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
#include <bits/stdc++.h>
using namespace std;
bool same_character(string s, string t) {
  long long int n = s.length();
  for (long long int i = 0; i < n; i++) {
    for (long long int j = 0; j < n; j++) {
      if (s[i] == t[j]) {
        return true;
      }
    }
  }
  return false;
}
long long int min_squirrel(long long int* arr, long long int n, long long int i,
                           long long int y) {
  long long int t = 0;
  if (i == n - 1) {
    t += arr[n - 1] - y + 1;
    return t;
  }
  if (arr[i] >= y) {
    t += arr[i] - y;
  }
  t++;
  if (arr[i] < arr[i + 1]) {
    t += min_squirrel(arr, n, i + 1, arr[i]) + 1;
  } else {
    t += arr[i] - arr[i + 1] + min_squirrel(arr, n, i + 1, arr[i + 1]) + 1;
  }
  return t;
}
void solve() {
  long long int n;
  cin >> n;
  long long int arr[n];
  for (long long int i = 0; i < n; i++) {
    cin >> arr[i];
  }
  cout << min_squirrel(arr, n, 0, 0);
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  int t = 1;
  while (t > 0) {
    solve();
    t--;
  }
  return 0;
}
