When you were young, you were awe-struck by the battle scene in The Lord of the Rings: The Two Towers. From then on, you were determined to become the greatest archer of all time. After years of training, you are finally at the International Archery Olympiad (IAO), in Auckland.
On each of the two days of the IAO, all contestants are given a score and ranked by that score. After the second day of competition, all contestants are given an overall score equal to the sum of their two scores and their overall rank is then calculated from this.
|Day 1 Score||50||70||20||40||0|
|Day 1 Rank||2||1||4||3||5|
|Day 2 Score||30||20||40||50||40|
|Day 2 Rank||4||5||2||1||2|
A contestant's rank is equal to the number of competitors with strictly greater scores than theirs, plus one. In the above example, there are two overall scores strictly greater than Katniss's, so her overall rank is (2+1)=3. There are no overall scores strictly greater than Legolas's, so his overall rank is (0+1)=1. (Notice that Legolas and Merida are both ranked 1, as no one has a strictly greater score than either of them.)
Sick with anticipation of the results, you sneak a look at a judge's laptop. The scores aren't shown, nor is your overall rank, but you do manage to glimpse your first-day rank and your second-day rank. You want to work out what your overall rank could be.
Your task is to write a program which, given the number of contestants in the IAO and your rank on each day, determines your best and worst possible overall rank.