310935: CF1911D. Two Shuffled Sequences

D. Two Shuffled Sequencestime limit per test3.0 smemory limit per test256 megabytesinputstandard inputoutputstandard output

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

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

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).

ExamplesInput

7
7 2 7 3 3 1 4

Output

YES
2
3 7 
5
7 4 3 2 1 

Input

5
4 3 1 5 3

Output

YES
1
3 
4
5 4 3 1 

Input

5
1 1 2 1 2

Output

NO

Input

5
0 1 2 3 4

Output

YES
0

5
4 3 2 1 0 

题目大意：
给定一个整数序列a，原本由一个严格递增序列和一个严格递减序列合并而成，合并后的序列被随机打乱。要求找出原来的两个序列，一个严格递增，一个严格递减。如果找不到，则输出“NO”。

输入输出数据格式：
输入：
第一行包含一个整数n（1≤n≤2×10^5），表示序列a的元素个数。
第二行包含n个整数a_1, a_2, ..., a_n（0≤a_i≤2×10^5），表示序列a的各个元素。

输出：
如果无法将给定的序列a拆分为递增和递减序列，则第一行输出“NO”。
否则，第一行输出“YES”，接着在第二行输出递增序列的元素个数n_i（可以为0），在第三行输出递增序列本身（如果n_i=0，则该行可以为空），在第四行输出递减序列的元素个数n_d（可以为0），在第五行输出递减序列本身（如果n_d=0，则该行可以为空）。n_i和n_d之和应等于n，且输出的两个序列的并集应是给定序列的一个排列。题目大意： 给定一个整数序列a，原本由一个严格递增序列和一个严格递减序列合并而成，合并后的序列被随机打乱。要求找出原来的两个序列，一个严格递增，一个严格递减。如果找不到，则输出“NO”。 输入输出数据格式： 输入： 第一行包含一个整数n（1≤n≤2×10^5），表示序列a的元素个数。 第二行包含n个整数a_1, a_2, ..., a_n（0≤a_i≤2×10^5），表示序列a的各个元素。 输出： 如果无法将给定的序列a拆分为递增和递减序列，则第一行输出“NO”。 否则，第一行输出“YES”，接着在第二行输出递增序列的元素个数n_i（可以为0），在第三行输出递增序列本身（如果n_i=0，则该行可以为空），在第四行输出递减序列的元素个数n_d（可以为0），在第五行输出递减序列本身（如果n_d=0，则该行可以为空）。n_i和n_d之和应等于n，且输出的两个序列的并集应是给定序列的一个排列。