#基点付きマグマ class L: point=None def __init__(self,val): self.val = val def __eq__(self,other): return self.val==other.val def __imul__(self,other): self.val *= other.val #ユーザー定義 return self def __mul__(self,other): return self.__class__(self.val*other.val) #ユーザー定義 def copy(self): return self.__class__(self.val) L.point=L(1) #ユーザー定義 # 区間作用を行わない場合もL.pointの作用を区間積に用いるため、 # Lをdummyにせず自明群{1}などを用いる必要があることに注意。 # Lの基点が恒等変換に対応する左L作用つきN加群 class M: one=None def __init__(self,val): self.val = val def __eq__(self,other): return self.val==other.val def __mul__(self,other): return self.__class__(self.val+other.val) #ユーザー定義 def __pow__(self,n): return self.__class__(self.val*n) #ユーザー定義 def __ixor__(self,x): self.val*=x.val #ユーザー定義 return self def __xor__(self,x): return self.__class__(self.val*x.val) #ユーザー定義 def copy(self): return self.__class__(self.val) M.one=M(0) #ユーザー定義 # 配列による初期化O(N) # 一点取得O(1) # 区間積取得O(N^{1/2})(Mのモノイド性を使う) # 一点代入O(N^{1/2})(MのN加群性を使う) # 区間代入O(N^{1/2})(MのN加群性を使う) # 一点乗算はなし。 # 区間乗算O(N^{1/2})(Mの可換性を使う) # 一点作用はなし。 # 区間作用O(N^{1/2}) class IntervalMultiplyLazySqrtDecomposition: def __init__(self,a): self.N = len(a) self.N_sqrt = int( self.N**0.5 ) + 1 self.N_d = ( self.N + self.N_sqrt - 1 ) // self.N_sqrt self.N_m = self.N_d * self.N_sqrt self.a = a[:] self.b = [M.one.copy()for d in R(self.N_d)] self.lazy_substitution = self.b[:] self.suspended = [False] * self.N_d self.lazy_action = [L.point.copy()for d in R(self.N_d)] self.lazy_multiplication = self.b[:] self.a += [M.one.copy()for d in R(self.N_m)] i_min = 0 i_ulim = self.N_sqrt for d in R(self.N_d): for i in R(i_min,i_ulim):self.b[d] *= self.a[i] i_min = i_ulim i_ulim += self.N_sqrt def Set(self,i,u): d = i // self.N_sqrt i_min = d * self.N_sqrt i_ulim = i_min + self.N_sqrt if self.suspended[d]: if self.lazy_substitution[d] != u: SolveSuspendedSubstitution( d , self.lazy_substitution[d] ) self.a[i] = u # N加群性を使った self.b[d] = ( self.lazy_substitution[d] ** self.N_sqrt - 1 ) * u else: self.SolveSuspendedAction( d ) if self.a[i] != u: self.a[i] = u self.SetProduct( d ) def IntervalSet(self,i_start,i_final,u): i_min = max( i_start , 0 ) i_ulim = min( i_final + 1 , self.N ) d_0 = ( i_min + self.N_sqrt - 1 ) // self.N_sqrt d_1 = max( d_0 , i_ulim // self.N_sqrt ) d_0_N_sqrt = d_0 * self.N_sqrt d_1_N_sqrt = d_1 * self.N_sqrt i_0 = min( d_0_N_sqrt , i_ulim ) i_1 = max( i_0 , d_1_N_sqrt ) if i_min < i_0: # この時d_0 > 0になる。 d_0_minus = d_0 - 1 d_0_N_sqrt_minus = d_0_N_sqrt - self.N_sqrt if self.suspended[d_0_minus]: self.IntervalSet_Body( d_0_N_sqrt_minus , i_min , self.lazy_substitution[d_0_minus] ) self.IntervalSet_Body( i_min , i_0 , u ) self.IntervalSet_Body( i_0 , d_0_N_sqrt , self.lazy_substitution[d_0_minus] ) self.suspended[d_0_minus] = False # N加群性を使った。 self.b[d_0_minus] = self.lazy_substitution[d_0_minus] ** ( self.N_sqrt - ( i_0 - i_min ) ) * ( u ** ( i_0 - i_min ) ) else: self.SolveSuspendedAction( d_0_minus ) self.IntervalSet_Body( i_min , i_0 , u ) self.b[d_0_minus] = ( self.IntervalProduct_Body( d_0_N_sqrt_minus , i_min ) * ( u ** ( i_0 - i_min ) ) ) * self.IntervalProduct_Body( i_0 , d_0_N_sqrt ) power = u ** self.N_sqrt for d in R(d_0,d_1): self.b[d] = power self.lazy_substitution[d] = u self.suspended[d] = True self.lazy_multiplication[d] = M.one.copy() self.lazy_action[d] = L.point.copy() if i_1 < i_ulim: # この時d_1 < self.N_dになる。 