Longest Increasing Subsequence (LIS)

Given an array of numbers, find the longest subsequence (the elements don't have to be next to each other) such that the numbers are strictly increasing.

Since there can be multiple such subsequences of the same (longest) length, print the lexicographically smallest one.

A sequence $x$ is lexicographically smaller than a sequence $y$ of the same length if, at the first position where they differ, $x$ has the smaller element.

Input

First line of input will be a single number $n$, the length of the array.
In the next line will be $n$ numbers $a_1,a_2,\dots ,a_n$.

Output

In the first line, a single number $k$ - the length of the longest strictly increasing subsequence.
In the second line, $k$ numbers - the lexicographically smallest longest strictly increasing subsequence.

Example

8
3 6 1 2 8 2 4 5

4
1 2 4 5

The longest strictly increasing subsequence has 4 elements, and the only one of that length is $1,2,4,5$.

Constraints

$1\le n\le 1000$
$1\le a_i\le 10^9$