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14-05-80. 50372 - Number Quadruplets

IMPC - 2013-2014

Start: Mar.16.2013 at 12:00:00 PM
Finish: Mar.16.2013 at 05:00:00 PM
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Time limit 2000/4000/4000/4000 ms. Memory limit 65000/65000/65000/65000 Kb.
By Arban Uka.

Number Quadruplets

Assume that we have the following relation:

a2 + b2 + c2 = d2
Question: Find the number of unique quadruplets of (a, b, c, d) that satisfy the above relation for the given d.

Note: the following three quadruplets are assumed to be the same. Thus, you count only one.
   12+22+22 = 32
   22+12+22 = 32
   22+22+12 = 32

Input specification
You will be given just one integer d where 1 ≤ d ≤ 100) and 1 ≤ (a,b,c) ≤ d.

Output specification
Show the number of unique quadruplets.

 Sample Input I     Sample Input II   
 10
 20
 Sample Output I     Sample Output II   
 6
 22

Explanation
There are six unique number quadruplets until ten.

  • 12 + 22 + 22 = 32
  • 22 + 42 + 42 = 62
  • 22 + 32 + 62 = 72
  • 12 + 42 + 82 = 92
  • 32 + 62 + 62 = 92
  • 42 + 42 + 72 = 92

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