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>
#include <cstring>
using namespace std;

static const int lim = 1<<15+1;

int main(){
	
	int dp[lim]={0};
	int n, k;
	
	for(int a=0; a*a<lim; ++a){
	for(int b=a; b*b<lim; ++b){
	for(int c=b; c*c<lim; ++c){
	for(int d=c; d*d<lim; ++d){
	
		k = a*a+b*b+c*c+d*d;
		
		if(k<lim)
			dp[k]++;
	}}}}
	
	while(cin >> n, n){
		cout << dp[n] << endl;
	}
		
	return 0;
		
}