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)

### subroutines

def count_rec(k, i, n)
  if k == 1
    i0 = Math.sqrt(n + 0.5).floor
    return (i0 * i0 == n && i0 >= i) ? 1 : 0
  end

  count = 0
  i0 = i

  loop do
    i0sq = i0 * i0
    n0 = n - i0sq
    break if n0 < i0sq
    count += count_rec(k - 1, i0, n0)
    i0 += 1
  end

  count
end

### main

loop do
  n = gets.to_i
  break if n == 0

  puts count_rec(4, 0, n)
end