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 PyPy3 (2.4.0) (judge verdict: Accepted)

import sys
sys.setrecursionlimit(2147483647)
INF = 1 << 60
MOD = 10**9 + 7 # 998244353
input = lambda:sys.stdin.readline().rstrip()

def Z(S):
    n = len(S)
    res = [0] * n
    res[0] = n
    l = r = 0
    for i in range(1, n):
        if res[i - l] < r - i: # 過去の結果が全て使える
            res[i] = res[i - l]
        else:
            l = i
            r = max(i, r) # i < r ならば過去の結果が一部使える
            while r < n and S[r - l] == S[r]: r += 1
            res[i] = r - l
    return res

def resolve():
    n = int(input())
    A = list(map(int, input().split()))
    B = list(map(int, input().split()))

    C = [A[i] ^ A[(i + 1) % n] for i in range(n)]
    D = [B[i] ^ B[(i + 1) % n] for i in range(n)]
    prefix = Z(C + D + D)
    res = []
    for k in range(n):
        if prefix[n + k] >= n:
            res.append(((n - k) % n, A[0] ^ B[k]))
    res.sort()
    for pair in res:
        print(*pair)
resolve()