CF2267D Backrooms Hill

Among the people from the city GR, there is a legend about a hill that leads to the backstage. An array $ b $ consisting of $ m $ integers is called a hill if there exists an index $ k $ ( $ 1\le k\le m $ ) such that the following conditions hold: - The first $ k $ elements are strictly increasing. Formally, for all $ i $ ( $ 1\le i\lt k $ ), $ b_i\lt b_{i+1} $ . - The last $ m-k+1 $ elements are strictly decreasing. Formally, for all $ i $ ( $ k\le i\lt m $ ), $ b_i\gt b_{i+1} $ . You are given an array $ a $ consisting of $ n $ distinct integers. You may perform the following operation any number of times: - Choose any index $ i $ ( $ 1\le i\le n-2 $ ). - Swap $ a_i $ and $ a_{i+2} $ in the array. Your task is to determine whether it is possible to turn array $ a $ into a hill by performing the operation any number of times.

Each test contains multiple test cases. The first line contains the number of test cases $ t $ ( $ 1 \le t \le 10^4 $ ). The description of the test cases follows. The first line of each test case contains an integer $ n $ ( $ 1\le n\le 2\cdot 10^5 $ ) — the length of array $ a $ . The second line of each test case contains $ n $ distinct integers $ a_1, a_2, \ldots, a_n $ ( $ 1\le a_i\le n $ ). It is guaranteed that the sum of $ n $ over all test cases does not exceed $ 2\cdot 10^5 $ .

For each test case, print "YES" if it is possible to make array $ a $ a hill. Otherwise, print "NO". You may print each letter in any case (lowercase or uppercase). For example, the strings "yEs", "yes", "Yes", and "YES" will be accepted as positive answers.

In the first test case, it is impossible to turn array $ a $ into a hill. In the second test case, array $ a $ is already a hill. In the third test case, you can perform the operations as follows: - Swap $ a_1 $ and $ a_3 $ . After this operation, array $ a $ becomes $ [4, 3, 5, 6, 2, 1] $ . - Swap $ a_2 $ and $ a_4 $ . After this operation, array $ a $ becomes $ [4, 6, 5, 3, 2, 1] $ . And array $ [4, 6, 5, 3, 2, 1] $ is a hill.