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 <cstdio>
using namespace std;

#define MAX 32768

int dp[5][MAX + 1];

int main(){
	dp[0][0] = 1;
	
	for(int i = 1; i * i <= MAX; ++i){
		int i2 = i * i;
		
		for(int j = i2; j <= MAX; ++j){
			for(int k = 1; k <= 4; ++k){
				dp[k][j] += dp[k - 1][j - i2];
			}
		}
	}
	
	for(int i = 1; i <= MAX; ++i){
		for(int k = 1; k <= 4; ++k){
			dp[0][i] += dp[k][i];
		}
	}
	
	int n;
	while( scanf("%d", &n), n != 0 ){
		printf("%d\n", dp[0][n]);
	}
}