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
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.io.File;
import java.io.FileWriter;
import java.util.StringTokenizer;
import java.math.BigInteger;
import java.util.Arrays;
import java.util.LinkedList;
public class JavaApplication79 {
    static class pair {
       int first; 
       int second;
       public pair(int x,int y){
           first =x;
           second = y;
           
       }
   
    }
    public static int nextInt(StringTokenizer tok){
        return Integer.parseInt(tok.nextToken());
    }
    public static void main(String[] args) throws Exception{
       BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
      int n= Integer.parseInt(in.readLine());
      int m= Integer.parseInt(in.readLine());
      int x=0;
long sum=0;
sum+=m+1;
for(int i= 0 ; i< n-1; i++){
x=Integer.parseInt(in.readLine());
if(x<m){
   sum+=m-x+1; m=x;
}
else{
sum+=x-m+1;
    m=x;
}
}
sum+=n-1;
        System.out.println(sum);
    }
}