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Problem: Archery

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Input File: archin.txt
Output File: archout.txt
Time Limit: 1 second

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.

  Katniss Legolas Link Merida Robin
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
Overall Score 80 90 60 90 40
Overall Rank 3 1 4 1 5

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.


Your program should read from the file . The first and only line of input will contain three space-separated integers in this order:


Your program should write to the file . Your output file should contain one line with two integers, with exactly one space between them. The first integer is your best (i.e. smallest number) possible overall rank and the second integer is your worst (i.e. largest number) possible overall rank.

Sample Input 1

4 1 3

Sample Output 1

1 3


In this example, there are four contestants (including you), and you have rank 1 and 3 on the first and second days respectively. Here's one possible set of scores in which you have rank 1:

  You Katniss Link Merida
Day 1 Score 100 20 10 0
Day 1 Rank 1 2 3 4
Day 2 Score 20 30 50 10
Day 2 Rank 3 2 1 4
Overall Score 120 50 60 10
Overall Rank 1 3 2 4

On the other hand, if your Day 1 score in the above table was 25 instead, you would have an overall rank of 3. There is no set of scores consistent with your Day 1 and Day 2 ranks such that you come last.

Thus, your best possible rank is 1, and your worst possible rank is 3.

Sample Input 2

4 1 1

Sample Output 2

1 1


Since you came first on both days, you must have come first overall (no one could have got a strictly better score than you).

Sample Input 3

10 5 8

Sample Output 3

3 10


To evaluate your solution, the judges will run your program against several different input files. All of these files will adhere to the following bounds:


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Page generated: 27 November 2015,  8:22am AEDT