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Ravi has just received the results of his history exam. One of the problems was putting famous
historical battles into chronological order. The correct order was:
1. Blockade of Naboo 2. Battle of Geonosis 3. Battle of Yavin 4. Battle of Hoth 5. Battle of Endor
Ravi has studied (relatively) hard for the exam, so he remembered the exact years of all battles,
except for the Blockade of Naboo. He couldn't remember anything about it, so he randomly placed it
last instead of first, obtaining the order:
1. Battle of Geonosis 2. Battle of Yavin 3. Battle of Hoth 4. Battle of Endor 5. Blockade of Naboo
Since Ravi's order doesn't match the correct solution at any index, Ravi's score on that
problem was – to his disappointment – 0 out of 5 points, even though he knew the correct order of
four out of five battles!
This opens the question of fair scoring of an ordering problem. The example given above suggests that
scoring by counting the number of items in the correct absolute position isn't fair. Is there a better way?
One possibility is finding the longest subsequence (not necessarily contiguous) of correctly ordered
items. This isn't the best solution either: if an item is displaced by just one position from the correct
order, the score that it awards drops to zero, even though it was almost correctly ordered.
Ravi has thus suggested (using the MAWT – Might As Well Try a Mind Trick approach) the
following scoring method to his history teacher. For every two items, the student will receive 1 point
if the two items are in mutually correct order. In other words, the number of points is the number of
item pairs that the student has correctly ordered. The maximum number of points is then, of course,
the total number of pairs, which equals N * (N - 1) / 2, where N is the total number of entries.
The first line of input contains the positive integer N (2 ≤ N ≤ 2500), the number of items. The items
are distinct words consisting of 3 to 15 lowercase English letters.
The second line of input contains the N items, space-separated, listed in the correct order.
The third line of input contains the N items, space-separated, listed in Ravi's order.
The first and only line of output must contain, with no spaces, the following: the number of points that
Ravi would earn using his scoring method, a / (forward slash) character, and the maximum
possible number of points for that problem (again assuming Ravi's scoring method). (This is the
usual notation found on a typical graded exam.)
Input: 3 alpha beta gamma alpha gamma beta Output: 2/3 Clarification of the first example: Ravi has received points for the pairs (alpha, beta) and (alpha, gamma).
|Time Limit:||0.177515 sec|
|Source Limit:||50000 Bytes|
|Languages:||C, CPP14, JAVA, PYTH, PYTH 3.6, CS2, PAS fpc, PAS gpc, RUBY, PHP, GO, NODEJS, HASK, SCALA, D, PERL, FORT, WSPC, ADA, CAML, ICK, BF, ASM, CLPS, PRLG, ICON, SCM qobi, PIKE, ST, NICE, LUA, BASH, NEM, LISP sbcl, LISP clisp, SCM guile, JS, ERL, TCL, PERL6, TEXT, CLOJ, FS|
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