N_sqrt,i_1,m_lazy_substitution_d);IntervalSet_Body(i_1,i_ulim,u);IntervalSet_Body(i_ulim,d_1_N_sqrt_plus,m_lazy_substitution_d);m_suspENed_d = false;m_bd = m_M.Product(m_M.PW(m_lazy_substitution_d,m_N_sqrt -(i_ulim - i_1)),m_M.PW(u,i_ulim - i_1));}else{R& m_lazy_action_d = m_lazy_action[d_1];if(m_lazy_action_d == point){IntervalAct_Body(i_1,i_ulim,r);}else{IntervalAct_Body(d_1_N_sqrt,i_1,m_lazy_action_d);IntervalAct_Body(i_1,i_ulim,m_L.Product(r,m_lazy_action_d));IntervalAct_Body(i_ulim,d_1_N_sqrt_plus,m_lazy_action_d);m_lazy_action_d = point;}U& m_lazy_MU_d = m_lazy_MU[d_1];if(m_lazy_MU_d != one){IntervalMultiply_Body(d_1_N_sqrt,i_1,m_lazy_MU_d);IntervalMultiply_Body(i_1,i_ulim,m_M.Action(r,m_lazy_MU_d));IntervalMultiply_Body(i_ulim,d_1_N_sqrt_plus,m_lazy_MU_d);m_lazy_MU_d = one;}SetProduct(d_1);}}}RE;}TE <TY R,TY PT_MAGMA,TY U,TY R_MODULE> IN VO IntervalMultiplyLazySqrtDecomposition<R,PT_MAGMA,U,R_MODULE>::IntervalMultiply(CRI i_start,CRI i_final,CO U& u){CO U& one = m_M.One();if(u != one){CO R& point = m_L.Point();CO int i_min = max(i_start,0);CO int i_ulim = min(i_final + 1,m_N);CO int d_0 =(i_min + m_N_sqrt - 1)/ m_N_sqrt;CO int d_1 = max(d_0,i_ulim / m_N_sqrt);CO int d_0_N_sqrt = d_0 * m_N_sqrt;CO int d_1_N_sqrt = d_1 * m_N_sqrt;CO int i_0 = min(d_0_N_sqrt,i_ulim);CO int i_1 = max(i_0,d_1_N_sqrt);if(i_min < i_0){CO int d_0_minus = d_0 - 1;CO int d_0_N_sqrt_minus = d_0_N_sqrt - m_N_sqrt;U& m_bd = m_b[d_0_minus];m_bd = m_M.Product(m_bd,m_M.PW(u,i_0 - i_min));VE<bool>::reference m_suspENed_d = m_suspENed[d_0_minus];if(m_suspENed_d){U& m_lazy_substitution_d = m_lazy_substitution[d_0_minus];IntervalSet_Body(d_0_N_sqrt_minus,i_min,m_lazy_substitution_d);IntervalSet_Body(i_min,i_0,m_M.Product(m_lazy_substitution_d,u));IntervalSet_Body(i_0,d_0_N_sqrt,m_lazy_substitution_d);m_suspENed_d = false;}else{R& m_lazy_action_d = m_lazy_action[d_0_minus];if(m_lazy_action_d != point){IntervalAct_Body(d_0_N_sqrt_minus,d_0_N_sqrt,m_lazy_action_d);m_lazy_action_d = point;}U& m_lazy_MU_d = m_lazy_MU[d_0_minus];if(m_lazy_MU_d == one){IntervalMultiply_Body(i_min,i_0,u);}else{IntervalMultiply_Body(d_0_N_sqrt_minus,i_min,m_lazy_MU_d);IntervalMultiply_Body(i_min,i_0,m_M.Product(m_lazy_MU_d,u));IntervalMultiply_Body(i_0,d_0_N_sqrt,m_lazy_MU_d);m_lazy_MU_d = one;}}}CO U PW = m_M.PW(u,m_N_sqrt);for(int d = d_0;d < d_1;d++){U& m_bd = m_b[d];m_bd = m_M.Product(m_bd,PW);if(m_suspENed[d]){U& m_lazy_substitution_d = m_lazy_substitution[d];m_lazy_substitution_d = m_M.Product(m_lazy_substitution_d,u);}else{U& m_lazy_MU_d = m_lazy_MU[d];m_lazy_MU_d = m_M.Product(m_lazy_MU_d,u);}}if(i_1 < i_ulim){CO int d_1_N_sqrt_plus = d_1_N_sqrt + m_N_sqrt;U& m_bd = m_b[d_1];m_bd = m_M.Product(m_bd,m_M.PW(u,i_ulim - i_1));VE<bool>::reference m_suspENed_d = m_suspENed[d_1];if(m_suspENed_d){U& m_lazy_substitution_d = m_lazy_substitution[d_1];IntervalSet_Body(d_1_N_sqrt,i_1,m_lazy_substitution_d);IntervalSet_Body(i_1,i_ulim,m_M.Product(m_lazy_substitution_d,u));IntervalSet_Body(i_ulim,d_1_N_sqrt_plus,m_lazy_substitution_d);m_suspENed_d = false;}else{R& m_lazy_action_d = m_lazy_action[d_1];if(m_lazy_action_d != point){IntervalAct_Body(d_1_N_sqrt,d_1_N_sqrt_plus,m_lazy_action_d);m_lazy_action_d = point;}U& m_lazy_MU_d = m_lazy_MU[d_1];if(m_lazy_MU_d == one){IntervalMultiply_Body(i_1,i_ulim,u);}else{IntervalMultiply_Body(d_1_N_sqrt,i_1,m_lazy_MU_d);IntervalMultiply_Body(i_1,i_ulim,m_M.Product(m_lazy_MU_d,u));IntervalMultiply_Body(i_ulim,d_1_N_sqrt_plus,m_lazy_MU_d);m_lazy_MU_d = one;}}}}RE;}TE <TY R,TY PT_MAGMA,TY U,TY R_MODULE> IN U IntervalMultiplyLazySqrtDecomposition<R,PT_MAGMA,U,R_MODULE>::Get(CRI i){CO int d = i / m_N_sqrt;RE m_suspENed[d]?m_lazy_substitution[d]:m_M.Product(m_M.Action(m_lazy_action[d],m_a[i]),m_lazy_MU[d]);}TE <TY R,TY PT_MAGMA,TY U,TY R_MODULE> IN U IntervalMultiplyLazySqrtDecomposition<R,PT_MAGMA,U,R_MODULE>::IntervalProduct(CRI i_start,CRI i_final){CO int i_min = max(i_start,0);CO int i_ulim = min(i_final + 1,m_N);CO int d_0 =(i_min + m_N_sqrt - 1)/ m_N_sqrt;CO int d_1 = max(d_0,i_ulim / m_N_sqrt);CO int i_0 = min(d_0 * m_N_sqrt,i_ulim);CO int i_1 = max(i_0,d_1 * m_N_sqrt);U AN = m_M.One();if(i_min < i_0){CO int d_0_minus = d_0 - 1;AN = m_suspENed[d_0_minus]?m_M.PW(m_lazy_substitution[d_0_minus],i_0 - i_min):m_M.Product(m_M.Action(m_lazy_action[d_0_minus],IntervalProduct_Body(i_min,i_0)),m_M.PW(m_lazy_MU[d_0_minus],i_0 - i_min));}for(int d = d_0;d < d_1;d++){AN = m_M.Product(AN,m_b[d]);}if(i_1 < i_ulim){AN = m_M.Product(AN,m_suspENed[d_1]?m_M.PW(m_lazy_substitution[d_1],i_ulim - i_1):m_M.Product(m_M.Action(m_lazy_action[d_1],IntervalProduct_Body(i_1,i_ulim)),m_M.PW(m_lazy_MU[d_1],i_ulim - i_1)));}RE AN;}TE <TY R,TY PT_MAGMA,TY U,TY R_MODULE> IN VO IntervalMultiplyLazySqrtDecomposition<R,PT_MAGMA,U,R_MODULE>::SetProduct(CRI d){U& m_bd = m_b[d]= m_M.One();CO int i_min = d * m_N_sqrt;CO int i_ulim = i_min + m_N_sqrt;for(int i = i_min;i < i_ulim;i++){m_bd = m_M.Product(m_bd,m_a[i]);}RE;}TE <TY R,TY PT_MAGMA,TY U,TY R_MODULE> IN VO IntervalMultiplyLazySqrtDecomposition<R,PT_MAGMA,U,R_MODULE>::SolveSuspENedSubstitution(CRI d,CO U& u){CO int i_min = d * m_N_sqrt;IntervalSet_Body(i_min,i_min + m_N_sqrt,u);m_suspENed[d]= false;RE;}TE <TY R,TY PT_MAGMA,TY U,TY R_MODULE> IN VO IntervalMultiplyLazySqrtDecomposition<R,PT_MAGMA,U,R_MODULE>::IntervalSet_Body(CRI i_min,CRI i_ulim,CO U& u){for(int i = i_min;i < i_ulim;i++){m_a[i]= u;}RE;}TE <TY R,TY PT_MAGMA,TY U,TY R_MODULE> IN VO IntervalMultiplyLazySqrtDecomposition<R,PT_MAGMA,U,R_MODULE>::SolveSuspENedAction(CRI d){CO int i_min = d * m_N_sqrt;CO int i_ulim = i_min + m_N_sqrt;U& m_bd = m_b[d];R& m_lazy_action_d = m_lazy_action[d];if(m_lazy_action_d != m_L.Point()){IntervalAct_Body(i_min,i_ulim,m_lazy_action_d);m_bd = m_M.Action(m_lazy_action_d,m_bd);m_lazy_action_d = m_L.Point();}CO U& one = m_M.One();U& m_lazy_MU_d = m_lazy_MU[d];if(m_lazy_MU_d != one){IntervalMultiply_Body(i_min,i_ulim,m_lazy_MU_d);m_bd = m_M.Product(m_bd,m_M.PW(m_lazy_MU_d,m_N_sqrt));m_lazy_MU_d = one;}RE;}TE <TY R,TY PT_MAGMA,TY U,TY R_MODULE> IN VO IntervalMultiplyLazySqrtDecomposition<R,PT_MAGMA,U,R_MODULE>::IntervalAct_Body(CRI i_min,CRI i_ulim,CO R& r){for(int i = i_min;i < i_ulim;i++){U& m_ai = m_a[i];m_ai = m_M.Action(r,m_ai);}RE;}TE <TY R,TY PT_MAGMA,TY U,TY R_MODULE> IN VO IntervalMultiplyLazySqrtDecomposition<R,PT_MAGMA,U,R_MODULE>::IntervalMultiply_Body(CRI i_min,CRI i_ulim,CO U& u){for(int i = i_min;i < i_ulim;i++){U& m_ai = m_a[i];m_ai = m_M.Product(m_ai,u);}RE;}TE <TY R,TY PT_MAGMA,TY U,TY R_MODULE> IN U IntervalMultiplyLazySqrtDecomposition<R,PT_MAGMA,U,R_MODULE>::IntervalProduct_Body(CRI i_min,CRI i_ulim){U AN = m_M.One();for(int i = i_min;i < i_ulim;i++){AN = m_M.Product(AN,m_a[i]);}RE AN;}

