The average miner Vaganych took refresher courses. As soon as a miner completes the courses, he should take exams. The hardest one is a computer test called "Testing Pants for Sadness".

The test consists of n questions; the questions are to be answered strictly in the order in which they are given, from question 1 to question n. Question i contains ai answer variants, exactly one of them is correct. 

A click is regarded as selecting any answer in any question. The goal is to select the correct answer for each of the n questions. If Vaganych selects a wrong answer for some question, then all selected answers become unselected and the test starts from the very beginning, from question 1 again. But Vaganych remembers everything. The order of answers for each question and the order of questions remain unchanged, as well as the question and answers themselves.

Vaganych is very smart and his memory is superb, yet he is unbelievably unlucky and knows nothing whatsoever about the test's theme. How many clicks will he have to perform in the worst case?

Input

The first line contains a positive integer n (1 ≤ n ≤ 100). It is the number of questions in the test. The second line contains space-separated n positive integers ai (1 ≤ ai ≤ 109), the number of answer variants to question i.

Output

Print a single number — the minimal number of clicks needed to pass the test it the worst-case scenario. 

Please do not use the %lld specificator to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specificator.

Examples

Input

2
1 1


Output

2

Input

2
2 2


Output

5

Input

1
10


Output

10

Note

Note to the second sample. In the worst-case scenario you will need five clicks: 

  * the first click selects the first variant to the first question, this answer turns out to be wrong. 
  * the second click selects the second variant to the first question, it proves correct and we move on to the second question; 
  * the third click selects the first variant to the second question, it is wrong and we go back to question 1; 
  * the fourth click selects the second variant to the first question, it proves as correct as it was and we move on to the second question; 
  * the fifth click selects the second variant to the second question, it proves correct, the test is finished. 
import java.io.*;
import java.util.*;
import java.math.*;
import static java.lang.Math.*;

public class Main implements Runnable {

    StreamTokenizer in;
    BufferedReader reader;
    PrintWriter out;
    StringTokenizer tok;
    boolean timus = System.getProperty("ONLINE_JUDGE")!=null;
    boolean codeforces = true;
    final double eps = 1e-9;
    
    public static void main(String[] args) throws Exception {
        new Thread(new Main()).start();
    }
    
    @Override
    public void run() {
        try {
            if (codeforces) {
                reader = new BufferedReader(new InputStreamReader(System.in));
                in = new StreamTokenizer(reader);
                out= new PrintWriter (new OutputStreamWriter(System.out));
                tok = new StringTokenizer("");
                solve();
                out.flush();
            } else
            if (!timus) {
                long begMem = Runtime.getRuntime().totalMemory() - Runtime.getRuntime().freeMemory();
                long t1 = System.currentTimeMillis();
                reader = new BufferedReader(new InputStreamReader(System.in));
                in = new StreamTokenizer(reader);
                out= new PrintWriter (new OutputStreamWriter(System.out));
                tok = new StringTokenizer("");
                solve();
                long endMem = Runtime.getRuntime().totalMemory() - Runtime.getRuntime().freeMemory();
                out.flush();
                long t2 = System.currentTimeMillis();
                System.out.println("Time:"+(t2-t1));
                System.out.println("Memory:"+(endMem-begMem));
                System.out.println("Total memory: " + (Runtime.getRuntime().totalMemory() - Runtime.getRuntime().freeMemory()));
            } else {
                reader = new BufferedReader(new FileReader("input.txt"));
                in = new StreamTokenizer(reader);
                out= new PrintWriter (new FileWriter("output.txt"));
                tok = new StringTokenizer("");
                solve();
                out.flush();
                out.close();
            }
        }
        catch (Exception ex) {
            System.out.println("fail");
            System.exit(1);
        }
    }
    
    public class Chess {
        String coord;
        
        public Chess(String s){
            this.coord=s;
        }
        
        public int toInteger(char s) {
            if (s=='a'||s=='A') return 1;
            else if (s=='b'||s=='B') return 2;
            else if (s=='c'||s=='C') return 3;
            else if (s=='d'||s=='D') return 4;
            else if (s=='e'||s=='E') return 5;
            else if (s=='f'||s=='F') return 6;
            else if (s=='g'||s=='G') return 7;
            else if (s=='h'||s=='H') return 8;
            else return -1;
        }
        
        public String toString(int s) {
            if (s==1) return "a";
            else if (s==2) return "b";
            else if (s==3) return "c";
            else if (s==4) return "d";
            else if (s==5) return "e";
            else if (s==6) return "f";
            else if (s==7) return "g";
            else if (s==8) return "h";
            else return "0";
        }
        
        public pair getPair() {
            String j="";
            j+=coord.charAt(1);
            pair p = new pair(toInteger(coord.charAt(0)),Integer.parseInt(j));
            if (p.x!=-1)
            return p; else
                return new pair(0,0);
        }
        
        public String returnPair(pair p) {
            return toString(p.x)+p.y;
        }
    }
    
    public int nextInt() throws Exception {
        in.nextToken();
        return (int) in.nval;
    }
    
    public String next() throws Exception {
        in.nextToken();
        return in.sval;
    }
    
    public String nextLine() throws Exception {
        return reader.readLine();
    }
    
