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, math
def rs():
    return sys.stdin.readline().strip()
def ri():
    return int(sys.stdin.readline().strip())
def ras():
    return sys.stdin.readline().strip()
def rai():
    return map(int,sys.stdin.readline().strip().split())
def main():
    n = ri()
    arr = [ri() for x in xrange(n)]


#    min_count = 0

#    counts = []

    default_count = arr[0] + 1
#    counts[0] = default_count
    for i in xrange(1,n):
        default_count += 2 + abs(arr[i]-arr[i-1])
#        counts[i] = default_count

#    for i in xrange(n):
#        count = 0
#        for j in xrange(n):
#            count += arr[j]
#
    print default_count

if __name__ == "__main__":
    main()