You are given an array A of N integers that are not necessarily distinct. Additionally, you have a pointer p that initially points to the first element of A$.$

You are allowed to perform the following

types of operations:

$$ Increment p to point to the next element.

$$ Decrement p to point to the previous element.

$$ Erase the element p is currently pointing to$.$ Additionally, after the erase operation you must choose whether p will point to the previous or the next element.

Find the minimum number of operations required to erase all the elements in non$-$ decreasing order.

Input Format

The first line contains an integer, N$,$ denoting the number of elements in A$.$

Each line i of the subsequent lines $($where $0<=$ i $<$ N$)$ contains an integer describing A$[$i$].$ thos

Constraints

$1<=$ N $<=10^5$

$1<=$ A$[$i$]<=10^9$

Sample Test Cases

Case $1$

Input:

$1$

$1$

Output:

$1$

Explanation:

Here since only $1$ element is there we erase it in $1$ operation.

Case $2$

Input:

$4$

$1$

$2$

$3$

$4$

Output:

$4$

Explanation:

The $4$ operations are:

$->$erase and move right

$->$erase and move right

$->$erase and move right

$->$erase finish

Case $3$

Input:

$521332$

Output:

$8$