Best Solution Unknown

You are the responsible holder of a competition called Best Solution Unknown (BSU). The rules of this competition are simple but rather quirky.

First, all the $n$ participants stand in a row. Then, $n-1$ matches are held. In each match, the jury chooses two adjacent players. The chosen players are given an NP-hard problem, and they try their best to come up with a good solution. The one who provides a better solution wins a round, and the other one leaves the competition. After that, the players shift to form a valid row again, so the player adjacent to the player who left becomes adjacent to the winner. After all $n-1$ matches, only one player remains, and this player is declared the winner of the competition.

The strength of the $i$-th player, counting from the left, is $a_i$. You know the strength of each player before the competition. A player with greater strength wins the match. If the strengths are equal, either player may win. The strength of the winner of a match increases by one.

You do not know who plays in each match, or who wins a match when the strengths are equal. Find every participant who can become the winner of the competition.

The first line contains $n$ ($1 \le n \le 10^6$), the number of participants. The second line contains $n$ integers $a_i$ ($1 \le a_i \le 10^9$), the initial strength of the $i$-th participant.

The first line should contain $k$ ($1 \le k \le n$), the number of participants that can possibly win. The second line should contain $k$ integers $b_i$ in strictly increasing order, the indices of these participants ($1 \le b_1 < b_2 < \ldots < b_k \le n$).