Given an array of n numbers, you are asked if you can sort it by removing at most a single element from it. Note the array is considered to be sorted if it’s ordered in both ascending and descending directions.

Input

The first line of the input contains a single integer n (1 ≤ n ≤ ) the number of elements in the array. The next line contains n integers separated by a space .

Output

The program should print Yes in case it’s possible to make the list sorted by removing at most a single element and No otherwise.