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 <cstdio>
#include <cstring>
#include <cstdlib>
#include <cmath>
#include <vector>
#include <string>
#include <map>
#include <set>
#include <queue>
#include <stack>
#include <algorithm>

using namespace std;

#define rep(i,j) REP((i), 0, (j))
#define REP(i,j,k) for(int i=(j);(i)<(k);++i)
#define BW(a,x,b) ((a)<=(x)&&(x)<=(b))
#define MP make_pair
#define PB push_back
#define F first
#define S second
#define INF 1 << 30
#define EPS 1e-10

typedef pair<int, int> pi;
typedef pair<int, pi> pii;
typedef vector<int> vi;
typedef queue<int> qi;
typedef long long ll;

int n;

int dfs(int sum, int d, int c){
  //  printf("%d %d\n", sum, c);
  if(sum == n) return 1;
  if(c >= 4) return 0;
  int res = 0;
  for(int i = d; i*i <= n; i++){
    if(sum + i*i > n) break;;
    res += dfs(sum + i*i, i, c+1);
  }
  return res;
}

int main(){
  while(scanf("%d", &n) && n){
    printf("%d\n", dfs(0, 1, 0));
  }
  return 0;
}