Problem Statement

Xing Yang has N toys, each of which with a type T_i

He also has N displays, each of which can only hold a toy type D_i

In 1 operation, he can replace the type of toy i T_i with the value K, where K is the XOR of the types of all toys.

Determine if XY can make the types of all toys such that T_i = D_i for all toys, and find how many operations he will require.

Constraints

• 2 ≤ N ≤ 10⁵
• T_i and D_i are integers.
• 0 ≤ T_i, D_i < 2³⁰

Input

Input is given from Standard Input in the following format:

N
T1 T2 ... TN
D1 D2 ... DN

Output

If the objective is achievable, print the minimum necessary number of operations. Otherwise, print -1 instead.

Sample Input 1

3
0 1 2
3 1 0

Sample Output 1

2

At first, the XOR of all the elements of a is 3. If we replace T₁ with 3, T becomes (3, 1, 2).

Now, the XOR of all the elements of a is 0. If we replace T₃ with 0, T becomes (3, 1, 0), which matches b.

Sample Input 2

3
0 1 2
0 1 2

Sample Output 2

0

Sample Input 3

2
1 1
0 0

Sample Output 3

-1

Sample Input 4

4
0 1 2 3
1 0 3 2

Sample Output 4

5