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B. Roadside Trees (Simplified Edition)

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputSquirrel 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.

Examples

Input

2

1

2

Output

5

Input

5

2

1

2

1

1

Output

14

Codeforces (c) Copyright 2010-2019 Mike Mirzayanov

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