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.HashMap;
import java.util.Map;
import java.util.Scanner;

public class Main {

    /**
     * @param args
     */
    public static void main(String[] args) {
        Scanner sc=new Scanner(System.in);
        while(true){
            int n = sc.nextInt();
            if(n==0)break;
            Map<Integer,Integer>map =new HashMap<Integer,Integer>();
            for (int i = 0; i <= n; i++) {
                    map.put(i*i, i);
            }
            int ans=0;
            for (int i = 0; i <= n; i++) {
                if(i*i > n)break;
                for (int j = i; j <= n; j++) {
                    if(i*i + j*j> n)break;
                    for (int k = j; k <= n; k++) {
                        if(i*i + j*j + k*k> n)break;
                        int sum = n-(i*i+j*j+k*k);
                        if(map.containsKey(sum)){
                            if(map.get(sum) >= k){
                                ans++;
                            }
                        }
                    }
                }
            }
            System.out.println(ans);
        }
    }

}