// AAA ライブラリは以上に挿入する。

#define INCLUDE_MAIN
#include __FILE__

#else // INCLUDE_LIBRARY

#ifdef DEBUG
  #define _GLIBCXX_DEBUG
  #define SIGNAL signal( SIGABRT , &AlertAbort );
  #define ASSERT( A , MIN , MAX ) CERR( "ASSERTチェック： " , ( MIN ) , ( ( MIN ) <= A ? "<=" : ">" ) , A , ( A <= ( MAX ) ? "<=" : ">" ) , ( MAX ) ); assert( ( MIN ) <= A && A <= ( MAX ) )
  #define CERR( ... ) VariadicCout( cerr , __VA_ARGS__ ) << endl
  #define COUT( ... ) VariadicCout( cout << "出力： " , __VA_ARGS__ ) << endl
  #define CERR_A( A , N ) OUTPUT_ARRAY( cerr , A , N ) << endl
  #define COUT_A( A , N ) cout << "出力： "; OUTPUT_ARRAY( cout , A , N ) << endl
  #define CERR_ITR( A ) OUTPUT_ITR( cerr , A ) << endl
  #define COUT_ITR( A ) cout << "出力： "; OUTPUT_ITR( cout , A ) << endl
#else
  #pragma GCC optimize ( "O3" )
  #pragma GCC optimize ( "unroll-loops" )
  #pragma GCC target ( "sse4.2,fma,avx2,popcnt,lzcnt,bmi2" )
  #define SIGNAL 
  #define ASSERT( A , MIN , MAX ) assert( ( MIN ) <= A && A <= ( MAX ) )
  #define CERR( ... ) 
  #define COUT( ... ) VariadicCout( cout , __VA_ARGS__ ) << ENDL
  #define CERR_A( A , N ) 
  #define COUT_A( A , N ) OUTPUT_ARRAY( cout , A , N ) << ENDL
  #define CERR_ITR( A ) 
  #define COUT_ITR( A ) OUTPUT_ITR( cout , A ) << ENDL
#endif
#ifdef REACTIVE
  #define ENDL endl
#else
  #define ENDL "\n"
#endif
#ifdef USE_GETLINE
  #define SET_LL( A ) { GETLINE( A ## _str ); A = stoll( A ## _str ); }
  #define GETLINE_SEPARATE( SEPARATOR , ... ) string __VA_ARGS__; VariadicGetline( cin , SEPARATOR , __VA_ARGS__ )
  #define GETLINE( ... ) GETLINE_SEPARATE( '\n' , __VA_ARGS__ )
#else
  #define SET_LL( A ) cin >> A
  #define CIN( LL , ... ) LL __VA_ARGS__; VariadicCin( cin , __VA_ARGS__ )
  #define SET_A( A , N ) FOR( VARIABLE_FOR_SET_A , 0 , N ){ cin >> A[VARIABLE_FOR_SET_A]; }
  #define CIN_A( LL , A , N ) vector<LL> A( N ); SET_A( A , N );
#endif
#include <bits/stdc++.h>
using namespace std;
#define REPEAT_MAIN( BOUND ) int main(){ ios_base::sync_with_stdio( false ); cin.tie( nullptr ); SIGNAL; CEXPR( int , bound_test_case_num , BOUND ); int test_case_num = 1; if constexpr( bound_test_case_num > 1 ){ SET_ASSERT( test_case_num , 1 , bound_test_case_num ); } REPEAT( test_case_num ){ if constexpr( bound_test_case_num > 1 ){ CERR( "testcase " , VARIABLE_FOR_REPEAT_test_case_num , ":" ); } Solve(); CERR( "" ); } CHECK_REDUNDANT_INPUT; }
