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 Julia (0.5.0) (judge verdict: Accepted)

function Zalgo(s)
	N=length(s)
	ret=zeros(Int,N)
	ret[1]=N
	i=1
	j=0
	while i<N
		while i+j<N&&s[j+1]==s[i+j+1]
			j+=1
		end
		ret[i+1]=j
		if j==0
			i+=1
			continue
		end
		k=1
		while i+k<N&&k+ret[k+1]<j
			ret[i+k+1]=ret[k+1]
			k+=1
		end
		i+=k
		j-=k
	end
	ret
end
function main()
	N=parse(Int,readline())
	A=map(x->parse(Int,x),split(readline()))
	B=map(x->parse(Int,x),split(readline()))
	a=zeros(Int,3N)
	for i=1:N
		a[i]=B[i]$B[mod1(i+1,N)]
		a[i+N]=a[i+2N]=A[i]$A[mod1(i+1,N)]
	end
	L=Zalgo(a)
	for k=1:N
		if L[k+N]>=N
			println("$(k-1) $(A[k]$B[1])")
		end
	end
end
main()