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.Scanner;


public class Main {

	/**
	 * @param args
	 */
	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner sc = new Scanner(System.in);
		
		while(true){
			int input = sc.nextInt();
			
			if(input == 0){
				break;
			}
			
			int limit = (int)Math.sqrt(input);
			
			int count = 0;
			
			for(int i = 1; i <= limit; i++){
				if(i*i == input){
					count++;
					break;
				}
				
				for(int j = i; j <= limit; j++){
					if(i*i + j*j == input){
						count++;
						break;
					}
					
					for(int k = j; k <= limit; k++){
						if(i*i + j*j + k*k == input){
							count++;
							break;
						}
						
						for(int l = k; l <= limit; l++){
							if(i*i + j*j + k*k + l*l == input){
								count++;
								break;
							}
						}
							
					}
				}
			}
			
			System.out.println(count);
		}
	}

}