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
n = input()
l=[]
for i in range(0,n):
    h = input()
    l.append(h)

#print l

time = l[0]+1
#print time


for i in range(1,len(l)):
    eats = 0
    jumps = 0
    climbs = 0
    if l[i] > l[i-1]:
        jumps+=1
        climbs = l[i] - l[i-1]
        eats+=1
        time = time + jumps + climbs + eats
        #print "time "+str(time)
    else:
        if l[i] < l[i-1]:
            climbs = l[i-1]-l[i]
            jumps+=1
            eats+=1
            time = time + jumps + climbs + eats
            #print "time "+str(time)
        else:
            jumps+=1
            eats+=1
            time = time + jumps + eats

print time
