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++11 (judge verdict: Accepted)

#include <iostream>
#include <iomanip>
#include <sstream>
#include <stdio.h>
#include <list>
#include <vector>
#include <stack>
#include <queue>
#include <map>
#include <algorithm>
#include <math.h>
#include <utility>
#include <string>                                       
#include <ctype.h>
#include <cstring>
#include <cstdio>
#include <sstream>
#include <functional>

using namespace std;

#define FOR(i,k,n) for(int i = (k); i < (n); i++)
#define REP(i,n) FOR(i,0,n)
#define INF 114514810
#define ll long long

vector<int> v;
int n;
short dp[4][200][33000];
int solve(int i, int j, int res)
{
	if (i == 4)
	{
		if (res == n) return 1;
		else return 0;
	}
	if (j == v.size() || v[j] > res+n || res>n) return 0;
	if (dp[i][j][res] >= 0) return dp[i][j][res];
	return dp[i][j][res] = solve(i, j + 1, res) + solve(i + 1, j, res + v[j]);
}

int main()
{
	for (int i = 0;; i++)
	{
		v.push_back(i*i);
		if (i*i > 33000) break;
	}

	while (cin >> n, n)
	{
		REP(i, 4)REP(j, v.size())REP(k, n + 1) dp[i][j][k] = -1;
		cout << solve(0, 0, 0) << endl;
	}
	return 0;
}