#P1545A. AquaMoon and Strange Sort

AquaMoon and Strange Sort

No submission language available for this problem.

Description

AquaMoon has nn friends. They stand in a row from left to right, and the ii-th friend from the left wears a T-shirt with a number aia_i written on it. Each friend has a direction (left or right). In the beginning, the direction of each friend is right.

AquaMoon can make some operations on friends. On each operation, AquaMoon can choose two adjacent friends and swap their positions. After each operation, the direction of both chosen friends will also be flipped: left to right and vice versa.

AquaMoon hopes that after some operations, the numbers written on the T-shirt of nn friends in the row, read from left to right, become non-decreasing. Also she wants, that all friends will have a direction of right at the end. Please find if it is possible.

The input consists of multiple test cases. The first line contains a single integer tt (1t501 \leq t \leq 50) — the number of test cases.

The first line of each test case contains a single integer nn (1n1051 \leq n \leq 10^5) — the number of Aquamoon's friends.

The second line contains nn integers a1,a2,,ana_1, a_2, \dots, a_n (1ai1051 \leq a_i \leq 10^5) — the numbers, written on the T-shirts.

It is guaranteed that the sum of nn for all test cases does not exceed 10510^5.

For each test case, if there exists a possible sequence of operations, print "YES" (without quotes); otherwise, print "NO" (without quotes).

You can print each letter in any case (upper or lower).

Input

The input consists of multiple test cases. The first line contains a single integer tt (1t501 \leq t \leq 50) — the number of test cases.

The first line of each test case contains a single integer nn (1n1051 \leq n \leq 10^5) — the number of Aquamoon's friends.

The second line contains nn integers a1,a2,,ana_1, a_2, \dots, a_n (1ai1051 \leq a_i \leq 10^5) — the numbers, written on the T-shirts.

It is guaranteed that the sum of nn for all test cases does not exceed 10510^5.

Output

For each test case, if there exists a possible sequence of operations, print "YES" (without quotes); otherwise, print "NO" (without quotes).

You can print each letter in any case (upper or lower).

Samples

Sample Input 1

3
4
4 3 2 5
4
3 3 2 2
5
1 2 3 5 4

Sample Output 1

YES
YES
NO

Note

The possible list of operations in the first test case:

  1. Swap a1a_1 and a2a_2. The resulting sequence is 3,4,2,53, 4, 2, 5. The directions are: left, left, right, right.
  2. Swap a2a_2 and a3a_3. The resulting sequence is 3,2,4,53, 2, 4, 5. The directions are: left, left, right, right.
  3. Swap a1a_1 and a2a_2. The resulting sequence is 2,3,4,52, 3, 4, 5. The directions are: right, right, right, right.