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
def main():
    n = int(input())
    a = []
    for i in range(n):
        a.append(int(input()))
    cost = 0
    curr_high = 0
    for i in range(n):

        cost += abs(curr_high-a[i]) + 1
        if i+1 < n:
            if a[i] <= a[i+1]:
                cost += 1
                curr_high = a[i]
            else:
                cost += a[i] - a[i+1]+1
                curr_high = a[i+1]
    print(cost)
if __name__ == '__main__':
    main()
