A group of $4046$ friends will play a videogame tournament. For that, $2023$ of them will go to one room which the computers are labeled with $a_1,a_2,\dots,a_{2023}$ and the other $2023$ friends go to another room which the computers are labeled with $b_1,b_2,\dots,b_{2023}$. The player of computer $a_i$ always challenges the players of computer $b_i,b_{i+2},b_{i+3},b_{i+4}$(the player doesn't challenge $b_{i+1}$). After the first round, inside both rooms, the players may switch the computers. After the reordering, all the players realize that they are challenging the same players of the first round. Prove that if one player has not switched his computer, then all the players have not switched their computers.