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>
using namespace std;

vector<int> Z_algorithm(vector<int> &S){
	vector<int> A(S.size());
	A[0] = S.size();
	int i = 1, j = 0;
	while (i < S.size()) {
		while (i+j < S.size() && S[j] == S[i+j]) ++j;
		A[i] = j;
		if (j == 0) { ++i; continue;}
		int k = 1;
		while (i+k < S.size() && k+A[k] < j) A[i+k] = A[k], ++k;
		i += k; j -= k;
	}
	return A;
}

int main(){
	int N, i;
	scanf("%d", &N);
	vector<int> a(N), b(N);
	for(i = 0; i < N; i++){
		scanf("%d", &a[i]);
	}
	for(i = 0; i < N; i++){
		scanf("%d", &b[i]);
	}
	vector<int> c(N), d(N);
	for(i = 0; i < N; i++){
		c[i] = (a[i] ^ a[(i + 1) % N]);
		d[i] = (b[i] ^ b[(i + 1) % N]);
	}
/*	printf("c:");
	for(i = 0; i < N; i++){
		printf("%d ", c[i]);
	}
	printf("\n");
	printf("d:");
	for(i = 0; i < N; i++){
		printf("%d ", d[i]);
	}
	printf("\n");
*/	vector<int> cdd(3 * N);
	for(i = 0; i < N; i++){
		cdd[0 * N + i] = c[i];
		cdd[1 * N + i] = d[i];
		cdd[2 * N + i] = d[i];
	}
	vector<int> A = Z_algorithm(cdd);
/*	printf("cdd:");
	for(i = 0; i < 3 * N; i++){
		printf("%d ", cdd[i]);
	}
	printf("\n");
	printf("A  :");
	for(i = 0; i < 3 * N; i++){
		printf("%d ", A[i]);
	}
	printf("\n");
*/	for(i = 0; i < N; i++){
		if(A[2 * N - i] >= N){
			printf("%d %d\n", i, a[i] ^ b[0]);
		}
	}
	return 0;
}