#define START_WATCH chrono::system_clock::time_point watch = chrono::system_clock::now()
#define CURRENT_TIME static_cast<double>( chrono::duration_cast<chrono::microseconds>( chrono::system_clock::now() - watch ).count() / 1000.0 )
#define CHECK_WATCH( TL_MS ) ( CURRENT_TIME < TL_MS - 100.0 )
#define CEXPR( LL , BOUND , VALUE ) constexpr LL BOUND = VALUE
#define SET_ASSERT( A , MIN , MAX ) SET_LL( A ); ASSERT( A , MIN , MAX )
#define SET_A_ASSERT( A , N , MIN , MAX ) FOR( VARIABLE_FOR_SET_A , 0 , N ){ SET_ASSERT( A[VARIABLE_FOR_SET_A] , MIN , MAX ); }
#define CIN_ASSERT( A , MIN , MAX ) decldecay_t( MAX ) A; SET_ASSERT( A , MIN , MAX )
#define CIN_A_ASSERT( A , N , MIN , MAX ) vector<decldecay_t( MAX )> A( N ); SET_A_ASSERT( A , N , MIN , MAX )
#define FOR( VAR , INITIAL , FINAL_PLUS_ONE ) for( decldecay_t( FINAL_PLUS_ONE ) VAR = INITIAL ; VAR < FINAL_PLUS_ONE ; VAR ++ )
#define FOREQ( VAR , INITIAL , FINAL ) for( decldecay_t( FINAL ) VAR = INITIAL ; VAR <= FINAL ; VAR ++ )
#define FOREQINV( VAR , INITIAL , FINAL ) for( decldecay_t( INITIAL ) VAR = INITIAL ; VAR + 1 > FINAL ; VAR -- )
#define AUTO_ITR( ARRAY ) auto itr_ ## ARRAY = ARRAY .begin() , end_ ## ARRAY = ARRAY .end()
#define FOR_ITR( ARRAY ) for( AUTO_ITR( ARRAY ) , itr = itr_ ## ARRAY ; itr_ ## ARRAY != end_ ## ARRAY ; itr_ ## ARRAY ++ , itr++ )
#define REPEAT( HOW_MANY_TIMES ) FOR( VARIABLE_FOR_REPEAT_ ## HOW_MANY_TIMES , 0 , HOW_MANY_TIMES )
#define SET_PRECISION( DECIMAL_DIGITS ) cout << fixed << setprecision( DECIMAL_DIGITS )
#define OUTPUT_ARRAY( OS , A , N ) FOR( VARIABLE_FOR_OUTPUT_ARRAY , 0 , N ){ OS << A[VARIABLE_FOR_OUTPUT_ARRAY] << (VARIABLE_FOR_OUTPUT_ARRAY==N-1?"":" "); } OS
#define OUTPUT_ITR( OS , A ) { auto ITERATOR_FOR_OUTPUT_ITR = A.begin() , END_FOR_OUTPUT_ITR = A.end(); bool VARIABLE_FOR_OUTPUT_ITR = ITERATOR_FOR_COUT_ITR != END_FOR_COUT_ITR; while( VARIABLE_FOR_OUTPUT_ITR ){ OS << *ITERATOR_FOR_COUT_ITR; ( VARIABLE_FOR_OUTPUT_ITR = ++ITERATOR_FOR_COUT_ITR != END_FOR_COUT_ITR ) ? OS : OS << " "; } } OS
#define RETURN( ... ) COUT( __VA_ARGS__ ); return

