Squirrel Liss loves nuts. There are $*n*$ trees (numbered $1$ to $*n*$ from west to east) along a street and there is a delicious nut on the top of each tree. The height of the tree $*i*$ is $*h*_{*i*}$. Liss wants to eat all nuts.

Now Liss is on the root of the tree with the number $1$. In one second Liss can perform one of the following actions:

• Walk up or down one unit on a tree.
• Eat a nut on the top of the current tree.
• Jump to the next tree. In this action the height of Liss doesn't change. More formally, when Liss is at height $*h*$ of the tree $*i*$ ($1 ≤ *i* ≤ *n* - 1$), she jumps to height $*h*$ of the tree $*i* + 1$. This action can't be performed if $*h* > *h*_{*i* + 1}$.

Compute the minimal time (in seconds) required to eat all nuts.

Input

The first line contains an integer $*n*$ ($1  ≤  *n* ≤ 10^{5}$) — the number of trees.

Next $*n*$ lines contains the height of trees: $*i*$-th line contains an integer $*h*_{*i*}$ ($1 ≤ *h*_{*i*} ≤ 10^{4}$) — the height of the tree with the number $*i*$.

Output

Print a single integer — the minimal time required to eat all nuts in seconds.