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
#                          JAI SHREE RAM

import math; from collections import *
import sys; from functools import reduce

# sys.setrecursionlimit(10**6)
def get_ints(): return map(int, input().strip().split())
def get_list(): return list(get_ints())
def get_string(): return list(input().strip().split())
def printxsp(*args): return print(*args, end="")
def printsp(*args): return print(*args, end=" ")

UGLYMOD = int(1e9)+7; SEXYMOD = 998244353; MAXN = int(1e5)

# sys.stdin=open("input.txt","r");sys.stdout=open("output.txt","w")

# for _testcases_ in range(int(input())):
N = int(input())
li = [] 
for i in range(N):
    li.append(int(input()))
t = li[0]
prev = li[0]
for i in range(1, N):
    if li[i] >= prev:
        t += (li[i] - prev) + 1
    else:
        t += prev - li[i] + 1
    prev = li[i]
print(t+N)



'''
>>> COMMENT THE STDIN!! CHANGE ONLINE JUDGE !!
THE LOGIC AND APPROACH IS MINE @luctivud ( UDIT GUPTA )
Link may be copy-pasted here if it's taken from other source.
DO NOT PLAGIARISE.
>>> COMMENT THE STDIN!! CHANGE ONLINE JUDGE !!
'''