d_1_N_sqrt_plus = d_1_N_sqrt + self.N_sqrt self.b[d_1] = self.b[d_1] if self.suspended[d_1]: self.IntervalSet_Body( d_1_N_sqrt , i_1 , self.lazy_substitution[d_1] ) self.IntervalSet_Body( i_1 , i_ulim , u ) self.IntervalSet_Body( i_ulim , d_1_N_sqrt_plus , self.lazy_substitution[d_1] ) self.suspended[d_1] = False self.b[d_1] = ( self.lazy_substitution[d_1] ** ( i_1 - d_1_N_sqrt ) ) * ( u ** ( i_ulim - i_1 ) ) * ( self.lazy_substitution[d_1] ** ( d_1_N_sqrt_plus - i_ulim ) ) else: self.SolveSuspendedAction( d_1 ) self.IntervalSet_Body( i_1 , i_ulim , u ) self.b[d_1] = ( self.IntervalProduct_Body( d_1_N_sqrt , i_1 ) * ( u ** ( i_ulim - i_1 ) ) ) * self.IntervalProduct_Body( i_ulim , d_1_N_sqrt_plus ) def IntervalAct(self,i_start,i_final,r): if r != L.point: i_min = max( i_start , 0 ) i_ulim = min( i_final + 1 , self.N ) d_0 = ( i_min + self.N_sqrt - 1 ) // self.N_sqrt d_1 = max( d_0 , i_ulim // self.N_sqrt ) d_0_N_sqrt = d_0 * self.N_sqrt d_1_N_sqrt = d_1 * self.N_sqrt i_0 = min( d_0_N_sqrt , i_ulim ) i_1 = max( i_0 , d_1_N_sqrt ) if i_min < i_0: # この時d_0 > 0になる。 d_0_minus = d_0 - 1 d_0_N_sqrt_minus = d_0_N_sqrt - self.N_sqrt; if self.suspended[d_0_minus]: u = self.lazy_substitution[d_0_minus] ^ r self.IntervalSet_Body( d_0_N_sqrt_minus , i_min , self.lazy_substitution[d_0_minus] ) self.IntervalSet_Body( i_min , i_0 , u ) self.IntervalSet_Body( i_0 , d_0_N_sqrt , self.lazy_substitution[d_0_minus] ) self.suspended[d_0_minus] = False # N加群性を使った。 self.b[d_0_minus] = ( self.lazy_substitution[d_0_minus] ** ( self.N_sqrt - ( i_0 - i_min ) ) ) * ( u ** ( i_0 - i_min ) ) else: if self.lazy_action[d_0_minus] == L.point:self.IntervalAct_Body( i_min , i_0 , r ) else: self.IntervalAct_Body( d_0_N_sqrt_minus , i_min , self.lazy_action[d_0_minus] ) self.IntervalAct_Body( i_min , i_0 , r * self.lazy_action[d_0_minus] ) self.IntervalAct_Body( i_0 , d_0_N_sqrt , self.lazy_action[d_0_minus] ) self.lazy_action[d_0_minus] = L.point.copy() if self.lazy_multiplication[d_0_minus] != M.one: IntervalMultiply_Body( d_0_N_sqrt_minus , i_min , self.lazy_multiplication[d_0_minus] ) IntervalMultiply_Body( i_min , i_0 , self.lazy_multiplication[d_0_minus] ^ r ) IntervalMultiply_Body( i_0 , d_0_N_sqrt , self.lazy_multiplication[d_0_minus] ) self.lazy_multiplication[d_0_minus] = M.one.copy() self.SetProduct( d_0_minus ) for d in R(d_0,d_1): self.b[d] = self.b[d] ^ r if self.suspended[d]:self.lazy_substitution[d] ^= r else: self.lazy_action[d] ^= r self.lazy_multiplication[d] ^= r if i_1 < i_ulim: # この時d_1 < self.N_dになる。 d_1_N_sqrt_plus = d_1_N_sqrt + self.N_sqrt if self.suspended[d_1]: u = self.lazy_substitution[d_1] ^ r self.IntervalSet_Body( d_1_N_sqrt , i_1 , self.lazy_substitution[d_1] ) self.IntervalSet_Body( i_1 , i_ulim , u ) self.IntervalSet_Body( i_ulim , d_1_N_sqrt_plus , self.lazy_substitution[d_1] ) self.suspended[d_1] = False # N加群性を使った。 