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: Wrong Answer)

def check(ccc, ddd, e, ans):
    m = 2147483647
    g = 1000000007
    for l in range(e):
        cl = ccc[l]
        if any(c != cl for c in ccc[l::e]):
            return
        dl = ddd[l]
        if any(d != dl for d in ddd[l::e]):
            return
    s = 0
    for c in ccc[:e]:
        s = (s * g + c) % m
    t = 0
    for d in ddd[:e]:
        t = (t * g + d) % m
    u = pow(g, e, m)
    for h in range(e):
        if s == t:
            bh = bbb[h]
            ans.update(((i - h) % n, aaa[i] ^ bh) for i in range(0, n, e))
            return
        t = (t * g + ddd[(e + h) % n] - ddd[h] * u) % m


def solve(n, aaa, bbb):
    ccc = [a1 ^ a2 for a1, a2 in zip(aaa, aaa[1:])] + [aaa[-1] ^ aaa[0]]
    ddd = [b1 ^ b2 for b1, b2 in zip(bbb, bbb[1:])] + [bbb[-1] ^ bbb[0]]

    ans = set()

    e = 1
    while e * e <= n:
        if n % e != 0:
            e += 1
            continue
        check(ccc, ddd, e, ans)
        check(ccc, ddd, n // e, ans)
        e += 1

    return ans


n = int(input())
aaa = list(map(int, input().split()))
bbb = list(map(int, input().split()))
ans = solve(n, aaa, bbb)
print(''.join('{} {}\n'.format(*answer) for answer in ans))