Problem: 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.

Example

Input

1
25
2003
211
20007
0


Output

1
3
48
7
738

Solution (in JAVA):

Solution:
import java.util.*;
public class Main { 
	static ArrayList<Integer> list = new ArrayList<Integer>();
	public static void main(String[] args) {
		Scanner stdIn = new Scanner(System.in);
		makeList();
		while(true) {
			int n = stdIn.nextInt();
			if(n == 0) break;
			int count = 0;
			for(int i = 0; i < list.size(); i++) {
				if(list.get(i) > n) break;
				for(int j = i; j < list.size(); j++) {
					if(list.get(i) + list.get(j) > n) break;
					for(int k = j; k < list.size(); k++) {
						if(list.get(i) + list.get(j) + list.get(k) > n) break;
						for(int l = k; l < list.size(); l++) {
							if(list.get(i) + list.get(j) + list.get(k) + list.get(l) == n) {
								count++;
								break;
							}
						}
					}
				}
			}
			System.out.println(count);
		}
	}
	public static void makeList() {
		for(int i = 0; i < 32768; i++) {
			if(i * i > 32768) {
				break;
			}
			list.add(i*i);
		}
	}
		
}