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 JAVA (judge verdict: Accepted)

import java.util.*;
import java.lang.*;
import java.io.*;

class Main
{

    private static int n;

    private static int rec(int sum,int pre,int cnt)
    {

	if(sum > n)
	    return 0;

	if(sum == n)
	    return 1;

	if(cnt >= 3)
	    {	   
		int dif = n-sum;
		
		    int res = (int)Math.sqrt(dif);
		    if(res >= pre)
			{
			    if(res*res == dif)return 1;
			}
		    return 0;
	    }
	
	
	int counter = 0;
	for(int i=pre;sum+Math.pow(i,2)<=n;i++)
	    {
		counter += rec(sum+i*i,i,cnt+1);
	    }
	return counter;
    }
    
      public static void main(String args[])throws IOException
    {
	BufferedReader in = new BufferedReader(new InputStreamReader(System.in));


	while(true)
	    {
		n = Integer.parseInt(in.readLine());
		if(n == 0)
		    break;
		System.out.println(rec(0,1,0));
	    }
    }
    
}