Problem3357--Roadside Trees (Simplified Edition)

3357: Roadside Trees (Simplified Edition)

Time Limit: 2 Sec  Memory Limit: 256 MB
Submit: 0  Solved: 0
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Description

time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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 hi. 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>hi+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 hi (1≤hi≤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.

Examples
Input
2
1
2
Output
5
Input
5
2
1
2
1
1
Output
14

Source/Category

 
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