Is it a Heap?

The Heap data structure can be implemented using an array.

The array must maintain the main heap property: for each i~(1 \le i \le n) next conditions must hold:

• If 2i \le n, then a_i \le a_{2i}

• If 2i + 1 \le n, then a_i \le a_{2i+1}

The array of integers is given. Determine whether it is a heap.

Output

Print "YES", if the array is a heap and "NO" otherwise.