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.

Examples

Input

3
0 2 1
1 2 3


Output

1 3


Input

5
0 0 0 0 0
2 2 2 2 2


Output

0 2
1 2
2 2
3 2
4 2


Input

6
0 1 3 7 6 4
1 5 4 6 2 3


Output

2 2
5 5


Input

2
1 2
0 0


Output
from collections import defaultdict
N = int(input())
a = list(map(int, input().split()))
b = list(map(int, input().split()))
A = []
B = []
ans = []
for i in range(N):
    A.append(a[i]^a[(i+1)%N])
    B.append(b[i]^b[(i+1)%N])
if A == B == [A[0]]*N:
    for i in range(N): 
        ans.append((i,a[i]^b[0]))
else:
    A += A    
    d = defaultdict(list)
    for i in range(N):
        d[B[i]].append(i)
    i = 0
    ans = []
    while i < N:
        ok = True
        for j in range(N):
            if B[N-j-1] != A[N-j-1+i]:
                if d[A[N-j-1]] == []:
                    i += N
                    ok = False
                    break
                else:
                    i += N - d[A[N-j-1+i]][-1] - 1
                    ok = False
                    break
        if ok:
            ans.append((i,a[i]^b[0]))
            if len(d[A[N-1+i]]) == 1:
                i += N
            else:
                i += N - d[A[N-1+i]][-2] - 1
for x in ans:
    print(*x)