Problem: 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.

Example

Input

1
25
2003
211
20007
0


Output

1
3
48
7
738

Solution (in JAVA):

Solution:
import java.util.Arrays;
import java.util.Scanner;

public class Main {
	MyScanner sc = new MyScanner();
	Scanner sc2 = new Scanner(System.in);
	int mod = 1000000007;

	void run() {
		for (;;) {
			int N = sc.nextInt();
			if (N == 0) {
				return;
			}
			int[][] table = new int[4][200];
			for (int i = 0; i < 4; i++) {
				for (int j = 0; j < 200; j++) {
					table[i][j] = (int) (Math.pow(j + 1, 2) * (i + 1));
				}
			}

			int cnt = 0;
			// select one
			for (int i = 0; i < 200; i++) {
				if (table[0][i] == N) {
					cnt++;
				}
			}

			// select two
			for (int i = 0; i < 200; i++) {
				if (table[1][i] == N) {
					cnt++;
				}
			}
			for (int i = 0; i < 200; i++) {
				for (int j = i + 1; j < 200; j++) {
					if (table[0][i] + table[0][j] == N) {
						cnt++;
					}
				}
			}

			// select three
			for (int i = 0; i < 200; i++) {
				if (table[2][i] == N) {
					cnt++;
				}
			}
			for (int i = 0; i < 200; i++) {
				for (int j = 0; j < 200; j++) {
					if (i == j) {
						continue;
					}
					if (table[0][i] + table[1][j] == N) {
						cnt++;
					}
				}
			}
			for (int i = 0; i < 200; i++) {
				for (int j = i + 1; j < 200; j++) {
					for (int k = j + 1; k < 200; k++) {
						if (table[0][i] + table[0][j] + table[0][k] == N) {
							cnt++;
						}
					}
				}
			}

			// select four
			for (int i = 0; i < 200; i++) {
				if (table[3][i] == N) {
					cnt++;
				}
			}
			for (int i = 0; i < 200; i++) {
				for (int j = 0; j < 200; j++) {
					if (i == j) {
						continue;
					}
					if (table[0][i] + table[2][j] == N) {
						cnt++;
					}
				}
			}
			for (int i = 0; i < 200; i++) {
				for (int j = i + 1; j < 200; j++) {
					if (table[1][i] + table[1][j] == N) {
						cnt++;
					}
				}
			}
			for (int i = 0; i < 200; i++) {
				for (int j = i + 1; j < 200; j++) {
					for (int k = 0; k < 200; k++) {
						if (i == k || j == k) {
							continue;
						}
						if (table[0][i] + table[0][j] + table[1][k] == N) {
							cnt++;
						}
					}
				}
			}
			for (int i = 0; i < 200; i++) {
				for (int j = i + 1; j < 200; j++) {
					for (int k = j + 1; k < 200; k++) {
						int target = N - (table[0][i] + table[0][j]
								+ table[0][k]);
						int left = k + 1;
						int right = 200;
						int mid = (left + right) / 2;
						while (right - left > 0) {
							if (target == table[0][mid]) {
								cnt++;
								break;
							}
							if (target < table[0][mid]) {
								right = mid;
							} else {
								left = mid + 1;
							}
							mid = (left + right) / 2;
						}
					}
				}
			}
			System.out.println(cnt);
		}
	}

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

	void debug(Object... o) {
		System.out.println(Arrays.deepToString(o));
	}

	void debug2(int[][] array) {
		for (int i = 0; i < array.length; i++) {
			for (int j = 0; j < array[i].length; j++) {
				System.out.printf("%02d ", array[i][j]);
			}
			System.out.println();
		}
	}

	class MyScanner {
		int nextInt() {
			try {
				int c = System.in.read();
				while (c != '-' && (c < '0' || '9' < c))
					c = System.in.read();
				if (c == '-')
					return -nextInt();
				int res = 0;
				do {
					res *= 10;
					res += c - '0';
					c = System.in.read();
				} while ('0' <= c && c <= '9');
				return res;
			} catch (Exception e) {
				return -1;
			}
		}

		double nextDouble() {
			return Double.parseDouble(next());
		}

		String next() {
			try {
				StringBuilder res = new StringBuilder("");
				int c = System.in.read();
				while (Character.isWhitespace(c))
					c = System.in.read();
				do {
					res.append((char) c);
				} while (!Character.isWhitespace(c = System.in.read()));
				return res.toString();
			} catch (Exception e) {
				return null;
			}
		}
	}
}