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 Lagrangefs 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 4^{2} + 3^{2} and 3^{2} + 4^{2} are the same representation.

For example, letfs check the case of 25. This integer has just three representations 1^{2} +2^{2} +2^{2} +4^{2} ,
3^{2} + 4^{2} , and 5^{2} . Thus you should report 3 in this case. Be careful not to count 4^{2} + 3^{2} and
3^{2} + 4^{2} separately.

The input is composed of at most 255 lines, each containing a single positive integer less than
2^{15} , followed by a line containing a single zero. The last line is not a part of the input data.

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.

1 25 2003 211 20007 0

1 3 48 7 738

Source: ACM International Collegiate Programming Contest
, Asia Regional Aizu, Aizu, Japan, 2003-11-02

http://web-ext.u-aizu.ac.jp/conference/ACM/

http://web-ext.u-aizu.ac.jp/conference/ACM/