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
    
def deeznuts(n,t):
    s = 0
    cp = 0
    if n == 1 :
        return t[0]+1
    for i in range(n-1):
        s = s+1+t[i]-cp
        if t[i]>t[i+1]:
            s = s+1-t[i+1]+t[i]
            cp = t[i+1]
        if t[i]<=t[i+1]:
            s = s+1
            cp = t[i]
    if t[n-1]>t[n-2]:
        return s+t[n-1]-t[n-2]+1
    return s+1    

if __name__ == '__main__':    
    input = sys.stdin.read()
    data = list(map(int, input.split()))
    n = (data[0])
    t = list(data[1:])
    print(deeznuts(n,t))