Parity Sort

2000ms

262144K

Description:

You have an array of integers $$$a$$$ of length $$$n$$$. You can apply the following operation to the given array:

Swap two elements $$$a_i$$$ and $$$a_j$$$ such that $$$i \neq j$$$, $$$a_i$$$ and $$$a_j$$$ are either both even or both odd.

Determine whether it is possible to sort the array in non-decreasing order by performing the operation any number of times (possibly zero).

For example, let $$$a$$$ = [$$$7, 10, 1, 3, 2$$$]. Then we can perform $$$3$$$ operations to sort the array:

Swap $$$a_3 = 1$$$ and $$$a_1 = 7$$$, since $$$1$$$ and $$$7$$$ are odd. We get $$$a$$$ = [$$$1, 10, 7, 3, 2$$$];
Swap $$$a_2 = 10$$$ and $$$a_5 = 2$$$, since $$$10$$$ and $$$2$$$ are even. We get $$$a$$$ = [$$$1, 2, 7, 3, 10$$$];
Swap $$$a_4 = 3$$$ and $$$a_3 = 7$$$, since $$$3$$$ and $$$7$$$ are odd. We get $$$a$$$ = [$$$1, 2, 3, 7, 10$$$].

Input:

The first line of input data contains a single integer $$$t$$$ ($$$1 \le t \le 10^4$$$) — the number of test cases.

The description of the test cases follows.

The first line of each test case contains one integer $$$n$$$ ($$$1 \le n \le 2 \cdot 10^5$$$) — the length of array $$$a$$$.

The second line of each test case contains exactly $$$n$$$ positive integers $$$a_1, a_2, \dots, a_n$$$ ($$$1 \le a_i \le 10^9$$$) — the elements of array $$$a$$$.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2 \cdot 10^5$$$.

Output:

For each test case, output on a separate line:

YES if the array can be sorted by applying the operation to it some number of times;
NO otherwise.

You can output YES and NO in any case (for example, strings yEs, yes, Yes and YES will be recognized as positive response).

Sample Input:

6
5
7 10 1 3 2
4
11 9 3 5
5
11 3 15 3 2
6
10 7 8 1 2 3
1
10
5
6 6 4 1 6

Sample Output:

YES
YES
NO
NO
YES
NO

Note:

The first test case is explained in the problem statement.

Informação

Provedor Codeforces

Código CF1851B