Check Whether All Elements Are Equal (Kiểm tra mọi phần tử bằng nhau)

Source: Phước Hưng OJ

Version: Phuoc Hung OJ Extended

Problem

Given an integer array

the array is called all-equal if

Determine whether the given array is all-equal. For $n=1$, the condition is always true.

Input

The first line contains $n$. The second line contains $a_0,a_1,\ldots,a_{n-1}$.

Output

Print YES if all elements are equal; 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

5
7 7 7 7 7

Output

YES

Explanation

The sample follows the mathematical definition above.