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A parade of all elephants is to commence soon at the Byteotian zoo. The zoo employees have encouraged these enormous animals to form a single line, as the manager wills it to be the initial figure of the parade.
Unfortunately, the manager himself came to the parade and did not quite like what he saw - he had intended an entirely different order of the elephants. Therefore he enforced his ordering, claiming the animals would seem most majestic this way, and made the employees reorder the elephants accordingly.
As a pack of moving elephants can wreak havoc, the employees decided to have them rearranged by swapping one pair at a time. Luckily the animals need not stand next to each other in order to swap positions in the line. Making an elephant move, however, is not as easy as it sounds. In fact, the effort one has to put into it is proportional to the animal's mass. Hence, the effort involved in swapping a pair of elephants of respective masses m1 and m2 can be estimated by m1+m2. What is the minimum effort involved in rearranging the elephants according to manager's will?
Write a programme that:
The first line of the standard input contains a single integer n (2 ≤ n ≤ 1,000,000) denoting the number of elephants in the zoo. We assume that the elephants are numbered from 1 to n to simplify things. The second line holds n integers mi (100 ≤ mi ≤ 6,500 dla 1 ≤ i ≤ n) separated by single spaces and denoting the masses of respective elephants (in kilogrammes).
The third line of input contains n pairwise different integers ai (1 ≤ ai ≤ n) separated by single spaces and denoting the numbers of successive elephants in the initial ordering. The fourth line holds n pairwise different integers bi (1 ≤ bi ≤ n) separated by single spaces and denoting the numbers of successive elephants in the ordering desired by the zoo manager. You may assume that the sequences (ai) and (bi) differ.
The first and only line of the standard output should contain a single integer denoting the minimum summary effort involved in reordering the elephants from the order represented by the sequence to the one represented by (bi).
6 2400 2000 1200 2400 1600 4000 1 4 5 3 6 2 5 3 2 4 6 1
One of the optimal rearrangements consists of swapping the following pairs of elephants: