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
inf = float("inf")
# sys.setrecursionlimit(1000000)


# abc='abcdefghijklmnopqrstuvwxyz'
# abd={'a': 0, 'b': 1, 'c': 2, 'd': 3, 'e': 4, 'f': 5, 'g': 6, 'h': 7, 'i': 8, 'j': 9, 'k': 10, 'l': 11, 'm': 12, 'n': 13, 'o': 14, 'p': 15, 'q': 16, 'r': 17, 's': 18, 't': 19, 'u': 20, 'v': 21, 'w': 22, 'x': 23, 'y': 24, 'z': 25}
mod,MOD=1000000007,998244353
# vow=['a','e','i','o','u']
# dx,dy=[-1,1,0,0],[0,0,1,-1]

# from collections import deque, Counter, OrderedDict,defaultdict
# from heapq import nsmallest, nlargest, heapify,heappop ,heappush, heapreplace
from math import ceil,floor,log,sqrt,factorial,pow,pi,gcd,log10,atan,tan
# from bisect import bisect_left,bisect_right


def get_array(): return list(map(int , sys.stdin.readline().strip().split()))
def get_ints(): return map(int, sys.stdin.readline().strip().split())
def get_strs(): return map(str, sys.stdin.readline().strip().split())
def input(): return sys.stdin.readline().strip()

n = int(input())
Arr = []
for i in range(n):
    Arr.append(int(input()))
ans = Arr[0]+1
curr = Arr[0]
for i in range(1,n):
    # if Arr[i]>=Arr[i-1]:
    #     ans+=1 + (Arr[i] - curr) +1
    #     curr = Arr[i]
    # else:
    #     ans+=(curr-Arr[i]) + 1 + 1
    #     curr = Arr[i]
    ans+=abs(curr-Arr[i])+2
    curr = Arr[i]
print(ans)

