
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 = 2^{n} we call the permutation a_{1}, a_{2}, ... , a_{s} of all nbit binary words the Yellow code if for all 1 <= k < s words ak and a_{k+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 nbit Yellow code or detect that there is none. Input 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. Output For each test case, output 2^{n} nbit binary vectors in the order they appear in some nbit Yellow code, one on a line. If there is no nbit 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. Sample Input 4 2 0 Sample Output 0000 1010 0101 1111 0010 1001 0111 1100 0001 1011 0100 1110 0011 1000 0110 1101 00 10 01 11 Author: Andrew Stankevich 