On a planet with M and N city, linked by roads between some roads, known: (1) in any one country has at least three cities, (2) of a country in any one city and the country at least half of the city by road, (3) any one city with other countries have connected to a city and only through the road, (4) of the two countries up to only two roads between cities is linked together, (5) if the number of cities in the two countries is less than 2 M, in at least one path between the two countries are linked together, to prove: there is a connection at least M + N/2 city circular line,