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<bits/stdc++.h>
using namespace std;

#define REP(i,n) for(int i=0;i<(n);i++)
#define ALL(v) (v).begin(),(v).end()
#define int long long
typedef pair<int,int> P;

//-----------------------------------------------------------------------

signed main()
{
    cin.tie(0);
    ios::sync_with_stdio(false);

    int n;
    while(cin>>n,n)
    {   
        int cnt=0;
        for(int a=1;a*a<=n;a++) if(a*a==n) cnt++;
        
        for(int a=1;a*a<n;a++)
        for(int b=a;a*a+b*b<=n;b++) if(a*a+b*b==n) cnt++;
        
        for(int a=1;a*a<n;a++)
        for(int b=a;a*a+b*b<n;b++)
        for(int c=b;a*a+b*b+c*c<=n;c++) if(a*a+b*b+c*c==n) cnt++;
        
        for(int a=1;a*a<n;a++)
        for(int b=a;a*a+b*b<n;b++)
        for(int c=b;a*a+b*b+c*c<n;c++) 
        for(int d=c;a*a+b*b+c*c+d*d<=n;d++) if(a*a+b*b+c*c+d*d==n) cnt++;
        cout<<cnt<<endl;
    }
}