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 $\text{ XOR }$? The XOR of integers $A$ and $B$, $A \text{ XOR } B$, is defined as follows: When $A \text{ XOR } B$ 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, $3 \text{ XOR } 5 = 6$. (In base two: $011 \text{ XOR } 101 = 110$.)

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.