self.b[d_1] = ( self.lazy_substitution[d_1] ** ( self.N_sqrt - ( i_ulim - i_1 ) ) ) * ( u ** ( i_ulim - i_1 ) ) else: if self.lazy_action[d_1] == L.point:self.IntervalAct_Body( i_1 , i_ulim , r ) else: self.IntervalAct_Body( d_1_N_sqrt , i_1 , self.lazy_action[d_1] ) self.IntervalAct_Body( i_1 , i_ulim , r * self.lazy_action[d_1] ) self.IntervalAct_Body( i_ulim , d_1_N_sqrt_plus , self.lazy_action[d_1] ) self.lazy_action[d_1] = L.point.copy() if self.lazy_multiplication[d_1] != M.one: self.IntervalMultiply_Body( d_1_N_sqrt , i_1 , self.lazy_multiplication[d_1] ) self.IntervalMultiply_Body( i_1 , i_ulim , self.lazy_multiplication[d_1] ^ r ) self.IntervalMultiply_Body( i_ulim , d_1_N_sqrt_plus , self.lazy_multiplication[d_1] ) self.lazy_multiplication[d_1] = M.one.copy() self.SetProduct( d_1 ) def IntervalMultiply(self,i_start,i_final,u): if u != M.one: i_min = max( i_start , 0 ) i_ulim = min( i_final + 1 , self.N ) d_0 = ( i_min + self.N_sqrt - 1 ) // self.N_sqrt d_1 = max( d_0 , i_ulim // self.N_sqrt ) d_0_N_sqrt = d_0 * self.N_sqrt d_1_N_sqrt = d_1 * self.N_sqrt i_0 = min( d_0_N_sqrt , i_ulim ) i_1 = max( i_0 , d_1_N_sqrt ) if i_min < i_0: # この時d_0 > 0になる。 d_0_minus = d_0 - 1 d_0_N_sqrt_minus = d_0_N_sqrt - self.N_sqrt # N加群性を使った。 self.b[d_0_minus] *= u ** ( i_0 - i_min ) if self.suspended[d_0_minus]: self.IntervalSet_Body( d_0_N_sqrt_minus , i_min , self.lazy_substitution[d_0_minus] ) self.IntervalSet_Body( i_min , i_0 , self.lazy_substitution[d_0_minus] * u ) self.IntervalSet_Body( i_0 , d_0_N_sqrt , self.lazy_substitution[d_0_minus] ) self.suspended[d_0_minus] = False else: if self.lazy_action[d_0_minus] != L.point: self.IntervalAct_Body( d_0_N_sqrt_minus , d_0_N_sqrt , self.lazy_action[d_0_minus] ) self.lazy_action[d_0_minus] = L.point.copy() if self.lazy_multiplication[d_0_minus] == M.one:self.IntervalMultiply_Body( i_min , i_0 , u ) else: self.IntervalMultiply_Body( d_0_N_sqrt_minus , i_min , self.lazy_multiplication[d_0_minus] ) self.IntervalMultiply_Body( i_min , i_0 , self.lazy_multiplication[d_0_minus] * u ) self.IntervalMultiply_Body( i_0 , d_0_N_sqrt , self.lazy_multiplication[d_0_minus] ) self.lazy_multiplication[d_0_minus] = M.one.copy() power = u ** self.N_sqrt for d in R(d_0,d_1): # N加群性を使った。 self.b[d] *= power if self.suspended[d]:self.lazy_substitution[d] *= u else:self.lazy_multiplication[d] *= u if i_1 < i_ulim: # この時d_1 < self.N_dになる。 d_1_N_sqrt_plus = d_1_N_sqrt + self.N_sqrt # N加群性を使った。 self.b[d_1] *= u ** ( i_ulim - i_1 ) if self.suspended[d_1]: self.IntervalSet_Body( d_1_N_sqrt , i_1 , self.lazy_substitution[d_1] ) self.IntervalSet_Body( i_1 , i_ulim , self.lazy_substitution[d_1] * u ) self.IntervalSet_Body( i_ulim , d_1_N_sqrt_plus , self.lazy_substitution[d_1] ) self.suspended[d_1] = False else: if self.lazy_action[d_1] != L.point: self.IntervalAct_Body( d_1_N_sqrt , d_1_N_sqrt_plus , self.lazy_action[d_1] ) self.lazy_action[d_1] = L.point.copy() if self.lazy_multiplication[d_1] == M.one:self.IntervalMultiply_Body( i_1 , i_ulim , u ) else: self.IntervalMultiply_Body( d_1_N_sqrt , i_1 , self.lazy_multiplication[d_1] ) self.IntervalMultiply_Body( i_1 , i_ulim , self.lazy_multiplication[d_1] * u ) self.IntervalMultiply_Body( i_ulim , d_1_N_sqrt_plus , self.lazy_multiplication[d_1] ) self.lazy_multiplication[d_1] = M.one.copy() def Get(self,i): d = i // self.N_sqrt return self.lazy_substitution[d] if self.suspended[d]else ( self.a[i] ^ self.lazy_action[d] ) * self.lazy_multiplication[d] def IntervalProduct(self,i_start,i_final): i_min = max( i_start , 0 ) i_ulim = min( i_final + 1 , self.N ) d_0 = ( i_min + self.N_sqrt - 1 ) // self.N_sqrt d_1 = max( d_0 , i_ulim // self.N_sqrt ) i_0 = min( d_0 * self.N_sqrt , i_ulim ) i_1 = max( i_0 , d_1 * self.N_sqrt ) answer = M.one.copy() if i_min < i_0: # この時d_0 > 0になる。 # N加群性を使った。 d_0_minus = d_0 - 1 answer = ( self.lazy_substitution[d_0_minus] ** ( i_0 - i_min ) )if self.suspended[d_0_minus]else( ( self.IntervalProduct_Body( i_min , i_0 ) ^ self.lazy_action[d_0_minus] ) * ( self.lazy_multiplication[d_0_minus] ** ( i_0 - i_min ) ) ) for d in R(d_0,d_1):answer *= self.b[d] if i_1 < i_ulim: # この時d_1 < self.N_dになる。 # N加群性を使った。 answer *= ( self.lazy_substitution[d_1] ** ( i_ulim - i_1 ) )if self.suspended[d_1]else( ( self.IntervalProduct_Body( i_1 , i_ulim ) ^ self.lazy_action[d_1] ) * ( self.lazy_multiplication[d_1] ** ( i_ulim - i_1 ) ) ) return answer #private: def SetProduct(self,i): self.b[d] = M.one.copy() i_min = d * self.N_sqrt i_ulim = i_min + self.N_sqrt for i in R(i_min,i_ulim):self.b[d] *= self.a[i] def SolveSuspendedSubstitution(self,d,u): i_min = d * self.N_sqrt self.IntervalSet_Body( i_min , i_min + self.N_sqrt , u ) self.suspended[d] = False def IntervalSet_Body(self,i_min,i_ulim,u): for i in R(i_min,i_ulim):self.a[i] = u def SolveSuspendedAction(self,d): i_min = d * self.N_sqrt i_ulim = i_min + self.N_sqrt if self.lazy_action[d] != L.point: self.IntervalAct_Body( i_min , i_ulim , self.lazy_action[d] ) self.b[d] ^= self.lazy_action[d] self.lazy_action[d] = L.point.copy() if self.lazy_multiplication[d] != M.one: self.IntervalMultiply_Body( i_min , i_ulim , self.lazy_multiplication[d] ) # N加群性を使った。 self.b[d] = self.b[d] * ( self.lazy_multiplication[d] ** self.N_sqrt ) self.lazy_multiplication[d] = M.one.copy() def IntervalAct_Body(self,i_min,i_ulim,r): for i in R(i_min,i_ulim):self.a[i] ^= r def IntervalMultiply_Body(self,i_min,i_ulim,u): for i in R(i_min,i_ulim):self.a[i] *= u def IntervalProduct_Body(self,i_min,i_ulim): answer = M.one.copy() for i in R(i_min,i_ulim):answer *= self.a[i] return answer I,R=input,range J=lambda:map(int,I().split()) N=int(I()) A=list(J()) Q=int(I()) pe=[] C=[0]*99 for i in R(2,99): if C[i]<1: pe+=[i] j=i*2 while j<99:C[j],j=1,j+i C=len(pe) t=[] for p in pe: E=[M.one.copy()for i in R(N)] for i in R(N): while A[i]%p<1: A[i]//=p E[i].val+=1 t+=[IntervalMultiplyLazySqrtDecomposition(E)] for q in R(Q): type,l,r,x=J() l-=1 r-=1 if type<2: for c in R(C): e=M.one.copy() while x%pe[c]<1: x//=pe[c] e.val+=1 t[c].IntervalSet(l,r,e) elif type<3: for c in R(C): e=M.one.copy() while x%pe[c]<1: x//=pe[c] e.val+=1 t[c].IntervalMultiply(l,r,e) else: answer=1 for c in R(C): if pe[c]<=x:answer*=t[c].IntervalProduct(l,r).val+1 else:break print(answer%998244353)