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: Wrong Answer)

package main

import "fmt"

const D int = 30

func to_binary_matrix(a []int, N int) [][D]bool {
	A := make([][D]bool, N)
	for i := 0; i < N; i++ {
		A[i] = [D]bool{}
		for d := 0; d < D; d++ {
			A[i][d] = a[i]%2 == 1
			a[i] /= 2
			if a[i] == 0 {
				break
			}
		}
	}
	return A
}

func print_binary_matrix(A [][D]bool, N int) {
	for i := 0; i < N; i++ {
		for d := D - 1; d >= 0; d-- {
			x := 0
			if A[i][d] {
				x = 1
			}
			fmt.Printf("%d ", x)
		}
		fmt.Println()
	}
}

func to_int(x [D]bool) int {
	y := 0
	if x[D-1] {
		y = 1
	}
	for d := D - 2; d >= 0; d-- {
		if x[d] {
			y = y*2 + 1
		} else {
			y = y * 2
		}

	}
	return y
}

func calc_x(a, b [D]bool) [D]bool {
	x := [D]bool{}
	for d := 0; d < D; d++ {
		x[d] = a[d] != b[d]
	}
	return x
}

func check_x(a, b, x [D]bool) bool {
	for d := 0; d < D; d++ {
		if (a[d] != b[d]) != x[d] {
			return false
		}
	}
	return true
}

func check_x_digit(a, b, x [D]bool, dd int) bool {
	return (a[dd] != b[dd]) == x[dd]
}

func main() {
	var N int
	fmt.Scan(&N)
	a := make([]int, N)
	for i := 0; i < N; i++ {
		fmt.Scan(&a[i])
	}
	b := make([]int, N)
	for i := 0; i < N; i++ {
		fmt.Scan(&b[i])
	}

	A := to_binary_matrix(a, N)
	B := to_binary_matrix(b, N)

	for k := 0; k < N; k++ {
		// calc x
		x := calc_x(A[k], B[0])

		// check
		ok := true
		if N > D {
			// probabilistic
			for j := 1; j < D; j++ {
				if !check_x_digit(A[(k+j)%N], B[j], x, (7*j)%D) {
					ok = false
					break
				}
				if !check_x_digit(A[(k+j)%N], B[j], x, (13*j)%D) {
					ok = false
					break
				}
			}
		} else {
			// deterministic
			for j := 1; j < N; j++ {
				if !check_x(A[(k+j)%N], B[j], x) {
					ok = false
					break
				}
			}
		}

		if ok {
			fmt.Printf("%d %d\n", k, to_int(x))
		}
	}
}