CF1144C.Two Shuffled Sequences

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 $[x_1 \lt x_2 \lt \dots \lt x_k]$. And strictly decreasing sequence is a sequence of integers $[y_1 \gt y_2 \gt \dots \gt y_l]$. 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".

最初存在两个整数序列——其中一个严格递增，另一个严格递减。

严格递增序列是指整数序列 $[x_1 \lt x_2 \lt \dots \lt x_k]$；严格递减序列是指整数序列 $[y_1 \gt y_2 \gt \dots \gt y_l]$。注意：空序列以及仅含一个元素的序列，既可视为递增序列，也可视为递减序列。

这两个序列被合并为一个序列 $a$，随后序列 $a$ 被打乱（随机重排）。例如，对于递增序列 $[1, 3, 4]$ 和递减序列 $[10, 4, 2]$，可能得到的打乱后序列 $a$ 包括 $[1, 2, 3, 4, 4, 10]$ 或 $[4, 2, 1, 10, 4, 3]$。

输入中给出的就是这个被打乱后的序列 $a$。

你的任务是找出任意一对满足条件的初始序列：其中一个严格递增，另一个严格递减。注意：空序列以及仅含一个元素的序列，既可视为递增序列，也可视为递减序列。

如果输入存在矛盾，即无法将给定序列 $a$ 拆分为一个递增序列和一个递减序列，则输出 "NO"。

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 $a$.

输入的第一行包含一个整数 $n$（$1 \le n \le 2 \cdot 10^5$）—— 表示数组 $a$ 的元素个数。

输入的第二行包含 $n$ 个整数 $a_1, a_2, \dots, a_n$（$0 \le a_i \le 2 \cdot 10^5$），其中 $a_i$ 是数组 $a$ 的第 $i$ 个元素。

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 ($inc_1 \lt inc_2 \lt \dots \lt inc_{n_i}$) — 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 ($dec_1 \gt dec_2 \gt \dots \gt dec_{n_d}$) — 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).

如果输入中存在矛盾，无法将给定序列 $a$ 拆分为一个严格递增序列和一个严格递减序列，则在第一行输出 "NO"。

否则，在第一行输出 "YES"，并在后续行中输出任意一对满足条件的序列。注意：空序列以及仅含一个元素的序列均可被视为（严格）递增序列或（严格）递减序列。

在第二行输出 $n_i$ —— 严格递增序列中的元素个数。$n_i$ 可以为零，此时该递增序列为一个空序列。

在第三行按值的严格递增顺序输出 $n_i$ 个整数 $inc_1, inc_2, \dots, inc_{n_i}$（即满足 $inc_1 \lt inc_2 \lt \dots \lt inc_{n_i}$），即该严格递增序列本身。若 $n_i = 0$，可留该行为空（或直接输出一个空行）。

在第四行输出 $n_d$ —— 严格递减序列中的元素个数。$n_d$ 可以为零，此时该递减序列为一个空序列。

在第五行按值的严格递减顺序输出 $n_d$ 个整数 $dec_1, dec_2, \dots, dec_{n_d}$（即满足 $dec_1 \gt dec_2 \gt \dots \gt dec_{n_d}$），即该严格递减序列本身。若 $n_d = 0$，可留该行为空（或直接输出一个空行）。

应满足 $n_i + n_d = n$，且所输出的两个序列的并集必须是给定序列的一个排列（在输出 "YES" 的情况下）。