You are given an array A of N integers that are not necessarily distinct. Additionally, y$$u 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 eraselsperation 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 N Subsequent lines contain an integer describing A$[$i$]$

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

$1<=$N$<=10^9$

Sample Input ;

$1$

$1$

Sample Output:

$1$

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

Sample Input

$4$

$1$

$2$

$3$

$4$

Sample Output

$4$

The $4$ operations are

$->$ erase and move right

$->$ erase and move right

$->$ erase and move right

$->$ erase finish

Sample Input

$5$

$2$

$1$

$3$

$3$

$2$

Sample Output

$8$