Mountain Range

Problem Description

For a sequence $a_1, a_2, \dots, a_n$, a subsegment $a_l, a_{l+1}, \dots, a_r$ is called mountain-shaped if there exists an index $mid \in [l+1, r-1]$ such that $a_l, a_{l+1}, \dots, a_{mid}$ is non-decreasing, $a_{mid}, a_{mid+1}, \dots, a_r$ is non-increasing, and $r - l + 1 \ge 3$.

For an integer $k$ ($3 \le k \le n$), if the subsegments $[1, k], [k+1, 2k], \dots, [(m-1)k+1, mk], [mk+1, n]$ are all mountain-shaped, and $mk \le n$, $n - mk < k$, then we call the sequence $a$ a mountain range.

You are given a positive integer sequence $a$, where a value of $-1$ may stand for any number. Find all integers $k$ for which $a$ is a mountain range.

Input Format

The first line contains an integer $n$ ($1 \le n \le 10^5$), the length of the sequence.

The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ($1 \le a_i \le 10^9$ or $a_i = -1$).

Output Format

The first line contains an integer $m$, the number of valid $k$.

Then output $m$ lines, each containing one valid integer $k$ in ascending order.

Sample Input

11
7 -1 11 10 -1 -1 26 14 9 12 -1

Sample Output

1
4