You are given S - a sequence of n integers S = s₁, s₂ ... s_n. Please, compute if it is possible to split S into two parts: s₁, s₂ ... s_i and s_i+1, s_i+2 ... s_n (1 <= i < n) in such a way that the first part is strictly decreasing while the second is strictly increasing one.

Input data specification

In the first line you are given an integer 2 <= n <= 100 and in the following line n integers
-100 <= s_i <= 100.

Output data specification

One word Yes or No.

Example 1

Input:
5
-1 2 -1 1 -1

Output:
No

Example 2

Input:
6
3 1 -2 -2 -1 3

Output:
Yes

Example 3

Input:
6
2 2 1 0 1 2

Output:
No