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 io;
import sys;
import math;
import bisect as bs;

# IO Method #

def read_int() :
	return map(int, raw_input().split());

def read_string() :
	return raw_input().split();

def read_float() :
	return map(float, raw_input().split());

# End #



# Main Entry #

if __name__ == '__main__': 

	tc = input();
	arr = [];
	for _ in xrange(tc) :
		arr.append(input());
		pass

	res = arr[0];
	for ii in xrange(1, tc) :
		res += abs(arr[ii] - arr[ii-1]);
		res += 1;
		pass
	res += tc;

	print res;
	pass


# End #
