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 <cstdio>
#include <iostream>
#include <algorithm>
#include <cstring>
using namespace std;
typedef long long LL;
const LL P = ((1LL << 30) + 1);
const LL N = 1234567891;
const LL N2 = 1000000009;

LL a[2000005],b[2000005],c[2000005],d[2000005];
LL pc[2000005],pd[2000005],pwr[2000005],pc2[2000005],pd2[2000005],pwr2[2000005];
LL n,m;

LL judge(LL l,LL r){
	return (pc[n - 1] == (pd[r] - (pd[l - 1] * pwr[r - l + 1] % N) + N) % N) && (pc2[n - 1] == (pd2[r] - (pd2[l - 1] * pwr2[r - l + 1] % N2) + N2) % N2);
}

int main(){
	ios::sync_with_stdio(false);
	pwr[0] = 1; for(LL i = 1;i <= 200000;i ++) pwr[i] = (pwr[i - 1] * P) % N;
	pwr2[0] = 1; for(LL i = 1;i <= 200000;i ++) pwr2[i] = (pwr2[i - 1] * P) % N2;
	cin >> n;
	for(LL i = 1;i <= n;i ++) cin >> a[i];
	for(LL i = 1;i <= n;i ++) cin >> b[i];
	for(LL i = n + 1;i <= (n << 1);i ++) b[i] = b[i - n];
	
	for(LL i = 1;i < n;i ++) c[i] = a[i] ^ a[i + 1];
	for(LL i = 1;i < (n << 1);i ++) d[i] = b[i] ^ b[i + 1];
	
	for(LL i = 1;i < n;i ++) pc[i] = (pc[i - 1] * P + c[i]) % N;
	for(LL i = 1;i < (n << 1);i ++) pd[i] = (pd[i - 1] * P + d[i]) % N;
	for(LL i = 1;i < n;i ++) pc2[i] = (pc2[i - 1] * P + c[i]) % N2;
	for(LL i = 1;i < (n << 1);i ++) pd2[i] = (pd2[i - 1] * P + d[i]) % N2;
	
	for(LL i = n + 1;i >= 2;i --){
		if(judge(i,i + n - 2))
			cout << (n + 1 - i) << ' ' << (a[n + 2 - i] ^ b[1]) << endl;
	}
	return 0;
} 