Bipartite Array

题意翻译

定义一个数列是 `二分的`，当且仅当用以下方法构造一张无向图，该图是一张二分图： - 这张图有 $n$ 个从 $1$ 编号到 $n$ 的节点 - 对于且仅对于所有满足 $i < j,a_i>a_j$ 的数对 $(i,j)$，在 $i$ 号节点和 $j$ 号节点间连有一条无向边。 定义一次 `操作` 为将某个 $a_i$ 变为它的相反数，现给你一个长度为 $n （n\leq 10^6）$ 的排列，要求你判断是否可以通过有限次 `操作` 使该排列变为 `二分的` 数列。 若无可行方案，输出 `NO`，否则输出 `YES`，并输出任意一个通过 `操作` 变为的 `二分的` 数列。

题目描述

You are given a permutation $ p $ consisting of $ n $ integers $ 1, 2, \dots, n $ (a permutation is an array where each element from $ 1 $ to $ n $ occurs exactly once). Let's call an array $ a $ bipartite if the following undirected graph is bipartite: - the graph consists of $ n $ vertices; - two vertices $ i $ and $ j $ are connected by an edge if $ i < j $ and $ a_i > a_j $ . Your task is to find a bipartite array of integers $ a $ of size $ n $ , such that $ a_i = p_i $ or $ a_i = -p_i $ , or report that no such array exists. If there are multiple answers, print any of them.

输入输出格式

输入格式

The first line contains a single integer $ t $ ( $ 1 \le t \le 2 \cdot 10^5 $ ) — the number of test cases. The first line of each test case contains a single integer $ n $ ( $ 1 \le n \le 10^6 $ ) — the size of the permutation. The second line contains $ n $ integers $ p_1, p_2, \dots, p_n $ . The sum of $ n $ over all test cases doesn't exceed $ 10^6 $ .

输出格式

For each test case, print the answer in the following format. If such an array $ a $ does not exist, print "NO" in a single line. Otherwise, print "YES" in the first line and $ n $ integers — array $ a $ in the second line.

输入输出样例

输入样例 #1

4
3
1 2 3
6
1 3 2 6 5 4
4
4 1 3 2
8
3 2 1 6 7 8 5 4

输出样例 #1

YES
1 2 3
NO
YES
-4 -1 -3 -2
YES
-3 -2 1 6 7 -8 -5 -4