Beads

Byteasar has decided to start making necklaces, so he bought a very long string of colourful coral beads at a bargain price. He also owns a machine that, for a chosen integer $k$ ($k > 0$), cuts the string into consecutive pieces of exactly $k$ beads each: the first piece is beads $1, \dots, k$, the second is beads $k+1, \dots, 2k$, and so on. If the total number of beads is not a multiple of $k$, the final leftover piece (which would be shorter than $k$) is discarded. Each bead's colour is a positive integer.

Byteasar values variety and wants to choose $k$ so that the cutting produces as many different pieces as possible. The whole string has a fixed start and end, and these two ends are not interchangeable; the machine always begins cutting from the start. Within a single cut piece, however, the two ends ARE interchangeable, so a piece may be read in either direction. For example, the pieces $(1,2,3)$ and $(3,2,1)$ count as the same piece. Write a program that finds an optimal value of $k$ for Byteasar.

The first line contains an integer $n$ ($1 \le n \le 200\,000$): the number of beads on the string. The second line contains $n$ positive integers $a_1, a_2, \dots, a_n$ ($1 \le a_i \le n$), separated by single spaces, giving the colours of the beads in order from the start of the string.

On the first line print two integers separated by a single space: the maximum number of different pieces obtainable over all choices of $k$, and the number $l$ of values of $k$ that attain this maximum. On the second line print those $l$ values of $k$ in increasing order, separated by single spaces.