Problem:
Problem B: Lagrange's Four-Square Theorem

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.

Sample Input

1
25
2003
211
20007
0

Output for the Sample Input

1
3
48
7
738

Solution in C (judge verdict: Accepted)

#include <stdio.h>
int s[1<<15];
int main(void)
{
    int i, j, k, n;
    for(i=1;i*i<(1<<15);++i) s[i*i]=i;
    while (scanf("%d", &n), n) {
        int res=s[n]>0;

        for(i=1;i*i<n;++i) res+=(s[n-i*i]>=i);

        for(i=1;i*i<n-1;++i)
        for(j=i;i*i+j*j<n;++j) res+=(s[n-i*i-j*j]>=j);

        for(i=1;i*i<n-2;++i)
        for(j=i;i*i+j*j<n-1;++j)
        for(k=j;i*i+j*j+k*k<n;++k) res+=(s[n-i*i-j*j-k*k]>=k);

        printf("%d\n", res);
    }
    return 0;
}