Statement

Array of integers is unimodal, if:

• it is strictly increasing in the beginning;
• after that it is constant;
• after that it is strictly decreasing.

The first block (increasing) and the last block (decreasing) may be absent. It is allowed that both of this blocks are absent.

For example, the following three arrays are unimodal: $[5,7,11,11,2,1]$ , $[4,4,2]$ , $[7]$ , but the following three are not unimodal: $[5,5,6,6,1]$ , $[1,2,1,2]$ , $[4,5,5,6]$ .

Write a program that checks if an array is unimodal.

Format

Input

The first line contains integer $n$ ( $1<=n<=100$ ) — the number of elements in the array.

The second line contains $n$ integers $a_{1},a_{2},...,a_{n}$ ( $1<=a_{i}<=1000$ ) — the elements of the array.

Output

Print "YES" if the given array is unimodal. Otherwise, print "NO".

Sample

6
1 5 5 5 4 2

YES

5
10 20 30 20 10

YES

4
1 2 1 2

NO

7
3 3 3 3 3 3 3

YES