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 <iostream>
#define llint long long

using namespace std;

llint n;
short dp[1<<8][1<<15][5];

int main(void)
{
	dp[1][0][0] = 1;
	llint N = 1<<15, M = 1<<8;
	for(int i = 0; i < M-1; i++){
		for(int j = 0; j < N; j++){
			for(int k = 0; k <= 4; k++){
				dp[i+1][j][k] += dp[i][j][k];
				if(j+i*i < N && k+1 <= 4) dp[i][j+i*i][k+1] += dp[i][j][k];
			}
		}
	}
	
	while(1){
		cin >> n;
		if(n == 0) break;
		llint ans = 0;
		for(int i = 1; i <= 4; i++) ans += dp[M-1][n][i];
		cout << ans << endl;
	}
	return 0;
}