You are given an array ~a~ of length ~N~. You repeatedly perform the following operation:

• Let the XOR of all elements in ~a~ be ~x~. Select an integer ~i~ ~(1 \le i \le N)~ and replace ~a_i~ with ~x~.

Your goal is to match ~a~ with another array ~b~. Determine if it is possible to achieve the goal, and the minimum number of operations required.

Input Specification

The first line will contain the ~N~ ~(1 \le N \le 10^5)~.

The second line will contain ~N~ integers, ~a_i~ ~(0 \le a_i < 2^{30})~, the original array.

The third line will contain ~N~ integers, ~b_i~ ~(0 \le b_i < 2^{30})~, the array you wish to achieve.

Output Specification

Output the minimum number of operations required. If it is impossible, output -1.

Sample Input 1

3
0 1 2
3 1 0

Sample Output 1

2

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