######################################################### """ ## 和&積(MOD無し) ####################################### def mul2(a,b): return a*b def add2(a,b): return a+b def mul_inv2(a): return 1/a def add_inv2(a): return -a def identity(n): return Matrix([[int(i==j) for i in range(n)] for j in range(n)]) ########################################################### ## 和&積(MOD有り) ####################################### MOD=10**9+7 def mul2(a,b): return a*b%MOD def add2(a,b): return (a+b)%MOD def mul_inv2(a): return pow(a,MOD-2,MOD) def add_inv2(a): return -a%MOD def identity(n): return Matrix([[int(i==j) for i in range(n)] for j in range(n)]) ########################################################### ## 論理和&論理積 ####################################### def mul2(a,b): return a&b def add2(a,b): return a^b def mul_inv2(a): return None def add_inv2(a): return a mask=(1<<32-1) def identity(n): return Matrix([[int(i==j)*mask for i in range(n)] for j in range(n)]) ########################################################### """ ######################################################### class Matrix(): def __init__(self,A,H,W): self._matrix=[] if type(A[0])==int: self.H=H self.W=W self._matrix=A else: self.H=len(A) self.W=len(A[0]) for aa in A: self._matrix.extend(aa) def __getitem__(self,item): H,W,A=self.H,self.W,self._matrix if type(item)==tuple: i,j=item return self._matrix[i*W+j] else: return self._matrix[item] def __setitem__(self,item,val): H,W,A=self.H,self.W,self._matrix i,j=item self._matrix[i*W+j]=val def __add__(self,B): # assert (self.row,self.column)==(other.row,other.column), "sizes of matrices are different" H,W,A=self.H,self.W,self._matrix AB=[[0]*W for _ in range(H)] for h in range(H): for w in range(W): AB[h*W+w]=add2(A[h*W+w],B._matrix[h*W+w]) return Matrix(AB,H,W) def __mul__(self,other): H,W,A=self.H,self.W,self._matrix if type(other)==Vector: vec=other res=[0]*W for i in range(H): for j in range(W): res[i]=add2(res[i],mul2(A[i*W+j],vec[j])) return Vector(res) else: # assert self.column!=other.row, "sizes of matrices are different" AB=[0]*(other.W*H) for i in range(H): for j in range(other.W): temp=0 for k in range(W): temp=add2(temp,mul2(A[i*W+k],other._matrix[k*other.W+j])) AB[i*W+j]=temp return Matrix(AB,H,other.W) def __truediv__(self,c): H,W,A=self.H,self.W,self._matrix res=A.copy() for h in range(H): for w in range(W): res[h*W+w]=mul2(res[h*W+w],mul_inv2(c)) return Matrix(res,H,W) def __floordiv__(self,c): H,W,A=self.H,self.W,self._matrix res=A.copy() for h in range(H): for w in range(W): res[h*W+w]=res[h*W+w]//c return Matrix(res,H,W) def __mod__(self,c): H,W,A=self.H,self.W,self._matrix res=A.copy() for h in range(H): for w in range(W): res[h*W+w]=res[h*W+w]%c return Matrix(res,H,W) def __pow__(self,m): # assert self.column==self.row, "the size of row must be the same as that of column" H,W,A=self.H,self.W,self._matrix if m==0: return identity(H) else: m-=1 res=self while m: if m%2==1: res*=self self=self*self m>>=1 return res def __eq__(self,other): if type(other)==Matrix: return self._matrix==other._matrix return False def __ne__(self,other): if type(other)==Matrix: return self._matrix!=other._matrix return True def __len__(self): return self.H def __str__(self): H,W,A=self.H,self.W,self._matrix res=[] for i in range(self.H): for j in range(self.W): res.append(str(self._matrix[i*W+j])) res.append(" ") res.append("\n") return "".join(res) def __hash__(self): H,W,A=self.H,self.W,self._matrix res=[] for h in range(self.H): for w in range(self.W): res.append(self._matrix[h*W+w]) return tuple(res) def det(self): H,W,A=self.H,self.W,self._matrix n=H res=1 for i in range(n): if A[i*W+i]==0: res=add_inv2(res) for k in range(i+1,n): if A[k*W+i]!=0: for w in range(W): A[i*W+w],A[k*W+w]=A[k*W+w],A[i*W+w] break else: return 0 c=mul_inv2(A[i*W+i]) for j in range(i+1,n): l=mul2(c,A[j*W+i]) for k in range(i+1,n): A[j*W+k]=add2(A[j*W+k],add_inv2(l*A[i*W+k])) for i in range(n): res=mul2(res,A[i*W+i]) return res def map(self,func): # act func to all elements H,W,A=self.H,self.W,self._matrix res=A.copy() for h in range(H): for w in range(W): res[h*W+w]=func(res[h*W+w]) return Matrix(res,H,W) def count(self,x): H,W,A=self.H,self.W,self._matrix cnt=0 for h in range(self.H): for w in range(self.W): cnt+=(self._matrix[h*W+w]==x) return cnt def rank(self): """ = dimension""" H,W,A=self.H,self.W,self._matrix A=A[:] rank=0 p,q=[],[] for w in range(W): for h in range(rank,H): if A[h*W+w]!