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>

typedef long long int lli;

lli dp[1<<17][5];

lli sq(lli x) {
    return x*x;
}

int main(void) {
    dp[0][0]=1;
    for(lli x=1; sq(x)<1<<16; x++)
        for(int i=0; i+sq(x)<1<<16; i++)
            for(int j=0; j<4; j++)
                dp[sq(x)+i][j+1] += dp[i][j];

    while(1) {
        int n;
        scanf("%d",&n);
        if(!n) break;
        printf("%lld\n",dp[n][1]+dp[n][2]+dp[n][3]+dp[n][4]);
    }
    return 0;
}