Unimodal Array

1000ms

262144K

Description:

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.

Input:

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

The second line contains n integers a₁, a₂, ..., a_n (1 ≤ a_i ≤ 1 000) — the elements of the array.

Output:

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

You can output each letter in any case (upper or lower).

Sample Input:

6
1 5 5 5 4 2

Sample Output:

YES

Sample Input:

5
10 20 30 20 10

Sample Output:

YES

Sample Input:

4
1 2 1 2

Sample Output:

NO

Sample Input:

7
3 3 3 3 3 3 3

Sample Output:

YES

Note:

In the first example the array is unimodal, because it is strictly increasing in the beginning (from position 1 to position 2, inclusively), that it is constant (from position 2 to position 4, inclusively) and then it is strictly decreasing (from position 4 to position 6, inclusively).

Informação

Provedor Codeforces

Código CF831A