In the country Máxico are two islands, the island "Mayor" and island "Menor". The island "Mayor" has $k>3$ states, with exactly $n>3$ cities each one. The island "Menor" has only one state with $31$ cities. "Aeropapantla" and "Aerocenzontle" are the airlines that offer flights in Máxico. "Aeropapantla" offer direct flights from every city in Máxico to any other city in Máxico. "Aerocenzontle" only offers direct flights from every city of the island "Mayor" to any other city of the island "Mayor". If the percentage of flights that connect two cities in the same state it´s the same for the flights of each airline, What is the least number of cities that can be in the island "Mayor"?