Check a Nondecreasing Array (Kiểm tra mảng không giảm)

Source: Phước Hưng OJ

Version: Phuoc Hung OJ Extended

Problem

Given $a_0,a_1,\ldots,a_{n-1}$, the array is nondecreasing if

Equal adjacent values are allowed. Determine whether the array satisfies this condition without sorting it.

Input

The first line contains $n$. The second line contains $n$ integers $a_i$.

Output

Print YES if the array is nondecreasing; otherwise print NO.

Subtask

Subtask 1 (20 points): $1\le n\le10$, $|a_i|\le10^3$.

Subtask 2 (30 points): $1\le n\le5000$, $|a_i|\le10^6$.

Subtask 3 (50 points): $1\le n\le2\cdot10^5$, $|a_i|\le10^9$.

Example

Input

6
-3 -3 0 4 4 10

Output

YES

Explanation

The sample follows the mathematical definition above.