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 java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.*;

public class Codeforces {

    static Scanner sc = new Scanner(System.in);
    static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

    public static long GCD(long a,long b){
        if (b == 0)
            return a;
        return GCD(b,a%b);
    }

    static int highestPowerOf2(int n) {
        int p = (int)(Math.log(n) /
                Math.log(2));
        return (int)Math.pow(2, p);
    }

    public static int binSearch(long[] a,long x){
        int l = 0;
        int r = a.length - 1;
        while (l <= r){
            int mid = l + (r-l)/2;
            if (a[mid]==x)
                return 1;
            else if (a[mid] < x)
                l = mid+1;
            else
                r = mid-1;
        }
        return -1;
    }

    public static int upperBound(long[] arr,long key){
        int start=0;int end=arr.length-1;
        int idx=-1;
        int mid;
        while(start<=end){
            int i=(start+end)/2;
            if(arr[i]<key){
                start=i+1;
            }
            else if(arr[i]>key){
                end=i-1;
            }
            else{
                idx=i;
                start=i+1;
            }
        }

        return idx;    }

    public static int lowerBound(long[] arr,long key){
        int start=0;int end=arr.length-1;
        int idx=-1;
        int mid;
        while(start<=end){
            int i=(start+end)/2;
            if(arr[i]<key){
                start=i+1;
            }
            else if(arr[i]>key){
                end=i-1;
            }
            else{
                idx=i;
                end=i-1;
            }
        }
        return idx;
    }

    public static int searchInsert(long[] nums, long target) {
        int s=0,e=nums.length-1;
        int mid;
        if(target<nums[0]){
            return 0;
        }
        while(s<=e){
            mid=(s+e)/2;
            if(nums[mid]>target){
                e=mid-1;
            }
            else if(nums[mid]==target){
                return mid;
            }
            else{
                s=mid+1;
            }
        }
        return s;
    }

    public static class Pair<T1,T2>{
        T1 first;
        T2 second;
        Pair(T1 a,T2 b){
            this.first = a;
            this.second = b;
        }

        @Override
        public String toString() {
            return "[" + first + ", " + second + "]";
        }
    }

    static boolean isPrime(long n) {
        if (n <= 1)
            return false;
        if (n <= 3)
            return true;

        if (n % 2 == 0 || n % 3 == 0)
            return false;

        for (long i = 5; i <= Math.sqrt(n); i = i + 6)
            if (n % i == 0 || n % (i + 2) == 0)
                return false;

        return true;
    }

    public static long fastExpo(long a,int n,int mod){
        if (n == 0)
            return 1;
        else{
            if ((n&1) == 1){
                long x = fastExpo(a,n/2,mod);
                return (((a*x)%mod)*x)%mod;
            }
            else{
                long x = fastExpo(a,n/2,mod);
                return (((x%mod)*(x%mod))%mod)%mod;
            }
        }
    }

    public static long modInverse(long n,int p){
        return fastExpo(n,p-2,p);
    }

    public static long nCr(int n,int r,long[] fact,int mod){
        long val =  (((fact[n] * modInverse(fact[r],mod))%mod)*modInverse(fact[n-r],mod))%mod;
        return val;
    }

    public static void factorial(long[] fact,int n,int mod){
        for (int i=1;i<=n;i++){
            fact[i] = (fact[i-1] * i)%mod;
        }
    }

    public static int log2(long val){
        return (int) Math.floor(Math.log(val)/Math.log(2));
    }

    public static void solve() throws IOException {
        int n = sc.nextInt();
        int[] a = new int[n];
        for (int i=0;i<n;i++){
            a[i] = sc.nextInt();
        }
        int ans = a[0] + 1;
        int curr = a[0];
        for (int i=1;i<n;i++){
            if (curr <=  a[i]){
                ans += a[i] - curr + 2;
            }
            else{
                ans += curr - a[i] + 2;
            }
            curr = a[i];
        }
        System.out.println(ans);
    }
    public static void main(String[] args) throws IOException{
        int t;
        //t = sc.nextInt();
        t = 1;
        while (t-- > 0){
            solve();
        }
    }
}

