Supernumbers in a Permutation

A permutation of $n$ elements is a sequence of length $n$ made up of distinct numbers from the set {1, 2, ..., $n$}. For example, the sequence 2, 1, 4, 5, 3 is a permutation of 5 elements.

In this problem we care about the longest increasing subsequences of a permutation. In the example permutation above, the longest increasing subsequences have length 3, and there are exactly two of them: 2, 4, 5 and 1, 4, 5.

A supernumber is any number that belongs to at least one of the longest increasing subsequences. In the permutation 2, 1, 4, 5, 3 the supernumbers are 1, 2, 4, 5, while the number 3 is not a supernumber.

Your task is to find all supernumbers of a given permutation.

Write a program that:

• reads a permutation from standard input,
• finds all supernumbers,
• prints the supernumbers to standard output.

The input consists of two lines. The first line contains a single integer $n$ ($1 \le n \le 100000$). The second line contains the $n$ integers of the permutation, separated by single spaces.

The output consists of two lines. The first line contains $m$, the number of supernumbers in the input permutation. The second line contains the supernumbers, in increasing order, separated by single spaces.