Bear and Ladder

Bearland has infinitely many cities, numbered starting from 1. Some pairs of cities are connected with bidirectional roads: - There are roads 1-2, 3-4, 5-6, 7-8, and so on (there is a road between cities 2*i+1 and 2*i+2 for every non-negative integer i). - There are roads 1-3, 3-5, 5-7, 7-9, ... (between every two consecutive odd numbers). - There are roads 2-4, 4-6, 6-8, 8-10, ... (between eve