Two Shuffled Sequences

## 题目描述 最初存在两个整数序列，一个严格递增，另一个严格递减。 严格递增序列是一个整数序列 [$x_{1}$<$x_{2}$<$x_{3}$<...<$x_{k}$] 严格递减序列是一个整数序列 [$y_{1}$>$y_{2}$>$y_{3}$>...>$y_{k}$] ### 请注意，空序列和由一个元素组成的序列可以视为递增或递减。 它们被合并成一个序列A。然后，A中的元素被随机调换了。例如，对于递增序列[1，3，4]和递减序列[10，4，2]的一些可能的结果：序列A[1，2，3，4，4，10]，[4，2，1，10，4，3]，[4，1，10，4，3]等。 这个无序的序列a在输入中给出。 你的任务是找到任意两个合适的初始序列。其中一个应该严格递增，另一个应该严格递减。 如果输入中存在矛盾，并且无法将给定的序列A分为递增和递减序列，则打印“NO”。 *** ## 输出格式 第一行：YES或NO 如题意； 第二行：严格递增序列元素个数； 第三行：输出严格递增序列； 第四行：严格递减序列元素个数； 第五行：输出严格递减序列； *** Translation by@三点水一个各。

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".

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 $ .

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).

7
7 2 7 3 3 1 4

YES
2
3 7 
5
7 4 3 2 1 

5
4 3 1 5 3

YES
1
3 
4
5 4 3 1 

5
1 1 2 1 2

NO

5
0 1 2 3 4

YES
0

5
4 3 2 1 0