It’s Time for a Montage

The heroes of your favorite action TV show are preparing for the final showdown with the villains. At the core, there are two main rivals: a crucial hero who aims to save the universe, and an equally important villain who seeks to destroy it. However, through countless recursive spin-offs, they may have slightly less important sidekicks (a hero and a villain who are rivals themselves), who in turn may have their own (even less important) sidekicks, and so on. Note that there is an equal number of heroes and villains, and each rival pair has at most one sidekick pair.

Initially, each character will fight their rival, and the winner is determined by who has the higher Power Level. If a hero and their corresponding villain have the same Power Level, their battle is resolved by their sidekicks’ fight, with the winning sidekick acting as a tiebreaker. (If rivals of equal Power Level do not have sidekicks, the hero wins with the help of random passersby.) Importantly, once a battle is won by either side, the sidekicks cannot interfere — this is because the creators of the show decided that fans might be upset if a main character were defeated by minor characters, so such victories are ignored regardless of Power Levels.

After all rival battles (and any tiebreakers) are concluded, the most important surviving character will defeat the rest of the opposing side, determining the fate of the universe. Fortunately, the heroes can guarantee victory through hard, rigorous training. Each day of training increases the Power Level of every hero by $1$, while the villains’ Power Levels remain unchanged.

But you already knew all this. The real question is: how many days of training will it take?

Input The first line contains the number of rival pairs n~(1 \le n \le 1000).

The second line contains $n$ integers h_1, \dots, h_n~(1 \le h_i \le 1000), where h_i is the Power Level of the $i$-th most important hero.

The third line contains $n$ integers v_1, \dots, v_n~(1 \le v_i \le 1000), where v_i is the Power Level of the $i$-th most important villain.

Output Output the minimum number of days the heroes need to train in order for their side to win.