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 ≤ 105) — the number of trees.

Next n lines contains the height of trees: i-th line contains an integer h**i (1 ≤ h**i ≤ 104) — the height of the tree with the number i.

Output

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

Samples

2
1
2

5

5
2
1
2
1
1

14