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
N = int(input())
A = list(map(int,input().split()))
B = list(map(int,input().split()))

X = []
for a,b in zip(A,A[1:]):
    X.append(a ^ b)
X.append(A[-1] ^ A[0])

Y = []
for a,b in zip(B,B[1:]):
    Y.append(a ^ b)
Y.append(B[-1] ^ B[0])

def z_algorithm(s):
    N = len(s)
    ret = [0]*N
    ret[0] = N
    i,j = 1,0
    while i < N:
        while i+j < N and s[j] == s[i+j]:
            j += 1
        ret[i] = j
        if j == 0:
            i += 1
            continue
        k = 1
        while i+k < N and k + ret[k]<j:
            ret[i+k] = ret[k]
            k += 1
        i += k
        j -= k
    return ret

za = z_algorithm(X + [-1] + Y + Y)
for i in range(N):
    if za[-N-i] == N:
        print(i, A[i]^B[0])