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 math
#n, m = input().split()
#n = int (n)
#m = int (m)
#k = int (k)
#s = input()
x = int(input())

#h = list(map(int, input().split()))
#b = list(map(int, input().split()))
h =[0]*x
for i in range (x):
    h[i] = int(input())
#x1, y1, x2, y2 =map(int,input().split())
#n = int(input())
#f = []
#f = [0]*n
#t = [0]*n
#f = []
s = h[0]+1

#h = [""] * n
#f1 = sorted(f, key = lambda tup: tup[0])

#f1 = sorted(t, key = lambda tup: tup[0])
 
for i in range (1, x):
    s += 2 + abs(h[i]-h[i-1])
print(s)

