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 Python (3.4.3) (judge verdict: Time Limit Exceeded)

import sys
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines
n, *lst = map(int, read().split())
al = lst[:n]
bl = lst[n:]


def convert(A):
    return [x ^ y for x, y in zip(A, A[1:])] + [A[-1] ^ A[0]]


a = convert(al)
b = convert(bl)
alal, aa = al + al, a + a


def p_arr(p):
    n = len(p)
    arr = [0] * n
    arr[0] = -1
    k, j = -1, 0
    while j < n - 1:
        if k == -1 or p[j] == p[k]:
            j += 1
            k += 1
            arr[j] = k
        else:
            k = arr[k]
    return arr


def kmp(s, p):
    slen, plen = len(s), len(p)
    i, j = 0, 0
    arr = p_arr(p)
    lst = []
    while i < slen - 1 and j < plen:
        if j == -1 or s[i] == p[j]:
            i += 1
            j += 1
        else:
            j = arr[j]
        if j == plen:
            lst.append(i - j)
            i -= j
            j = -1
    return lst


K = kmp(aa, b)
X = [al[k] ^ bl[0] for k in K]
print('\n'.join('{} {}'.format(k, x) for k, x in zip(K, X)))