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;

using ll = long long int;
using P = pair<ll, ll>;
using P3 = pair<double,P>;
using PP = pair<P, P>;
constexpr int INF = 1 << 30;
constexpr ll MOD = ll(1e9) + 7;
constexpr int di[] = {0, 1, 0, -1};
constexpr int dj[] = {1, 0, -1, 0};
constexpr double EPS = 1e-8;

int rec(int x, int y, int c){
    if(c == 0){
        return x==0;
    }
    if(x < y*y) return 0;
    int res = 0;
    for(int i=y;i*i<=x;i++){
        res += rec(x-i*i, i, c-1);
    }
    return res;
}

int solve(){
    int n;
    cin >> n;
    if(n == 0) return 1;
    cout << rec(n, 0, 4) << endl;
    return 0;
}

int main(){
    // solve();
    while(solve()==0);
    // int t; cin >> t; for(;t>0;t--) solve();
    return 0;
}