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<string>
#include<vector>
#include<cstdio>
#include<sstream>
#include<algorithm>
#include<cmath>
#include<map>
using namespace std;
int stoi(string x){stringstream ss;ss<<x;int tmp;ss>>tmp;return tmp;}
string itos(int x){stringstream ss;ss<<x;return ss.str();}
int n;
int dfs(int h,int sum,int use){
	//cout<<h<<" "<<sum<<" "<<use<<endl;
	if(use>4)return 0;
	if(sum>n)return 0;
	if(sum==n)return 1;
	int ret=0;
	for(int i=h;i*i<=n;i++){
	if(sum+i*i>n||use==4)break;
	ret+=dfs(i,sum+i*i,use+1);
	}
	return ret;
}
int main(){
	while(cin>>n,n!=0){
	cout<<dfs(1,0,0)<<endl;
	}

	return 0;
}