You are given array $A$, $B$ each containing $N$ inetegers. You have to create array $C$ of $N$ inetegers where $C_i = A_i \mathbin{\&} B_i$ (Here, $\mathbin{\&}$ denotes the Bitwise AND operation). You can shuffle elements of  $A$, $B$  however you want. Find maximum value of $C_1 \mathbin{\&} C_2 \mathbin{\&} \dots \mathbin{\&} C _N$.

 Input format

• The first line contains $T$ denoting the number of test cases. The description of $T$ test cases is as follows:
• For each test case:
  • The first line contains an integer $N$ denotes size of array $A$, $B$.
  • The next line contains $N$ space-separated integers $A_1, A_2, \dots, A_N$ - denoting the elements of $A$.

  • The next line contains $N$ space-separated integers $B_1, B_2, \dots, B_N$ - denoting the elements of $B$.

Output format

For each test case, print maximum value of $C_1 \mathbin{\&} C_2 \mathbin{\&} \dots \mathbin{\&} C _N$ in a separate line.

Constraints

$1 \leq T \leq 10^5 \\ 1 \leq N \leq 10^5\\ \\0\leq A_i, B_i \leq 10^9$

The sum of  $N$ over all test cases does not exceed $10^5$.