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.

Examples

Input

Output

3
1 2 3

Yes

4
5 4 8 2

Yes

7
1 4 5 0 6 7 2

No

6
1 10 2 3 4 5

Yes

6
1 10 -1 20 30 40

Yes

6
1 10 -1 20 30 20

No

Hint

You can define a function that would check for the existence of a solution for ONLY the non-decreasing part. Then use the same function on the initial array and the reversed array.