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 sys

def readints() :
    l = sys.stdin.readline()
    return map(int, l.split(' '))

def readstring() :
    l = sys.stdin.readline()[:-1]
    return l

def readint() :
    l = sys.stdin.readline()
    return int(l)

def clearchars(s, chars) :
    for c in chars :
        s = s.replace(c, '')
    return s

def gcd(a, b) :
    if (a < b ) :
        a, b = b, a
    if b == 0 :
        return a
    return gcd(b, a % b)

def hist(a) :
    h = {}
    for x in a :
        try : 
            h[x] += 1
        except KeyError :
            h[x] = 1
    return h

def lucky(n) :
    s = set(str(n))
    return all(map(lambda x: x in '47', s))    

def yslice(a, j) :
    return map(lambda x: x[j], a)

def dist2(a, b) :
    return ((a[0] - b[0]) ** 2 + (a[1] - b[1]) ** 2) ** 0.5

def chain_len(a) :
    l = .0
    for d, e in zip(a, a[1:]) :
        l += dist2(d, e)
    return l

def is_prime(x) :
    sq = int(x ** 0.5) 
    for i in range(2, sq + 1) :
        if x % i == 0 :
            return False
    return True

digits = '0123456789'

def noe() :
    print "NO"
    exit(0)

def yese() :
    print "YES"
    exit(0)

n = readint()
t = -1
hb = 0
for i in range(n) :
    h = readint()
    t += abs(h - hb) + 2
    hb = h
print t
