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.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.Arrays;
import java.util.StringTokenizer;


public class Main {
static class FastScanner {

BufferedReader reader;
StringTokenizer tokenizer;

public FastScanner(InputStream stream) {
this.reader = new BufferedReader(new InputStreamReader(stream));
}

public int nextInt() throws IOException {
return Integer.parseInt(next());
}

public int[] nextIntegerArray(int n) throws IOException {
int[] a = new int[n];
for (int i = 0; i < a.length; i++) {
a[i] = nextInt();
}
return a;
}

public long[] nextLongArray(int n) throws IOException {
long[] a = new long[n];
for (int i = 0; i < a.length; i++) {
a[i] = nextLong();
}
return a;
}

public int nextInt(int radix) throws IOException {
return Integer.parseInt(next(), radix);
}

public long nextLong() throws IOException {
return Long.parseLong(next());
}

public long nextLong(int radix) throws IOException {
return Long.parseLong(next(), radix);
}

public double nextDouble() throws IOException {
return Double.parseDouble(next());
}

public BigInteger nextBigInteger() throws IOException {
return new BigInteger(next());
}

public BigInteger nextBigInteger(int radix) throws IOException {
return new BigInteger(next(), radix);
}

public String next() throws IOException {
if (tokenizer == null || !tokenizer.hasMoreTokens()) {
tokenizer = new StringTokenizer(reader.readLine());
return this.next();
}
return tokenizer.nextToken();
}

public void close() throws IOException {
this.reader.close();
}
}

                   //SOLUTION //


	FastScanner in = new FastScanner(System.in);
	PrintWriter out = new PrintWriter(System.out);
	
	public static void main(String[] args) throws IOException{
    new Main().solve();
    }//void main
	
	void solve() throws IOException{
		int n=in.nextInt(),h1=0,h2;
		long count=0;
		for(int i=0; i< n; i++){
			h2=in.nextInt();
			if(h2>=h1)
				count+=h2-h1+1;
			else
				count+=h1-h2+1;
			h1=h2;
			count++;
		}
		out.println(--count);
		in.close();
		out.close();
	}
	
}
