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)

ns = $<.map(&:to_i)[0..-2]
squares = (0..Math.sqrt(ns.max).to_i).map {|x| x * x}
m = squares.size-1

ns.each do |n| 
    count = 0 
    (0..m).each do |i| 
        x = squares[i]
        break if 4 * x > n 
        (i..m).each do |j| 
            y = squares[j]
            break if x + y * 3 > n 
            l = m 
            (j..m).each do |k| 
                z = squares[k]
                s = x + y + z 
                l -= 1 while s + squares[l] > n 
                break if l < k 
                count += 1 if s + squares[l] == n
            end
        end
    end 
    p count
end