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 Go (1.6) (judge verdict: Time Limit Exceeded)

package main

import "fmt"

func main() {
	n, a, b := input()
	c := xorArr(a)
	d := xorArr(b)
	for i := 0; i < n; {
		f, s := equal(i, c, d)
		if f {
			fmt.Println(i, b[0]^a[i])
		}
		i += s
	}
}

func equal(k int, c, d []int) (bool, int) {
	n := len(c)
	s := 1
	for i := range c {
		if d[0] != c[(i+k+1)%n] {
			if s == 1 {
				s = i + 1
			}
		}
		if d[i] != c[(i+k)%n] {
			return false, s
		}
	}
	return true, s
}

func xorArr(a []int) []int {
	n := len(a)
	c := make([]int, n, n)
	for i := range a {
		c[i] = a[i] ^ a[(i+1)%n]
	}
	return c
}

func input() (int, []int, []int) {
	var n int
	fmt.Scan(&n)
	a := make([]int, n, n)
	b := make([]int, n, n)
	for i := range a {
		fmt.Scan(&a[i])
	}
	for i := range b {
		fmt.Scan(&b[i])
	}
	return n, a, b
}