Given an array of 100 integers(64bit signed). Task is to pick a subset for which the xor of the elements of the subset is maximized.

Example : 1= 01 3= 11 2= 10

if we pick 1,2 then their xor is maximum (01 ^ 10 = 11). also we can pick only 3 but the maximum result is 3 anyhow.

The original problem is described in the following link: http://www.lightoj.com/volume_showproblem.php?problem=1272

This problem is included in Gaussian Elimination section but I can't find how GE can be applied to this problem.

Can anybody give me any hints? It would be helpful. Thanks in advance.