Solve the programming task below in a Python markdown code block.
Chef found N magical cards in his drawer. Each card has a number written on each of its faces. He places all the cards on the table in a front face-up manner.

Chef denotes the numbers on the front face by A_{1}, A_{2},..., A_{N} and on the back face by B_{1}, B_{2},..., B_{N}. Chef can choose some (possibly zero or all) cards and flip them, then he will calculate the [bitwise AND] of all the numbers currently in a face-up manner.

Now Chef wonders what is the *maximum* bitwise AND that he can achieve and what is the *minimum* number of cards he has to flip to achieve this value. Can you help him find it?

------ Input Format ------ 

- The first line of the input contains a single integer T denoting the number of test cases. The description of T test cases follows.
- Each test case contains three lines of input.
- The first line contains a single integer N - the number of cards.
- The second line contains N space-separated integers A_{1}, A_{2},..., A_{N} - the numbers on the front face of the cards
- The third line contains N space-separated integers B_{1}, B_{2},..., B_{N} - the numbers on the back face of the cards

------ Output Format ------ 

For each test case, print a single line containing two space-separated integers, first denoting the maximum bitwise AND possible and second denoting the minimum number of flips required to achieve it.

------ Constraints ------ 

$1 ≤ T ≤ 10^{4}$
$1 ≤ N ≤ 10^{5}$
$0 ≤ A_{i} ≤ 2^{30} - 1$
$0 ≤ B_{i} ≤ 2^{30} - 1$
- Sum of $N$ over all testcases does not exceeds $10^{5}$.

----- Sample Input 1 ------ 
3
3
4 6 8
2 1 2
3
0 2 0
2 0 8
3
1 2 1
2 3 6
----- Sample Output 1 ------ 
2 2
0 0
2 2
----- explanation 1 ------ 
Test case $1$: The maximum AND is obtained after flipping the first and third cards achieving a configuration of $[2, 6, 2]$ which yields a bitwise AND of $2$.

Test case $2$: Every possible configuration of the cards yields a bitwise AND equal to $0$. So to ensure the minimum number of operations, Chef performs no flip.