In a group of $n$ people each one has an Easter Egg. They exchange their eggs in the following way: On each exchange two people exchange the eggs they currently have. Each two exchange eggs between themselves at least once. After a certain amount of such exchanges it turned out that each one of the $n$ people had the same egg he had from the beginning. Determine the least amount of exchanges needed, if: a) $n=5$; b) $n=6$.