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: Time Limit Exceeded)

n = int(input())
a = list(map(int, input().split()))
b = list(map(int, input().split()))
c = [0] * n
d = [0] * (2 * n - 1)
for i in range(n - 1):
    c[i] = b[i] ^ b[i + 1]
    d[i] = a[i] ^ a[i + 1]
c[n - 1] = b[0] ^ b[-1]
d[n - 1] = a[0] ^ a[-1]
for i in range(n - 1):
    d[n + i] = d[i]
t = [0] * (n + 1)
t[0] = -1
j = -1
for i in range(n):
    while j >= 0 and c[i] != c[j]:
        j = t[j]
    j += 1
    t[i + 1] = j
m = 0
ans = []
while m < n:
    for i in range(n):
        if c[i] != d[m + i]:
            m += i - t[i]
            if i > 0:
                i = t[i]
            break
    else:
        ans.append(m)
        m = m + n - t[n]
        i = t[n]
for k in ans:
    print(k, a[k] ^ b[0])