An array \(A\) of length \(N\) is a palindrome if \(A_i = A_{N-i+1}\) for every \(1 \le i \le N\). Determine whether the given array is a palindrome.

Input

The first line contains \(N\). The second line contains \(N\) integers \(A_i\).

The input satisfies:

• \(1 \le N \le 10^5\)
• \(|A_i| \le 10^9\)

Output

Print YES if A is a palindrome; otherwise, print NO.

Example

Input

5
1 2 3 2 1

Output

YES