Larry has been given a permutation of a sequence of natural numbers incrementing from as an array. He must determine whether the array can be sorted using the following operation any number of times:
- Choose any consecutive indices and rotate their elements in such a way that .
For example, if :
A rotate
[1,6,5,2,4,3] [6,5,2]
[1,5,2,6,4,3] [5,2,6]
[1,2,6,5,4,3] [5,4,3]
[1,2,6,3,5,4] [6,3,5]
[1,2,3,5,6,4] [5,6,4]
[1,2,3,4,5,6]
YES
On a new line for each test case, print YES if can be fully sorted. Otherwise, print NO.
Function Description
Complete the larrysArray function in the editor below. It must return a string, either YES or NO.
larrysArray has the following parameter(s):
- A: an array of integers
Input Format
The first line contains an integer , the number of test cases.
The next pairs of lines are as follows:
- The first line contains an integer , the length of .
- The next line contains space-separated integers .
Constraints
- integers that increment by from to
Output Format
For each test case, print YES if can be fully sorted. Otherwise, print NO.
Sample Input
3
3
3 1 2
4
1 3 4 2
5
1 2 3 5 4
Sample Output
YES
YES
NO
Explanation
In the explanation below, the subscript of denotes the number of operations performed.
Test Case 0:
is now sorted, so we print on a new line.
Test Case 1:
.
.
is now sorted, so we print on a new line.
Test Case 2:
No sequence of rotations will result in a sorted . Thus, we print on a new line.