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
from collections import Counter, defaultdict

BS="0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ"
def to_base(s, b):
    res = ""
    while s:
        res+=BS[s%b]
        s//= b
    return res[::-1] or "0"
alpha = "abcdefghijklmnopqrstuvwxyz"
from math import floor, ceil,pi



n = int(input())
nums = [int(input()) for i in range(n)]

tot = 0

pos = 0
height = 0
while pos < len(nums):

    cur = nums[pos]
    tot += (cur-height)+1
    height = cur
    #print(pos, tot, height)
    if pos == len(nums)-1:
        break
    else:
        ne = nums[pos+1]
        if ne < height:
            tot += height-ne
            height = ne
        tot += 1
    pos += 1
    #print(pos, tot)
print(tot)