// 型のエイリアス
#define decldecay_t( VAR ) decay_t<decltype( VAR )>
template <typename F , typename...Args> using ret_t = decltype( declval<F>()( declval<Args>()... ) );
template <typename T> using inner_t = typename T::type;
using uint = unsigned int;
using ll = long long;
using ull = unsigned long long;
using ld = long double;
using lld = __float128;
template <typename INT> using T2 = pair<INT,INT>;
template <typename INT> using T3 = tuple<INT,INT,INT>;
template <typename INT> using T4 = tuple<INT,INT,INT,INT>;
using path = pair<int,ll>;

// 入出力用
template <class Traits> inline basic_istream<char,Traits>& VariadicCin( basic_istream<char,Traits>& is ) { return is; }
template <class Traits , typename Arg , typename... ARGS> inline basic_istream<char,Traits>& VariadicCin( basic_istream<char,Traits>& is , Arg& arg , ARGS&... args ) { return VariadicCin( is >> arg , args... ); }
template <class Traits> inline basic_istream<char,Traits>& VariadicGetline( basic_istream<char,Traits>& is , const char& separator ) { return is; }
template <class Traits , typename Arg , typename... ARGS> inline basic_istream<char,Traits>& VariadicGetline( basic_istream<char,Traits>& is , const char& separator , Arg& arg , ARGS&... args ) { return VariadicGetline( getline( is , arg , separator ) , separator , args... ); }
template <class Traits , typename Arg> inline basic_ostream<char,Traits>& operator<<( basic_ostream<char,Traits>& os , const vector<Arg>& arg ) { auto begin = arg.begin() , end = arg.end(); auto itr = begin; while( itr != end ){ ( itr == begin ? os : os << " " ) << *itr; itr++; } return os; }
template <class Traits , typename Arg1 , typename Arg2> inline basic_ostream<char,Traits>& operator<<( basic_ostream<char,Traits>& os , const pair<Arg1,Arg2>& arg ) { return os << arg.first << " " << arg.second; }
template <class Traits , typename Arg> inline basic_ostream<char,Traits>& VariadicCout( basic_ostream<char,Traits>& os , const Arg& arg ) { return os << arg; }
template <class Traits , typename Arg1 , typename Arg2 , typename... ARGS> inline basic_ostream<char,Traits>& VariadicCout( basic_ostream<char,Traits>& os , const Arg1& arg1 , const Arg2& arg2 , const ARGS&... args ) { return VariadicCout( os << arg1 << " " , arg2 , args... ); }

// デバッグ用
#ifdef DEBUG
  inline void AlertAbort( int n ) { CERR( "abort関数が呼ばれました。assertマクロのメッセージが出力されていない場合はオーバーフローの有無を確認をしてください。" ); }
  void AutoCheck( bool& auto_checked );
#endif

// 入力フォーマットチェック用
// 1行中の変数の個数をSEPARATOR区切りで確認
#define GETLINE_COUNT( S , VARIABLE_NUMBER , SEPARATOR ) GETLINE( S ); int VARIABLE_FOR_INDEX_FOR_GETLINE_FOR_ ## S = 0; int VARIABLE_FOR_SIZE_FOR_GETLINE_FOR_ ## S  = S.size(); { int size = S.size(); int count = 0; for( int i = 0 ; i < size ; i++ ){ if( S.substr( i , 1 ) == SEPARATOR ){ count++; } } assert( count + 1 == VARIABLE_NUMBER ); }
// 余計な入力の有無を確認
#ifdef DEBUG
  #define CHECK_REDUNDANT_INPUT 
#else
  #ifdef USE_GETLINE
    #define CHECK_REDUNDANT_INPUT string VARIABLE_FOR_CHECK_REDUNDANT_INPUT = ""; getline( cin , VARIABLE_FOR_CHECK_REDUNDANT_INPUT ); assert( VARIABLE_FOR_CHECK_REDUNDANT_INPUT == "" ); assert( ! cin )
  #else
    #define CHECK_REDUNDANT_INPUT string VARIABLE_FOR_CHECK_REDUNDANT_INPUT = ""; cin >> VARIABLE_FOR_CHECK_REDUNDANT_INPUT; assert( VARIABLE_FOR_CHECK_REDUNDANT_INPUT == "" ); assert( ! cin )
  #endif
#endif
// |N| <= BOUNDを満たすNをSから構築
#define STOI( S , N , BOUND ) decldecay_t( BOUND ) N = 0; { bool VARIABLE_FOR_POSITIVITY_FOR_GETLINE = true; assert( VARIABLE_FOR_INDEX_FOR_GETLINE_FOR_ ## S < VARIABLE_FOR_SIZE_FOR_GETLINE_FOR_ ## S ); if( S.substr( VARIABLE_FOR_INDEX_FOR_GETLINE_FOR_ ## S , 1 ) == "-" ){ VARIABLE_FOR_POSITIVITY_FOR_GETLINE = false; VARIABLE_FOR_INDEX_FOR_GETLINE_FOR_ ## S ++; assert( VARIABLE_FOR_INDEX_FOR_GETLINE_FOR_ ## S < VARIABLE_FOR_SIZE_FOR_GETLINE_FOR_ ## S ); } assert( S.substr( VARIABLE_FOR_INDEX_FOR_GETLINE_FOR_ ## S , 1 ) != " " ); string VARIABLE_FOR_LETTER_FOR_GETLINE{}; int VARIABLE_FOR_DIGIT_FOR_GETLINE{}; while( VARIABLE_FOR_INDEX_FOR_GETLINE_FOR_ ## S < VARIABLE_FOR_SIZE_FOR_GETLINE_FOR_ ## S ? ( VARIABLE_FOR_LETTER_FOR_GETLINE = S.substr( VARIABLE_FOR_INDEX_FOR_GETLINE_FOR_ ## S , 1 ) ) != " " : false ){ VARIABLE_FOR_DIGIT_FOR_GETLINE = stoi( VARIABLE_FOR_LETTER_FOR_GETLINE ); assert( N < BOUND / 10 ? true : N == BOUND / 10 && VARIABLE_FOR_DIGIT_FOR_GETLINE <= BOUND % 10 ); N = N * 10 + VARIABLE_FOR_DIGIT_FOR_GETLINE; VARIABLE_FOR_INDEX_FOR_GETLINE_FOR_ ## S ++; } if( ! VARIABLE_FOR_POSITIVITY_FOR_GETLINE ){ N *= -1; } if( VARIABLE_FOR_INDEX_FOR_GETLINE_FOR_ ## S < VARIABLE_FOR_SIZE_FOR_GETLINE_FOR_ ## S ){ VARIABLE_FOR_INDEX_FOR_GETLINE_FOR_ ## S ++; } }
#define STOI_A( S , A , N , BOUND ) vector<decldecay_t( BOUND )> A( N ); FOR( i , 0 , N ){ STOI( S , A ## i , BOUND ); A[i] = move( A ## i );} 

