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 CPP):

Solution:
#include <iostream>
#include <vector>
#include <algorithm>

using namespace std;

int main(){
	vector<int> s;
	for(int i = 0; i * i <= (1 << 15); ++i){
		s.push_back(i * i);
	}
	const int m = s.size();
	while(true){
		int n;
		cin >> n;
		if(n == 0){ break; }
		int answer = 0;
		for(int a = 0; a < m; ++a){
			if(s[a] > n){ break; }
			for(int b = a; b < m; ++b){
				if(s[a] + s[b] > n){ break; }
				for(int c = b; c < m; ++c){
					int sum = s[a] + s[b] + s[c];
					if(sum > n){ break; }
					if(binary_search(s.begin() + c, s.end(), n - sum)){
						++answer;
					}
				}
			}
		}
		cout << answer << endl;
	}
	return 0;
}