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
import math as m
def main():
    pass
def binary(n):
    #decimal to binary
    return (bin(n).replace("0b", ""))
def decimal(s):
    #binary to decimal
    return (int(s, 2))
def pow2(n):
    #power of a number base 2
    p = 0
    while n > 1:
        n //= 2
        p += 1
    return (p)
def isPrime(n):
    # if  number is prime in √n time
    if (n == 1):
        return (False)
    else:
        root = int(n ** 0.5)
        root += 1
        for i in range(2, root):
            if (n % i == 0):
                return (False)
        return (True)
def lts(l):
    #list to string ,no spaces
    s=''.join(map(str,l))
    return s
def stl(s):
    #for each character in string to list with no spaces -->
    l=list(s)
    #for space in string  -->
    #l=list(s.split(" "))
    return l
#1000000007
mod=int(1e9)+7
def sinp(): return sys.stdin.readline().strip()
def iinp(): return int(input())
def ninp(): return map(int, sys.stdin.readline().strip().split())
def linp(): return list(map(int, sys.stdin.readline().strip().split()))
def p(a): print(a)
def p2(a,b):print(a,b)
#for _ in range(iinp()):
n=iinp()
h=iinp()
t=h+1
prev=h
for i in range(n-1):
    h=iinp()
    diff=prev-h
    if(diff<0):
        t=t+2+abs(diff)
        prev=h
    elif(diff==0):
        t=t+2
        prev=h
    else:
        t=t+abs(diff)+1+1
        prev=h
print(t)




