So this is how tic tac toe would work if it was in n-space. Basically you must claim n+1 continuous spaces in some cross section or throughout the entire n-space. Being continuous means that the closest next space is no more than 1 location away in each coordinate but is also at least 1 location away in at least 1 coordinate (otherwise it'd be the same point). Excessively large dimensional space may cause an overflow and crash. Suggested upper limit of six dimensional maximum.
CS = Cross Section, so a 3d cross section means that in larger space than 3 space only three dimensions can change. It could be 1,2,4 in 5 space or 2,3,7 in 10 space, it doesn't matter which three just that is three.
This program will produce a Tic-Tac-Toe board for any space/dimension > 1.