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)

# -*- coding: utf-8 -*-
# import time
import sys
from collections import Counter, defaultdict
buff_readline = sys.stdin.readline
readline = sys.stdin.readline


def read_int_n():
    return list(map(int, buff_readline().split()))

gpw = None

class RH():
    def __init__(self, s, base, mod):
        self.base = base
        self.mod = mod
        self.rev = pow(base, mod-2, mod)

        l = len(s)
        self.h = h = [0]*(l+1)
        tmp = 0
        for i in range(l):
            tmp = (tmp*base + s[i]) % mod
            h[i+1] = tmp

        global gpw
        if gpw is None:
            self.pw = pw = [1]*(len(s)+1)
            v = 1
            for i in range(l):
                pw[i+1] = v = v * base % mod
            gpw = pw
        else:
            self.pw = gpw

    def calc(self, l, r):
        return (self.h[r] - self.h[l] * self.pw[r-l]) % self.mod


def slv(N, A, B):
    L = max(max(A), max(B)).bit_length()
    ba = []
    bb = []
    ah = []
    bh = []
    bnh = []
    for i in range(L):
        ta = []
        tb = []
        tbn = []
        for a, b in zip(A, B):
            ta.append(a >> i & 1)
            tb.append(b >> i & 1)
            tbn.append(tb[-1] ^ 1)
        ba.append(ta)
        bb.append(tb)
        ah.append(RH(ta, 641, 10**9+7))
        bh.append(RH(tb, 641, 10**9+7))
        bnh.append(RH(tbn, 641, 10**9+7))

    ans = []
    for k in range(N):
        x = 0
        for i in range(L):
            l = ah[i].calc(k, N)
            r = ah[i].calc(0, k)
            if l == bh[i].calc(0, N-k) and r == bh[i].calc(N-k, N):
                pass
            elif l == bnh[i].calc(0, N-k) and r == bnh[i].calc(N-k, N):
                x += 1 << i
            else:
                break
        else:
            ans.append('%d %d' % (k, x))

    return ans


def main():
    N = int(input())
    A = read_int_n()
    B = read_int_n()
    print(*slv(N, A, B), sep='\n')

    # import random
    # N = 2 * 10**5
    # # A = [random.randint(0, 1 << 30) for _ in range(N)]
    # # B = [random.randint(0, 1 << 30) for _ in range(N)]
    # A = [2 ** 30 for _ in range(N)]
    # B = [2 ** 30 for _ in range(N)]
    # print(N)
    # print(*A)
    # print(*B)
    # # print(*slv(N, A, B), sep='\n')


if __name__ == '__main__':
    main()