OpenKattis
National University of Singapore

Almost Sorted

You are given an array of of $n$ integers $a_1, a_2, \ldots , a_ n$. An array is almost sorted if it is possible to reverse a continuous subarray to obtain an ascending sorted array. In other words, an array is almost sorted if there exists $1\leq i\leq j\leq n$ such that $a_1\leq a_2\leq \ldots \leq a_{i-1} \leq a_ j \leq a_{j-1}\leq \ldots \leq a_{i+1} \leq a_ i \leq a_{j+1} \leq a_{j+2}\leq \ldots \leq a_ n$

If $a$ is almost sorted, output “Yes”, otherwise output “No” (both without quotes).

Input

The first line of each test case contains one integer n $(2\leq n\leq 300\, 000)$ — the length of the array.

The second line of each test case contains n integers $a_1,a_2,\ldots ,a_ n$ $(1\leq a_ i\leq 10^9)$ — the array given in the problem.

Output

Output “Yes” if $a$ is almost sorted, “No” otherwise.

Sample Input 1 Sample Output 1
4
1 3 2 4
Yes
Sample Input 2 Sample Output 2
4
1 4 2 3
No