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 {
	static Scanner sc = new Scanner(System.in);

	public static void main(String[] args) {
		while (true) {
			int N = sc.nextInt();
			if (N == 0) break;
			System.out.println(dfs(N, 1, 0));
		}
	}

	static int dfs(int cur, int prev, int d) {
		if (cur == 0) return 1;
		if (d == 4) return 0;
		int ret = 0;
		for (int i = prev;; ++i) {
			int sq = i * i;
			if (sq > cur) break;
			ret += dfs(cur - sq, i, d + 1);
		}
		return ret;
	}

}