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 JAVA (judge verdict: Accepted)

import java.util.*;

class Main{

    void solve(){
        Scanner sc = new Scanner(System.in);

        int max = (int)Math.pow(2, 15)+10;
        int[][] dp = new int[max][5];
        dp[0][0] = 1;
        for(int i=1; i*i<max; i++){
            for(int j=0; j+i*i<max; j++){
                for(int k=1; k<5; k++){
                    dp[j+i*i][k] += dp[j][k-1];
                }
            }
        }

        while(true){
            int n = sc.nextInt();
            if(n==0) break;
            int ans = dp[n][1] + dp[n][2] + dp[n][3] + dp[n][4];
            System.out.println(ans);
        }
    }

    public static void main(String[] args){
        new Main().solve();
    }
}