Given are two sequences a=\\{a_0,\ldots,a_{N-1}\\} and b=\\{b_0,\ldots,b_{N-1}\\} of N non-negative integers each.

Snuke will choose an integer k such that 0 \leq k < N and an integer x not less than 0, to make a new sequence of length N, a'=\\{a_0',\ldots,a_{N-1}'\\}, as follows:

* a_i'= a_{i+k \mod N}\ XOR \ x



Find all pairs (k,x) such that a' will be equal to b.

What is \mbox{ XOR }?

The XOR of integers A and B, A \mbox{ XOR } B, is defined as follows:

* When A \mbox{ XOR } B is written in base two, the digit in the 2^k's place (k \geq 0) is 1 if either A or B, but not both, has 1 in the 2^k's place, and 0 otherwise.

For example, 3 \mbox{ XOR } 5 = 6. (In base two: 011 \mbox{ XOR } 101 = 110.)

Constraints

* 1 \leq N \leq 2 \times 10^5
* 0 \leq a_i,b_i < 2^{30}
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


N
a_0 a_1 ... a_{N-1}
b_0 b_1 ... b_{N-1}


Output

Print all pairs (k, x) such that a' and b will be equal, using one line for each pair, in ascending order of k (ascending order of x for pairs with the same k).

If there are no such pairs, the output should be empty.

Examples

Input

3
0 2 1
1 2 3


Output

1 3


Input

5
0 0 0 0 0
2 2 2 2 2


Output

0 2
1 2
2 2
3 2
4 2


Input

6
0 1 3 7 6 4
1 5 4 6 2 3


Output

2 2
5 5


Input

2
1 2
0 0


Output
#include<bits/stdc++.h>
#define un unsigned
#define lo long
#define in int
#define sh short
#define fo for
using namespace std;
in n;
un lo lo a[200100],b[200100],ha,hb,tt[200100];
un lo lo ra[200100],rb[200100];
un lo lo Base=1900210023LL,Modu=3200320091LL;
template<typename T,typename V,int &N>
struct Hasher{
	void Hashing(V arr[],T &res,T bas,T mod){
		for(int i=0;i<N;i++)
			res=((res*bas)%mod+(T)(arr[i]))%mod;
		return;
	} 
	void DeleteHash(V val,T &res,T HighestValue,T mod){
		res=(res+mod-((T)(val)*HighestValue)%mod)%mod;
	}
	void AddHash(V val,T &res,T bas,T mod){
		res=((res*bas)%mod+(T)(val))%mod;
	}
};
in main(){
	#ifdef FILIN
		#ifndef LOCAL
			freopen(FILIN,"r",stdin);
			freopen(FILOUT,"w",stdout);
		#endif
	#endif
	ios::sync_with_stdio(0);
	cin.tie(NULL);
	cout.tie(NULL);
	cin>>n;
	fo(in i=0;i<n;i++) cin>>a[i];
	fo(in i=0;i<n;i++) ra[i]=a[i];
	fo(in i=0;i<n;i++) tt[i]=(a[i]^a[(i+1)%n]);
	fo(in i=0;i<n;i++) a[i]=tt[i];
	fo(in i=0;i<n;i++) cin>>b[i];
	fo(in i=0;i<n;i++) rb[i]=b[i];
	fo(in i=0;i<n;i++) tt[i]=(b[i]^b[(i+1)%n]);
	fo(in i=0;i<n;i++) b[i]=tt[i];
	Hasher<un lo lo,un lo lo,n> haxi;
	haxi.Hashing(a,ha,Base,Modu);
	haxi.Hashing(b,hb,Base,Modu);
	long long hv=1LL;
	fo(in i=1;i<n;i++) hv=(hv*Base)%Modu;
	fo(in i=0;i<n;i++){
		if(ha==hb)
			cout<<i<<' '<<(ra[i]^rb[0])<<endl;
		haxi.DeleteHash(a[i],ha,hv,Modu);
		haxi.AddHash(a[i],ha,Base,Modu);
	} 
	return 0;
}
