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<stdio.h>
char dp[5][1<<15][182];
int main(){
	dp[0][0][0]=1;
	for(int i=0;i<(1<<15)-1;i++){
		for(int j=0;j<182;j++){
			for(int k=0;k<4;k++){
				//printf("%d %d %d %d\n",i,j,k,dp[k][i][j]);
				if(dp[k][i][j]){
					for(int l=j;;l++){
						if(i+l*l<(1<<15))dp[k+1][i+l*l][l]+=dp[k][i][j];
						else break;
					}
				}
			}
		}
	}
	int a;
	while(scanf("%d",&a),a){
		int ret=0;
	//	for(int i=0;i<5;i++){
			for(int j=0;j<182;j++)
				ret+=(int)dp[4][a][j];
		//}
		printf("%d\n",ret);
	}
}