Description

Given a sequence of $n$ (where $1 \leq n \leq 200$) distinct integers, denoted as $b(1), b(2), \ldots, b(n)$, with $b(i) \neq b(j)$ for $i \neq j$,
if there exist indices $i_1 < i_2 < i_3 < \ldots < i_e$ such that $b(i_1) \leq b(i_2) \leq \ldots \leq b(i_e)$, then this is called a non-decreasing subsequence of length $e$.

The task is to find the longest non-decreasing subsequence after the original sequence is given.

For example, consider the sequence:
13, 7, 9, 16, 38, 24, 37, 18, 44, 19, 21, 22, 63, 15.

In this case, 13, 16, 18, 19, 21, 22, 63 is a non-decreasing subsequence of length 7,
while 7, 9, 16, 18, 19, 21, 22, 63 forms a longer non-decreasing subsequence of length 8.

Input Format

• The first line contains an integer $n$.
• The second line contains $n$ space-separated integers.

Output Format

• The first line should output the maximum length max (as shown in the sample).
• The second line should output one of the longest non-decreasing subsequences. The answer may not be unique; any valid sequence is acceptable. Special judging will be applied for this problem.

Sample Input

14
13 7 9 16 38 24 37 18 44 19 21 22 63 15

Sample Output

max=8
7 9 16 18 19 21 22 63

14
13 7 9 16 38 24 37 18 44 19 21 22 63 15

max=8