output_description: The output should be composed of lines, each containing a single integer. No
  other characters should appear in the output.
  
  The output integer corresponding to the input integer _n_ is the number of all
  representations of _n_ as the sum of at most four positive squares.
input_description: The input is composed of at most 255 lines, each containing a single positive
  integer less than 215 , followed by a line containing a single zero. The last
  line is not a part of the input data.
attempt: a = [[0] * 5 for _ in [0] * (1 << 15)]
  for i in range(int((1 << 15) ** 0.5)):
      a[i * i][1] += 1
      for j in range(i * i + 1, min(4 * i * i + 1, 1 << 15)):
          for k in range(2, 5):
              a[j][k] += a[j - i * i][k - 1]
  while 1:
      n = int(input())
      if n == 0:
          break
      print(sum(a[n]))
  
problem_description: B: Lagrange's Four-Square Theorem
  
  The fact that any positive integer has a representation as the sum of at most
  four positive squares (i.e. squares of positive integers) is known as
  Lagrange’s Four-Square Theorem. The first published proof of the theorem was
  given by Joseph-Louis Lagrange in 1770. Your mission however is not to explain
  the original proof nor to discover a new proof but to show that the theorem
  holds for some specific numbers by counting how many such possible
  representations there are.
  
  For a given positive integer n, you should report the number of all
  representations of n as the sum of at most four positive squares. The order of
  addition does not matter, e.g. you should consider 42 \+ 32 and 32 \+ 42 are
  the same representation.
  
  For example, let’s check the case of 25. This integer has just three
  representations 12 +22 +22 +42 , 32 \+ 42 , and 52 . Thus you should report 3
  in this case. Be careful not to count 42 \+ 32 and 32 \+ 42 separately.
samples: [{"input": "25\n    2003\n    211\n    20007\n    0", "output": "3\n    48\n    7\n    738"}]