46 - Andrew Stankevich's Contest, Warmup - 1003
Inspired by Gray code, professor John Yellow has invented his own code. Unlike in Gray code, in Yellow code the adjacent words have many different bits.
More precisely, for s = 2n we call the permutation a1, a2, ... , as of all n-bit binary words the Yellow code if for all 1 <= k < s words ak and ak+1 have at least [n/2] different bits and a1 and as also have at least [n/2] different bits. ([n/2] indicates the largest integer that does not exceed n/2.)
Given n you have to find the n-bit Yellow code or detect that there is none.
In each line of input file there is an integral number n (2 <= n <= 12). A line with n = 0 indicates the end of input, which should not be proceeded.
OutputFor each test case, output 2n n-bit binary vectors in the order they appear in some n-bit Yellow code, one on a line. If there is no n-bit Yellow code, output "none" on the first line.
Two consecutive cases should be separated by a single blank line. No blank line should be produced after the last test case.
4 2 0
0000 1010 0101 1111 0010 1001 0111 1100 0001 1011 0100 1110 0011 1000 0110 1101 00 10 01 11
Author: Andrew Stankevich