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: Time Limit Exceeded)

import java.util.Scanner;

public class Main {
	public static int[] square = new int[256];
	public static int count;
	
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		for (int i = 0; i < 256; i++) {
			square[i] = i * i;
		}
		
		int n = sc.nextInt();
		while (n != 0) {
			count = 0;
			int p = 255;
			while (square[p] > n) {
				p--;
			}
			for (int i = p; i > 0; i--) {
				dfs(i, n - square[i], 0);
			}
			System.out.println(count);
			
			n = sc.nextInt();
		}
	}
	
	public static void dfs(int p, int rest, int times) {
		if (times == 4) return;
		if (rest == 0) {
			count++;
			return;
		}
		if (rest < 0) return;
		
		while (square[p] > rest) {
			p--;
		}
		for (int i = p; i > 0; i--) {
			dfs(i, rest - square[i], times + 1);
		}
	}
}