XOR Replace

There is a sequence of length N: a = (a_1, a_2, ..., a_N). Here, each a_i is a non-negative integer.

Snuke can repeatedly perform the following operation:

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

Snuke's objective is to match a with another sequence b = (b_1, b_2, ..., b_N). Here, each b_i is a non-negative integer.

Determine whether the objective is achievable, and find the minimum necessary number of operations if the answer is positive.

Constraints

• 2 ≤ N ≤ 10^5
• a_i and b_i are integers.
• 0 ≤ a_i, b_i < 2^{30}

Input

Input is given from Standard Input in the following format:

N a_1 a_2 ... a_N b_1 b_2 ... b_N

Output

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

Examples

Input

3 0 1 2 3 1 0

Output

2

Input

3 0 1 2 0 1 2

Output

0

Input

2 1 1 0 0

Output

-1

Input

4 0 1 2 3 1 0 3 2

Output

5

inputFormat

Input

Input is given from Standard Input in the following format:

N a_1 a_2 ... a_N b_1 b_2 ... b_N

outputFormat

Output

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

Examples

Input

3 0 1 2 3 1 0

Output

2

Input

3 0 1 2 0 1 2

Output

0

Input

2 1 1 0 0

Output

-1

Input

4 0 1 2 3 1 0 3 2

Output

5

样例

3
0 1 2
3 1 0

2