Delicious Pineapple Pizza

Byeongchan runs "Pineapple Pizza is A Pizza", or PPAP for short, a company that makes very delicious pineapple pizza. But a rival company, doubting PPAP's pineapple pizza, has filed a complaint against PPAP! To defend the company, Byeongchan must make pineapple pizzas of the highest possible quality.

How delicious a pineapple pizza is depends on how good the pineapple and the dough are. If the pineapple has quality $C$ and the dough has quality $D$, the pizza has taste $C \text{ XOR } D$. Byeongchan has $N$ pineapples and doughs in total, and must use them to make $N$ pineapple pizzas. To prove that he always makes the finest pineapple pizza, Byeongchan wants to maximize the minimum taste among the $N$ special pineapple pizzas.

The first line gives $N$ (1 ≤ $N$ ≤ 100).

The second line gives integers $C_1, C_2, \dots, C_N$ (1 ≤ $C_i$ ≤ $10^9$). The third line gives integers $D_1, D_2, \dots, D_N$ (1 ≤ $D_i$ ≤ $10^9$).

Find the maximum possible value of the minimum taste among the $N$ pineapple pizzas.

If the pineapple-dough pairs are (1,2), (2,5), (3,4), (4,3), (5,1), then 1 XOR 2 = 3, 2 XOR 5 = 7, 3 XOR 4 = 7, 4 XOR 3 = 7, 5 XOR 1 = 4, so the minimum is 3. Other pairings also give a minimum of 3, but no pairing gives a minimum of 4 or more.