=0: break else: q.append(w) continue if w==W: return -1,[],[] p.append(w) for w in range(W): A[rank*W+w],A[h*W+w]=A[h*W+w],A[rank*W+w] inv=mul_inv2(A[rank*W+w]) for ww in range(W): A[rank*W+ww]=mul2(A[rank*W+ww],inv) for h in range(H): if h==rank: continue c=add_inv2(A[h*W+w]) for ww in range(W): A[h*W+ww]=add2(A[h*W+ww],mul2(c,A[rank*W+ww])) rank+=1 return rank class Vector(): def __init__(self,vec): self.n=len(vec) self._vector=vec def __getitem__(self,item): return self._vector[item] def __setitem__(self,item,val): self._vector[item]=val def __neg__(self): n,vec=self.n,self._vector res=[] for x in vec: res.append(add_inv2(x)) return Vector(res) def __add__(self,vec2): n,vec=self.n,self._vector res=vec.copy() for i in range(n): res[i]=add2(res[i],vec2[i]) return Vector(res) def __sub__(self,vec2): n,vec=self.n,self._vector res=vec.copy() for i in range(n): res[i]=add2(res[i],add_inv2(vec2[i])) return Vector(res) def __mul__(self,vec2): n,vec=self.n,self._vector if type(vec2)!=int: res=vec.copy() for i in range(n): res[i]=mul2(res[i],vec2[i]) return Vector(res) else: res=[mul2(vec2,vec[i]) for i in range(n)] return Vector(res) def __truediv__(self,c): n,vec=self.n,self._vector res=vec.copy() for i in range(n): res[i]=mul2(res[i],mul_inv2(c)) return Vector(res) def __floordiv__(self,c): n,vec=self.n,self._vector res=vec.copy() for i in range(n): res[i]=res[i]//c return Vector(res) def __mod__(self,c): n,vec=self.n,self._vector res=vec.copy() for i in range(n): res[i]=res[i]%c return Vector(res) def map(self,func): # act func to all elements n,vec=self.n,self._vector res=vec.copy() for i in range(n): res[i]=func(res[i]) return Vector(res) def __eq__(self,other): if type(other)==Vector: return self._vector==other._vector return False def __ne__(self,other): if type(other)==Vector: return self._vector!=other._vector return True def __len__(self): return self.n def __str__(self): res=[] for i in range(self.n): res.append(str(self._vector[i])) res.append(" ") return "".join(res) def __hash__(self): return tuple(self._vector) def count(self,x): cnt=0 for a in self._vector: cnt+=(a==x) return cnt def linear_equations(mat, vec): """ return (dim, [x,y,z], [[a0,b0,c0],[a1,b1,c1],...]) which means, solution = (x,y,z)+t0*(a0,b0,c0)+t1*(a1,b1,c1)+... Cation: float """ H, W = len(mat), len(mat[0]) # assert H == len(vec) aug=mat[:] aug.extend(vec) rank = 0 p,q = [],[] for w in range(W + 1): for h in range(rank, H): if aug[h*W+w] != 0: break else: q.append(w) continue if w == W: return -1, [], [] p.append(w) for w in range(W): aug[rank*W+w], aug[h*W+w] = aug[h*W+w], aug[rank*W+w] inv = mul_inv2(aug[rank*W+w]) for ww in range(W + 1): aug[rank*W+ww] = mul2(aug[rank*W+ww], inv) for h in range(H): if h == rank: continue c = add_inv2(aug[h*W+w]) for ww in range(W + 1): aug[h*W+ww] = add2(aug[h*W+ww], mul2(c,aug[rank*W+ww])) rank += 1 dim = W - rank sol = [0] * W for h in range(rank): sol[p[h]] = aug[h*W+W-1] vecs = [[0] * W for _ in range(dim)] for h in range(dim): vecs[h][q[h]] = 1 for h in range(dim): for w in range(rank): vecs[h][p[w]] = add_inv2(aug[w*W+q[h]]) return dim, sol, vecs ########################################################### def example(): global input example=iter( """ 3 3 1 0 0 1 0 1 0 0 1 """ .strip().split("\n")) input=lambda:next(example) ## 和&積(MOD有り) ####################################### MOD=2 def mul2(a,b): return a*b%MOD def add2(a,b): return (a+b)%MOD def mul_inv2(a): return pow(a,MOD-2,MOD) def add_inv2(a): return -a%MOD def identity(n): return Matrix([[int(i==j) for i in range(n)] for j in range(n)]) def bit_rep(bit,N): return format(bit, "0" + str(N) + "b") ########################################################### import sys input=sys.stdin.readline # example() N=int(input()) A=list(map(int, input().split())) mat=[] for a in A: vec=[] for b in bit_rep(a,62): vec.append(int(b)) mat.append(vec) mat=Matrix(mat,N,N) rank=mat.rank() print(pow(2,rank))