Omkar and Medians

题意翻译

对于一个长度为 $2\times k-1$ 的序列 $a$，我们定义一个长度为 $k$ 的序列 $b$ 是 $a$ 的 _Omk序列_ 仅当其满足对于任意整数 $i\in[1,k]$，$b_i$ 的值等于 $a_1,a_2,\cdots,a_{2\times i-1}$ 这 $2\times i-1$ 个数的中位数。 现在给定 $k$ 和一个长度为 $k$ 的序列 $b$，你需要判断是否存在长度为 $2\times k-1$ 的序列 $a$ 使得 $b$ 是 $a$ 的 _Omk序列_。 $T$ 组数据。 $1\leq T\leq10^4;1\leq n,\sum n\leq2\times10^5;|b_i|\leq10^9;$

题目描述

Uh oh! Ray lost his array yet again! However, Omkar might be able to help because he thinks he has found the OmkArray of Ray's array. The OmkArray of an array $ a $ with elements $ a_1, a_2, \ldots, a_{2k-1} $ , is the array $ b $ with elements $ b_1, b_2, \ldots, b_{k} $ such that $ b_i $ is equal to the median of $ a_1, a_2, \ldots, a_{2i-1} $ for all $ i $ . Omkar has found an array $ b $ of size $ n $ ( $ 1 \leq n \leq 2 \cdot 10^5 $ , $ -10^9 \leq b_i \leq 10^9 $ ). Given this array $ b $ , Ray wants to test Omkar's claim and see if $ b $ actually is an OmkArray of some array $ a $ . Can you help Ray? The median of a set of numbers $ a_1, a_2, \ldots, a_{2i-1} $ is the number $ c_{i} $ where $ c_{1}, c_{2}, \ldots, c_{2i-1} $ represents $ a_1, a_2, \ldots, a_{2i-1} $ sorted in nondecreasing order.

输入输出格式

输入格式

Each test contains multiple test cases. The first line contains a single integer $ t $ ( $ 1 \leq t \leq 10^4 $ ) — the number of test cases. Description of the test cases follows. The first line of each test case contains an integer $ n $ ( $ 1 \leq n \leq 2 \cdot 10^5 $ ) — the length of the array $ b $ . The second line contains $ n $ integers $ b_1, b_2, \ldots, b_n $ ( $ -10^9 \leq b_i \leq 10^9 $ ) — the elements of $ b $ . It is guaranteed the sum of $ n $ across all test cases does not exceed $ 2 \cdot 10^5 $ .

输出格式

For each test case, output one line containing YES if there exists an array $ a $ such that $ b_i $ is the median of $ a_1, a_2, \dots, a_{2i-1} $ for all $ i $ , and NO otherwise. The case of letters in YES and NO do not matter (so yEs and No will also be accepted).

输入输出样例

输入样例 #1

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

输出样例 #1

NO
YES
NO
YES
YES

输入样例 #2

5
8
-8 2 -6 -5 -4 3 3 2
7
1 1 3 1 0 -2 -1
7
6 12 8 6 2 6 10
6
5 1 2 3 6 7
5
1 3 4 3 0

输出样例 #2

NO
YES
NO
NO
NO

说明

In the second case of the first sample, the array $ [4] $ will generate an OmkArray of $ [4] $ , as the median of the first element is $ 4 $ . In the fourth case of the first sample, the array $ [3, 2, 5] $ will generate an OmkArray of $ [3, 3] $ , as the median of $ 3 $ is $ 3 $ and the median of $ 2, 3, 5 $ is $ 3 $ . In the fifth case of the first sample, the array $ [2, 1, 0, 3, 4, 4, 3] $ will generate an OmkArray of $ [2, 1, 2, 3] $ as - the median of $ 2 $ is $ 2 $ - the median of $ 0, 1, 2 $ is $ 1 $ - the median of $ 0, 1, 2, 3, 4 $ is $ 2 $ - and the median of $ 0, 1, 2, 3, 3, 4, 4 $ is $ 3 $ . In the second case of the second sample, the array $ [1, 0, 4, 3, 5, -2, -2, -2, -4, -3, -4, -1, 5] $ will generate an OmkArray of $ [1, 1, 3, 1, 0, -2, -1] $ , as - the median of $ 1 $ is $ 1 $ - the median of $ 0, 1, 4 $ is $ 1 $ - the median of $ 0, 1, 3, 4, 5 $ is $ 3 $ - the median of $ -2, -2, 0, 1, 3, 4, 5 $ is $ 1 $ - the median of $ -4, -2, -2, -2, 0, 1, 3, 4, 5 $ is $ 0 $ - the median of $ -4, -4, -3, -2, -2, -2, 0, 1, 3, 4, 5 $ is $ -2 $ - and the median of $ -4, -4, -3, -2, -2, -2, -1, 0, 1, 3, 4, 5, 5 $ is $ -1 $ For all cases where the answer is NO, it can be proven that it is impossible to find an array $ a $ such that $ b $ is the OmkArray of $ a $ .

题意翻译

对于一个长度为 $2\times k-1$ 的序列 $a$，我们定义一个长度为 $k$ 的序列 $b$ 是 $a$ 的 _Omk序列_ 仅当其满足对于任意整数 $i\in[1,k]$，$b_i$ 的值等于 $a_1,a_2,\cdots,a_{2\times i-1}$ 这 $2\times i-1$ 个数的中位数。 现在给定 $k$ 和一个长度为 $k$ 的序列 $b$，你需要判断是否存在长度为 $2\times k-1$ 的序列 $a$ 使得 $b$ 是 $a$ 的 _Omk序列_。 $T$ 组数据。 $1\leq T\leq10^4;1\leq n,\sum n\leq2\times10^5;|b_i|\leq10^9;$