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>
#define REP(i,n) for (int i=0;i<(n);i++)
using namespace std;
int ans[32769][5];
int main(){
    vector<int>data;
    for(int i=1;i*i<=32768;i++)data.push_back(i*i);
    ans[0][0]=1;
    REP(i,data.size()){
        REP(j,32769){
            if(j+data[i]>32768)break;
            REP(k,4)ans[j+data[i]][k+1]+=ans[j][k];
        }
    }
    int n;
    while(1){
        cin>>n;
        if(n==0)break;
        int sum=0;
        REP(i,4)sum+=ans[n][i+1];
        cout<<sum<<endl;
    }
}