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 \le i \le n-1), she jumps to height h of the tree i+1. This action can't be performed if h \gt hi+1.
Compute the minimal time (in seconds) required to eat all nuts.

The first line contains an integer n (1 \le n \le 105) - the number of trees.

Next n lines contains the height of trees: i-th line contains an integer hi (1 \le hi \le 104) - the height of the tree with the number i.

Print a single integer - the minimal time required to eat all nuts in seconds.