// SをSEPARATORで区切りTを構築
#define SEPARATE( S , T , SEPARATOR ) string T{}; { assert( VARIABLE_FOR_INDEX_FOR_GETLINE_FOR_ ## S < VARIABLE_FOR_SIZE_FOR_GETLINE_FOR_ ## S ); int VARIABLE_FOR_INDEX_FOR_GETLINE_FOR_ ## S_prev = VARIABLE_FOR_INDEX_FOR_GETLINE_FOR_ ## S; assert( S.substr( VARIABLE_FOR_INDEX_FOR_GETLINE_FOR_ ## S , 1 ) != SEPARATOR ); string VARIABLE_FOR_LETTER_FOR_GETLINE{}; while( VARIABLE_FOR_INDEX_FOR_GETLINE_FOR_ ## S < VARIABLE_FOR_SIZE_FOR_GETLINE_FOR_ ## S ? ( VARIABLE_FOR_LETTER_FOR_GETLINE = S.substr( VARIABLE_FOR_INDEX_FOR_GETLINE_FOR_ ## S , 1 ) ) != SEPARATOR : false ){ VARIABLE_FOR_INDEX_FOR_GETLINE_FOR_ ## S ++; } T = S.substr( VARIABLE_FOR_INDEX_FOR_GETLINE_FOR_ ## S_prev , VARIABLE_FOR_INDEX_FOR_GETLINE_FOR_ ## S - VARIABLE_FOR_INDEX_FOR_GETLINE_FOR_ ## S_prev ); if( VARIABLE_FOR_INDEX_FOR_GETLINE_FOR_ ## S < VARIABLE_FOR_SIZE_FOR_GETLINE_FOR_ ## S ){ VARIABLE_FOR_INDEX_FOR_GETLINE_FOR_ ## S ++; } }

// 圧縮用
#define TE template
#define TY typename
#define US using
#define ST static
#define AS assert
#define IN inline
#define CL class
#define PU public
#define OP operator
#define CE constexpr
#define CO const
#define NE noexcept
#define RE return 
#define WH while
#define VO void
#define VE vector
#define LI list
#define BE begin
#define EN end
#define SZ size
#define LE length
#define PW Power
#define MO move
#define TH this
#define CRI CO int&
#define CRUI CO uint&
#define CRL CO ll&
#define VI virtual 
#define ST_AS static_assert
#define reMO_CO remove_const
#define is_COructible_v is_constructible_v
#define rBE rbegin
#define reSZ resize

#define INCLUDE_LIBRARY
#include __FILE__

#endif // INCLUDE_LIBRARY

#endif // INCLUDE_MAIN