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)

/*
  AOJ 1241
  Title:Lagrange's Four-Square Theorem
  @kankichi573
*/
#include <stdio.h>


int solve(int n,int c,int low)
{
  int i,ret;
  ret=0;
  for(i=low;i*i<=n;i++)
    {
      if(n==i*i)
	ret++;
      else if(c<4)
	ret+=solve(n-i*i,c+1,i);
    }
  return(ret);
}
main()
{
  int n,ret;
  while(scanf("%d",&n) && n)
    {
      ret=solve(n,1,1);
      printf("%d\n",ret);
    }
  return(0);
}