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