An array \(A\) is strictly increasing if \(A_i < A_{i+1}\) for every \(1 \le i < N\). Determine whether the given array is strictly increasing.

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 strictly increasing; otherwise, print NO.

Example

Input

5
1 2 4 8 9

Output

YES