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
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.List;

public class Main {
	public static void main(String[] args) throws Exception {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		String[] sa = br.readLine().split(" ");
		int n = Integer.parseInt(sa[0]);
		sa = br.readLine().split(" ");
		int[] a = new int[n + 1];
		for (int i = 0; i < n; i++) {
			a[i] = Integer.parseInt(sa[i]);
		}
		a[n] = a[0];
		sa = br.readLine().split(" ");
		int[] b = new int[n + 1];
		for (int i = 0; i < n; i++) {
			b[i] = Integer.parseInt(sa[i]);
		}
		b[n] = b[0];
		br.close();

		int[] ax = new int[n];
		int[] bx = new int[n * 2 - 1];
		for (int i = 0; i < n; i++) {
			ax[i] = a[i] ^ a[i + 1];
			bx[i] = b[i] ^ b[i + 1];
		}
		System.arraycopy(bx, 0, bx, n, n - 1);

		MP mp = new MP(ax);
		List<Integer> list = mp.findAllFrom(bx);
		PrintWriter pw = new PrintWriter(System.out);
		if (!list.isEmpty() && list.get(0) == 0) {
			list.remove(0);
			list.add(n);
		}
		for (int i = list.size() - 1; i >= 0; i--) {
			int j = n - list.get(i);
			pw.println(j + " " + (a[j] ^ b[0]));
		}
		pw.flush();
	}

	static class MP {
		int n;
		int[] arr;
		int[] a;

		public MP(int[] arr1) {
			arr = arr1;
			n = arr.length;
			a = new int[n + 1];
			a[0] = -1;
			int j = -1;
			for (int i = 0; i < n; i++) {
				while (j >= 0 && arr[i] != arr[j]) {
					j = a[j];
				}
				j++;
				a[i + 1] = j;
			}
		}

		List<Integer> findAllFrom(int[] arr2) {
			List<Integer> ret = new ArrayList<>();
			int j = 0;
			for (int i = 0; i < arr2.length; i++) {
				while (j >= 0 && arr2[i] != arr[j]) {
					j = a[j];
				}
				j++;
				if (j == n) {
					ret.add(i - j + 1);
					j = a[j];
				}
			}
			return ret;
		}
	}
}
