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>
constexpr int MAX = 1<<15;
constexpr int SQRT = 182;
int dp[MAX][5][SQRT+1];
int main(){
	std::fill(dp[0][0],dp[0][0]+SQRT, 1);
	for(int i =1 ; i < MAX; i++){
		for(int k = 1; k <= 4; k++){
			for(int j = 1; j * j <= i; j++){dp[i][k][j] += dp[i-j*j][k-1][j];}
			for(int j = 1; j<= SQRT; j++){dp[i][k][j] += dp[i][k][j-1];}
		}
	}
	for(int N;;){
		std::cin >> N;
		if(N == 0){break;}
		std::cout << dp[N][1][SQRT]+dp[N][2][SQRT]+dp[N][3][SQRT]+dp[N][4][SQRT] << std::endl;
	}
}