A. Sorting with Twostime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou are given an array of integers a_1, a_2, \ldots, a_n. In one operation, you do the following:   Choose a non-negative integer m, such that 2^m \leq n.  Subtract 1 from a_i for all integers i, such that 1 \leq i \leq 2^m. Can you sort the array in non-decreasing order by performing some number (possibly zero) of operations?An array is considered non-decreasing if a_i \leq a_{i + 1} for all integers i such that 1 \leq i \leq n - 1.InputThe first line contains a single integer t (1 \leq t \leq 10^4) — the number of test cases. The description of the test cases follows.The first line of each test case contains a single integer n (1 \leq n \leq 20) — the length of array a.The second line of each test case contains n integers a_1, a_2, \ldots, a_n — the integers in array a (0 \leq a_i \leq 1000).OutputFor each test case, output "YES" if the array can be sorted, and "NO" otherwise.ExampleInput
851 2 3 4 556 5 3 4 496 5 5 7 5 6 6 8 744 3 2 162 2 4 5 3 281 3 17 19 27 57 179 1353 17 57 179 92101 2 3 4 0 6 7 8 9 10Output
YES
YES
YES
NO
NO
NO
YES
YES
NoteIn the first test case, the array is already sorted in non-decreasing order, so we don't have to perform any operations.In the second test case, we can choose m = 1 twice to get the array [4, 3, 3, 4, 4]. Then, we can choose m = 0 once and get the sorted in non-decreasing order array [3, 3, 3, 4, 4].In the third test case, we can choose m = 0 once and get the array [5, 5, 5, 7, 5, 6, 6, 8, 7]. Then, we can choose m = 2 twice and get the array [3, 3, 3, 5, 5, 6, 6, 8, 7]. After that, we can choose m = 3 once and get the sorted in non-decreasing order array [2, 2, 2, 4, 4, 5, 5, 7, 7].For the fourth and fifth test case, it can be shown that the array could not be sorted using these operations.
851 2 3 4 556 5 3 4 496 5 5 7 5 6 6 8 744 3 2 162 2 4 5 3 281 3 17 19 27 57 179 1353 17 57 179 92101 2 3 4 0 6 7 8 9 10
YES YES YES NO NO NO YES YES 
['constructive algorithms', 'sortings', '*800']