CMO 2000 Problem 4

Given an ordered $n$ -tuple $A=(a_1,a_2,\cdots ,a_n)$ of real numbers, where $n\ge 2$ , we define $b_k=\max{a_1,\ldots a_k}$ for each k. We define $B=(b_1,b_2,\cdots ,b_n)$ to be the "innovated tuple" of $A$ . The number of distinct elements in $B$ is called the "innovated degree" of $A$ . Consider all permutations of $1,2,\ldots ,n$ as an ordered $n$ -tuple. Find the arithmetic mean of the first term of the permutations whose innovated degrees are all equal to $2$