AQT has two multisets of integers ~A~ and ~B~, both of size ~2N+1~ for some non-negative integer ~N~. Help AQT determine the smallest non-negative integer ~c~ such that after XOR-ing each element in ~A~ by ~c~, the multisets ~A~ and ~B~ are equal.

Constraints

In all subtasks,

~0 \le A_i, B_i < 2^{63}~

~0 \le N \le 2 \cdot 10^5~

Subtask 1 [5%]

~0 \le A_i, B_i < 2^{15}~

~0 \le N \le 100~

Subtask 2 [15%]

~0 \le N \le 10^3~

Subtask 3 [80%]

No additional constraints.

Input Specification

The first line contains one integer ~N~.

The second line contains ~2N+1~ space separated integers, ~A_1, \dots, A_{2N+1}~.

The third line contains ~2N+1~ space separated integers, ~B_1, \dots, B_{2N+1}~.

Output Specification

Output the smallest possible value of ~c~ as described above on a single line. If no such value exists, output -1 on a single line.

Sample Input 1

3
84 80 88 84 93 84 86
5 1 12 7 9 5 5

Sample Output 1

81

Explanation of Sample Output 1

The smallest possible solution is ~c = 81~. If we XOR each element in ~A~ by ~81~, we have ~A = \{5, 1, 9, 5, 12, 5, 7\}~, which is equivalent to ~B~.

Sample Input 2

1
3 1 9
1 12 123

Sample Output 2

-1