B. Penchick and Satay Sticks
brute force; greedy; sortings
Penchick and his friend Kohane are touring Indonesia, and their next stop is in Surabaya!In the bustling food stalls of Surabaya, Kohane bought \(n\) satay sticks and arranged them in a line, with the \(i\)-th satay stick having length \(p_i\). It is given that \(p\) is a permutation\(^{\text{∗}}\) of length \(n\).Penchick wants to sort the satay sticks in increasing order of length, so that \(p_i=i\) for each \(1\le i\le n\). For fun, they created a rule: they can only swap neighboring satay sticks whose lengths differ by exactly \(1\). Formally, they can perform the following operation any number of times (including zero): Select an index \(i\) (\(1\le i\le n-1\)) such that \(|p_{i+1}-p_i|=1\); Swap \(p_i\) and \(p_{i+1}\). Determine whether it is possible to sort the permutation \(p\), thus the satay sticks, by performing the above operation.\(^{\text{∗}}\)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 \(t\) (\(1 \le t \le 2\cdot 10^5\)). 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 number of satay sticks.The second line of each test case contains \(n\) integers \(p_1, p_2, \ldots, p_n\) (\(1 \le p_i \le n\)) — the permutation \(p\) representing the length of the satay sticks.It is guaranteed that the sum of \(n\) over all test cases does not exceed \(2\cdot 10^5\).
For each test case, output ""YES"" if it is possible to sort permutation \(p\) by performing the operation. Otherwise, output ""NO"".You can output the answer in any case (upper or lower). For example, the strings ""yEs"", ""yes"", ""Yes"", and ""YES"" will be recognized as positive responses.
In the first test case, we can sort permutation \(p = [2, 1, 3, 4]\) by performing an operation on index \(1\) (\(|p_2 - p_1| = |1 - 2| = 1\)), resulting in \(p = [1, 2, 3, 4]\).In the second test case, it can be proven that it is impossible to sort permutation \(p = [4, 2, 3, 1]\) by performing the operation. Here is an example of a sequence of operations that can be performed on the permutation: Select \(i = 2\) (\(|p_3 - p_2| = |3 - 2| = 1\)). This results in \(p = [4, 3, 2, 1]\). Select \(i = 1\) (\(|p_2 - p_1| = |3 - 4| = 1\)). This results in \(p = [3, 4, 2, 1]\). Select \(i = 3\) (\(|p_4 - p_3| = |1 - 2| = 1\)). This results in \(p = [3, 4, 1, 2]\). Unfortunately, permutation \(p\) remains unsorted after performing the operations.