
ZOJ Problem Set  1738
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 FourSquare Theorem. The first published proof of the theorem was given by JosephLouis 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, let's 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
1 Source: Asia 2003, Aizu (Japan) 