Problem:
Score : 600 points

Problem Statement

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.

Sample Input 1

3
0 2 1
1 2 3

Sample Output 1

1 3

If (k,x)=(1,3),

a_0'=(a_1\ XOR \ 3)=1

a_1'=(a_2\ XOR \ 3)=2

a_2'=(a_0\ XOR \ 3)=3

and we have a' = b.

Sample Input 2

5
0 0 0 0 0
2 2 2 2 2

Sample Output 2

0 2
1 2
2 2
3 2
4 2

Sample Input 3

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

Sample Output 3

2 2
5 5

Sample Input 4

2
1 2
0 0

Sample Output 4

No pairs may satisfy the condition.

Solution in Perl (5.26.1) (judge verdict: Accepted)

use strict;
use warnings;
package ZAlgorithm;
sub z_algorithm(@){
	my$n=@_;
	return()if$n==0;
	my@z=(0);
	my$j=0;
	for my$i(1..$n-1){
		$z[$i]=$j+$z[$j]<=$i?0:$j+$z[$j]-$i<$z[$i-$j]?$j+$z[$j]-$i:$z[$i-$j];
		$z[$i]++while$i+$z[$i]<$n&&$_[$z[$i]]eq$_[$i+$z[$i]];
		$j=$i if$j+$z[$j]<$i+$z[$i];
	}
	$z[0]=$n;
	return@z;
}
package main;
my$N=<>;
my@A=map int,split$",<>;
my@B=map int,split$",<>;
my@T;
for(0..$N-1){
	$T[$_]=$B[$_]^$B[($_+1)%$N];
	$T[$_+$N]=$T[$_+2*$N]=$A[$_]^$A[($_+1)%$N];
}
my@z=ZAlgorithm::z_algorithm(@T);
for(0..$N-1){
	print$_,$",$A[$_]^$B[0],$/if$z[$_+$N]>=$N;
}