    public String nextString() throws Exception {
        while (!tok.hasMoreTokens())
            tok = new StringTokenizer(reader.readLine());
        return tok.nextToken();
    }
    
    public long nextLong() throws Exception {
        return Long.parseLong(nextString());
    }
    
    public double nextDouble() throws Exception {
        in.nextToken();
        return in.nval;
    }
    
    public class pair {
        int x;
        int y;
        
        public pair(int x, int y) {
            this.x=x;
            this.y=y;
        }
    }
    
    public int gcd(int a, int b) {
        if (a== 0||b==0) return 1;
        if (a<b) {
                int c=b;
                b=a;
                a=c;
        }
        while (a%b!=0) {
                a =a%b;
                if (a<b) {
                        int c=b;
                        b=a;
                        a=c;
                }
        }
        return b;
    }
    
     public int pow(int a, int n) {
         if (n==0) return 1;
         int k=n, b=1, c=a;
         while (k!=0) {
                 if (k%2==0) {
                         k/=2;
                         c*=c;
                 } else {
                         k--;
                         b*=c;
                 }
         }
         return b;
     }
    
    public int lcm(int a, int b) {
        return a*b/gcd(a,b);
    }
    
    public class pairs implements Comparable<pairs> {
        int x;
        int y;
        
        public pairs(int x, int y) {
            this.x=x;
            this.y=y;
        }

        @Override
        public int compareTo(pairs obj) {
            if (this.x<((pairs)obj).x) return 1;
            else if (this.x==(obj).x&&this.y<(obj).y) return 1;
            else if (this.x==(obj).x&&this.y==(obj).y)return 0; else
                return -1;
        }   
    }
    
    public class Graf {
        
        int [][] a;
        int [] colors;
        ArrayList <String> points = new ArrayList<String>();
        LinkedList <Integer> queue = new LinkedList <Integer>();
        boolean [] used;
        boolean cycle;
        int numberOfCycle;
        
        public Graf(int [][]a,String s[]) {
            this.a=new int [s.length][s.length];
            this.a=a;
            this.colors=new int [s.length];
            this.used=new boolean[s.length];
            for (int i=0; i<s.length;i++) {
                this.colors[i]=0;
                this.points.add(s[i]);
            }
            Arrays.fill(this.used, false);
        }
        
        public void bfs(int i) {
            this.queue.add(i);
            while (!this.queue.isEmpty())
            {
                i = this.queue.pop();
                out.print(points.get(i)+" ");
                this.used[i]=true;
                for (int j=0; j<this.points.size();j++) {
                    if (this.a[i][j]==1&&!this.queue.contains(j)&&!this.used[j]) {
                        this.a[i][j]=0;
                        this.a[j][i]=0;
                        this.queue.addLast(j);
                    }
                }
            }
        }
        
        public void dfs(int i) {
            this.colors[i]=1;
            out.print(points.get(i)+" ");
            for (int j=0; j<this.colors.length;j++) {
                if (this.a[i][j]==1&&this.colors[j]==0) {
                    this.colors[j]=1;
                    this.a[i][j]=0;
                    this.a[j][i]=0;
                    dfs(j);
                } else if (this.a[i][j]==1&&this.colors[j]==1) {
                    this.cycle=true;
                    this.numberOfCycle++;
                }
            }
            this.colors[i]=2;
        }   
    }
    
    public class Time {
        
        int h;
        int min;
        int sec;
        
        public Time(String s) {
            String [] st = s.split(":");
            this.h =Integer.parseInt(st[0]);
            this.min =Integer.parseInt(st[1]);
            this.sec =(st[2]!=null)? Integer.parseInt(st[2]):0;
        }
        
        public String toString(int a) {
            String h = Integer.toString(this.h);
            String min = Integer.toString(this.min);
            String sec = Integer.toString(this.sec);
            if (h.length()==1) {
                h='0'+h;
            }
            if (min.length()==1) {
                min='0'+min;
            }
            if (sec.length()==1) {
                sec='0'+sec;
            }
            if (a==5) {
                return h+":"+min;
            } else {
                return h+":"+min+":"+sec;
            }
        }
        
        public void to12HoursFormat () {
            h%=12;
        }
        
        public void add (int  h,int min,int s) {
            this.sec+=s;
            if (this.sec>=60) {
                this.min++;
                this.sec%=60;
            }
            this.min+=min;
            if (this.min>=60) {
                this.h++;
                this.min%=60;
            }
            this.h+=h;
            if (this.h>=24) {
                this.h%=24;
            }
        }
    }
    
    public int[] findPrimes(int x) {
        boolean[] erat = new boolean[x-1];
        List<Integer> t = new ArrayList<Integer>();
        int l=0, j=0;
        for (int i=2;i<x; i++) {
                if (erat[i-2]) continue;
                t.add(i);
                l++;
                j=i*2;
                while (j<x) {
                        erat[j-2]=true;
                        j+=i;
                }
        }
        int[] primes = new int[l];
        Iterator<Integer> iterator = t.iterator();
        for (int i = 0; iterator.hasNext(); i++) {
                primes[i]=iterator.next().intValue();
        }
        return primes;
    }   
    
    public void solve() throws Exception {
    }
}
