CF2195B Heapify 1

You are given a permutation $ a $ of length $ n $ $ ^{\text{∗}} $ . You can perform the following operation any number of times (possibly zero): - Select an index $ i $ ( $ 1 \le i \le \frac{n}{2} $ ), and swap $ a_i $ and $ a_{2i} $ . For example, when $ a=[1,4,2,3,5] $ , you can swap $ a_2 $ and $ a_4 $ to make it $ [1,3,2,4,5] $ , but you cannot swap $ a_2 $ and $ a_3 $ . Please determine if the sequence $ a $ can be sorted in increasing order. $ ^{\text{∗}} $ A permutation of length $ n $ is an array consisting of $ n $ distinct integers from $ 1 $ to $ n $ in arbitrary order. For example, $ [2,3,1,5,4] $ is a permutation, but $ [1,2,2] $ is not a permutation ( $ 2 $ appears twice in the array), and $ [1,3,4] $ is also not a permutation ( $ n=3 $ but there is $ 4 $ in the array).

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 a single integer $ n $ ( $ 1 \le n \le 2 \cdot 10^5 $ ). 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 $ .

If $ a $ can be sorted in increasing order, output "YES" on a separate line. Otherwise, output "NO" on a separate line. You can output the answer in any case. For example, the strings "yEs", "yes", and "Yes" will also be recognized as positive responses.

In the first test case, $ a $ is $ [1,4,3,2,5] $ . You can sort $ a $ in increasing order by swapping $ a_2 $ and $ a_4 $ . Therefore, the answer is "YES". In the second test case, $ a $ is $ [1,4,2,3,5] $ . It is impossible to sort $ a $ in increasing order. Therefore, the answer is "NO".