Problem:
Problem 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.

Input

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.

Output

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.

Sample Input

1
25
2003
211
20007
0

Output for the Sample Input

1
3
48
7
738

Solution in Ruby (judge verdict: Accepted)

def solve(n, k, t)
  return 1 if n == 0
  return 0 if k == 0
  ret = 0
  t.downto(Math.sqrt(n / k).to_i) do |x|
    ret += solve(v = n - x * x, k - 1, @cmp[x][v])
  end
  ret
end

@cmp = (0..Math.sqrt(2**15).to_i).map{ |i| (0..2**15).map{ |j| i * i > j ? Math.sqrt(j).to_i : i } }

while n = gets.to_i
  break if n == 0
  puts solve(n, 4, Math.sqrt(n).to_i)
end