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 INF 1e9
#define llINF 1e18
#define MOD 1000000007
#define pb push_back
#define mp make_pair 
#define F first
#define S second
#define ll long long
#define vi vector<ll>
#define vvi vector<vi>
#define BITLE(n) (1LL<<((ll)n))
#define SHIFT_LEFT(n) (1LL<<((ll)n))
#define SUBS(s,f,t) ((s).substr((f)-1,(t)-(f)+1))
#define ALL(a) (a).begin(),(a).end()
using namespace std;
ll dp[BITLE(16)][5];
int main(){
  cin.tie(0);
  ios::sync_with_stdio(false);
  ll n;
  while(cin>>n,n){
    vi hoge;
    for(int i=1;(i*i)<=SHIFT_LEFT(16);i++){
      hoge.pb(i*i);
    }
    for(int i=0;i<BITLE(16);i++)
      for(int j=0;j<5;j++)
	dp[i][j] = 0;
    dp[0][0] = 1;
    for(int i=0;i<hoge.size();i++){
      for(int j=0;j<SHIFT_LEFT(15);j++){
	if(j+hoge[i] > SHIFT_LEFT(15))break;
	for(int k=0;k<4;k++){
	  dp[j+hoge[i]][k+1] += dp[j][k];
	}
      }
    }
    ll ans = 0;
    for(int i=0;i<=4;i++)ans += dp[n][i];
    cout<<ans<<endl;
  }
  return 0;
}