class Two_SAT: def __init__(self,N=0): """ N 変数の 2-SAT を定義する. N: int """ self.N=N self.var_num=N self.__cost=2*N self.arc=[[] for _ in range(2*N)] self.rev=[[] for _ in range(2*N)] def cost(self): return self.__cost def var_to_index(self,v): if v>=0: return 2*v else: return 2*(-v-1)+1 def index_to_var(self,i): if i%2: return -(i+1)//2 else: return i//2 def add_variable(self,k=1): """ 新たに変数 k 個を加える. """ m=self.var_num self.var_num+=k self.__cost+=2*k self.arc+=[[] for _ in range(2*k)] self.rev+=[[] for _ in range(2*k)] return list(range(m,m+k)) def __add_clause(self,i,j): self.__cost+=1 self.arc[self.var_to_index(i)].append(self.var_to_index(j)) self.rev[self.var_to_index(j)].append(self.var_to_index(i)) def add_imply(self,i,j): """ X_i -> X_j を加える. """ self.__add_clause(i,j) self.__add_clause(~j,~i) def add_or(self,i,j): """ X_i or X_j を加える. """ self.add_imply(~i,j) def add_nand(self,i,j): """ not (X_i and X_j) を加える. """ self.add_imply(i,~j) def add_equivalent(self,*I): """ I=[i_0, ..., i_{k-1}] に対して, X_{i_0}=...=X_{i_{k-1}} を追加する. """ k=len(I) if k<=1: return for j in range(k-1): self.add_imply(I[j],I[j+1]) self.add_imply(I[-1],I[0]) def add_not_equal(self,i,j): """ X_i != X_j を追加する. """ self.add_equal(i,~j) def set_true(self,i): """ 変数 X_i を True にする. """ self.__add_clause(~i,i) def set_false(self,i): """ 変数 X_i を False にする. """ self.__add_clause(i,~i) def at_most_one(self,*I): """ X_i (i in I) を満たすような i は高々1つだけという条件を追加する. """ k=len(I) if k<=1: return A=self.add_variable(k) self.add_imply(I[0],A[0]) for i in range(1,k): self.add_imply(A[i-1],A[i]) self.add_imply(I[i],A[i]) self.add_nand(A[i-1],I[i]) def is_satisfy(self,Mode=0): """ Two-SAT は充足可能? Mode: 0 (Defalt): 充足可能? 1: 充足可能ならば,その変数の割当を与える (不可能なときはNone). 2: 充足不能の原因である変数を全て挙げる. """ N=self.var_num Group=[0]*(2*N) Order=[] for s in range(2*N): if Group[s]:continue S=[s] Group[s]=-1 while S: u=S.pop() for v in self.arc[u]: if Group[v]:continue Group[v]=-1 S.append(u);S.append(v) break else: Order.append(u) K=0 for s in Order[::-1]: if Group[s]!=-1:continue S=[s] Group[s]=K while S: u=S.pop() for v in self.rev[u]: if Group[v]!=-1:continue Group[v]=K S.append(v) K+=1 if Mode==0: for i in range(N): if Group[2*i]==Group[2*i+1]: return False return True elif Mode==1: T=[0]*N for i in range(N): if Group[2*i]>Group[2*i+1]: T[i]=1 elif Group[2*i]==Group[2*i+1]: return None return T elif Mode==2: return [i for i in range(self.var_num) if Group[2*i]==Group[2*i+1]] def solve(self): return self.is_satisfy(1) def Sieve_of_Eratosthenes(N): """ N までのエラトステネスの篩を実行 [Input] N:自然数 [Output] 素数かどうかのリスト ([0,0,1,1,0,1,...]) """ if N==0: return [0] T=[1]*(N+1) T[0]=T[1]=0 for x in range(4,N+1,2): T[x]=0 for x in range(9,N+1,3): T[x]=0 a=5 Flag=0 while a*a<=N: if T[a]: b=a*a c=2*a while b<=N: T[b]=0 b+=c a+=2+2*Flag Flag^=1 return T #================================================== def f(a,b): return P[int(str(a)+str(b))] #================================================== N=int(input()) A=[0]*N; B=[0]*N for i in range(N): A[i],B[i]=map(int,input().split()) P=Sieve_of_Eratosthenes(10**6) T=Two_SAT(N) for i in range(N): for j in range(N): if f(A[i],B[i]) or f(A[i],B[j]) or f(A[j],B[i]) or f(A[j],B[j]): T.add_nand(i,j) if f(A[i],B[i]) or f(A[i],A[j]) or f(B[j],B[i]) or f(B[j],A[j]): T.add_nand(i,~j) if f(B[i],A[i]) or f(B[i],B[j]) or f(A[j],A[i]) or f(A[j],B[j]): T.add_nand(~i,j) if f(B[i],A[i]) or f(B[i],A[j]) or f(B[j],A[i]) or f(B[j],A[j]): T.add_nand(~i,~j) print("Yes" if T.is_satisfy() else "No")