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
PROBLEM = 2
FILE = "P%i" %(PROBLEM) 
outFile = None
#outFile = "P%i_output" %(PROBLEM)
try:
    inFile = open(FILE+".txt")
except:
    pass
if outFile is not None:
    outFile = open(outFile+".txt","w")

def read():
    try:
        return inFile.readline().strip()
    except:
        return raw_input().strip()

def write(*args):
    newline = True
    if type(args[-1]) == bool:
        newline = args[-1]
        args = args[:-1]
    
    output = ""
    for i in xrange(len(args)):
        if i > 0:
            output += " "
        output += str(args[i])
        
    if outFile is None:
        if newline:
            print output
        else:
            print output,
            
    else:
        if newline:
            outFile.write(output+"\n")
        else:
            outFile.write(output+" ")


n = int(read())
h = 0
t = 0
for i in xrange(n):
    height = int(read())
    t += abs(height-h)
    h = height
        
t += n + (n-1)
write(t)


if outFile is not None:
    outFile.close()
