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 C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Diagnostics;

namespace AtCoder
{
    class Program
    {
        private static string Read() { return Console.ReadLine(); }
        private static int ReadInt() { return int.Parse(Read()); }
        private static long ReadLong() { return long.Parse(Read()); }
        private static double ReadDouble() { return double.Parse(Read()); }
        private static int[] ReadInts() { return Array.ConvertAll(Read().Split(), int.Parse); }
        private static long[] ReadLongs() { return Array.ConvertAll(Read().Split(), long.Parse); }
        private static double[] ReadDoubles() { return Array.ConvertAll(Read().Split(), double.Parse); }

        static bool Cyclic(int n, int[] A)
        {
            int N = A.Length;
            for (int i = 1; i < N / n; ++i)
            {
                for (int j = 0; j < n; ++j)
                {
                    if (A[j] != A[i * n + j]) { return false; }
                }
            }
            return true;
        }

        static int Cycle(int[] A)
        {
            int N = A.Length;
            for (int i = 1; i <= N; ++i)
            {
                if (N % i == 0 && Cyclic(i, A)) { return i; }
            }
            return N;
        }

        static bool Perfect(int[] A, int[] B, int n)
        {
            int N = A.Length;
            int xor = A[n] ^ B[0];
            for (int i = 1; i < N; ++i)
            {
                if ((A[(n + i) % N] ^ B[i]) != xor) { return false; }
            }
            return true;
        }

        static int[][] Solve(int N, int[] A, int[] B)
        {
            int[] C = Enumerable.Range(0, N).Select(i => A[i] ^ B[i]).ToArray();
            int cycle = Cycle(C);
            var ans = new List<int[]>();
            for (int i = 0; i < cycle; ++i)
            {
                if (Perfect(A, B, i))
                {
                    for (int j = i; j < N; j += cycle)
                    {
                        int xor = A[j] ^ B[0];
                        ans.Add(new int[] { j, xor });
                    }
                    break;
                }
            }
            return ans.ToArray();
        }

        static void Main(string[] args)
        {
            int N = ReadInt();
            int[] A = ReadInts();
            int[] B = ReadInts();
            var ans = Solve(N, A, B);
            foreach (var a in ans)
            {
                Console.WriteLine(string.Join(" ", a));
            }
        }
    }
}