Two Shuffled Sequences
Contest: Codeforces Round 550 (Div. 3)
Difficulty rating: 1000
Tags: constructive algorithms, sortings

Two integer sequences existed initially — one of them was strictly increasing, and the other one — strictly decreasing.

Strictly increasing sequence is a sequence of integers $$$[x_1 < x_2 < \dots < x_k]$$$. And strictly decreasing sequence is a sequence of integers $$$[y_1 > y_2 > \dots > y_l]$$$. Note that the empty sequence and the sequence consisting of one element can be considered as increasing or decreasing.

They were merged into one sequence $$$a$$$. After that sequence $$$a$$$ got shuffled. For example, some of the possible resulting sequences $$$a$$$ for an increasing sequence $$$[1, 3, 4]$$$ and a decreasing sequence $$$[10, 4, 2]$$$ are sequences $$$[1, 2, 3, 4, 4, 10]$$$ or $$$[4, 2, 1, 10, 4, 3]$$$.

This shuffled sequence $$$a$$$ is given in the input.

Your task is to find any two suitable initial sequences. One of them should be strictly increasing and the other one — strictly decreasing. Note that the empty sequence and the sequence consisting of one element can be considered as increasing or decreasing.

If there is a contradiction in the input and it is impossible to split the given sequence $$$a$$$ to increasing and decreasing sequences, print "NO".

Input format:
The first line of the input contains one integer $$$n$$$ ($$$1 \le n \le 2 \cdot 10^5$$$) — the number of elements in $$$a$$$.

The second line of the input contains $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$ ($$$0 \le a_i \le 2 \cdot 10^5$$$), where $$$a_i$$$ is the $$$i$$$-th element of $$$a$$$.

Output format:
If there is a contradiction in the input and it is impossible to split the given sequence $$$a$$$ to increasing and decreasing sequences, print "NO" in the first line.

Otherwise print "YES" in the first line and any two suitable sequences. Note that the empty sequence and the sequence consisting of one element can be considered as increasing or decreasing.

In the second line print $$$n_i$$$ — the number of elements in the strictly increasing sequence. $$$n_i$$$ can be zero, in this case the increasing sequence is empty.

In the third line print $$$n_i$$$ integers $$$inc_1, inc_2, \dots, inc_{n_i}$$$ in the increasing order of its values ($$$inc_1 < inc_2 < \dots < inc_{n_i}$$$) — the strictly increasing sequence itself. You can keep this line empty if $$$n_i = 0$$$ (or just print the empty line).

In the fourth line print $$$n_d$$$ — the number of elements in the strictly decreasing sequence. $$$n_d$$$ can be zero, in this case the decreasing sequence is empty.

In the fifth line print $$$n_d$$$ integers $$$dec_1, dec_2, \dots, dec_{n_d}$$$ in the decreasing order of its values ($$$dec_1 > dec_2 > \dots > dec_{n_d}$$$) — the strictly decreasing sequence itself. You can keep this line empty if $$$n_d = 0$$$ (or just print the empty line).

$$$n_i + n_d$$$ should be equal to $$$n$$$ and the union of printed sequences should be a permutation of the given sequence (in case of "YES" answer).

Constraints:
Time limit: 2.0 s
Memory limit: 256.0 MB

Example input:
7
7 2 7 3 3 1 4

Example output:
YES
2
3 7 
5
7 4 3 2 1

Example input:
5
4 3 1 5 3

Example output:
YES
1
3 
4
5 4 3 1

Editorial:
Let's count the number of occurrences of each element in the array $$$cnt$$$. Because the maximum possible element is $$$2 \cdot 10^5$$$, it can be done without any data structures.
Then let's check if $$$cnt_i$$$ is greater than $$$2$$$ for some $$$i$$$ from $$$0$$$ to $$$2 \cdot 10^5$$$, and if it is, then the answer is "NO", because this element should occur at least twice in one of the sequences.
Now let's output the increasing sequence. The number of elements in it is the number of elements $$$i$$$ such that $$$cnt_i = 2$$$. Let's iterate from left to right, print the suitable elements and decrease their $$$cnt$$$.
The number of elements in the decreasing sequence is just the number of elements with non-zero $$$cnt$$$. So let's iterate from right to left and just print suitable elements.