Hands that shed innocent blood!

There are n guilty people in a line, the i-th of them holds a claw with length Li. The bell rings and every person kills some of people in front of him. All people kill others at the same time. Namely, the i-th person kills the j-th person if and only if j < i and j ≥ i - Li.

You are given lengths of the claws. You need to find the total number of alive people after the bell rings.

Input

The first line contains one integer n (1 ≤ n ≤ 106) — the number of guilty people.

Second line contains n space-separated integers L1, L2, ..., Ln (0 ≤ Li ≤ 109), where Li is the length of the i-th person's claw.

Output

Print one integer — the total number of alive people after the bell rings.

Examples

Input

4
0 1 0 10


Output

1


Input

2
0 0


Output

2


Input

10
1 1 3 0 0 0 2 1 0 3


Output

3

Note

In first sample the last person kills everyone in front of him.
import java.io.*;
import java.util.*;

public class Main {
    private void solve() {
        int n = nextInt();
        int[]a = new int[n];
        int kol=0;
        int min=0;
        int kil=0;
        boolean[] b = new boolean[n];
        for(int i=0;i<n;i++)
            a[i]=nextInt();
        for(int i=n-1;i>=0;i--){
            if(a[i]==0)continue;
            min=i-a[i]<0?0:i-a[i];
            for(int j=min;j<i;j++){
                if(b[j])
                    break;
                 kol++;
                 b[j]=true;
            }
        }
        out.print(n-kol);
        
        /*boolean b=false;
        String s=next();
        String p;
        int l=s.length();
         for (int k=0;k<l;k=k+1){
          if(k+2!<=l && s.charAt(k)=="W" && s.charAt(k)=="U" && s.charAt(k)=="B" ) {
              b=true;
              k=k+2;
          } else {
              if (b=true)
                 p=p+" ";
            if (p.length()!=0){
                p=p+s.charAt(k);
            }
         }
              
          }  
          System.out.println(p);*/
        }
        
    public static void main(String[] args) {
        new Main().run();
    }

    BufferedReader br;
    StringTokenizer st;
    PrintWriter out;

    private void run() {
        try {
            br = new BufferedReader(new InputStreamReader(System.in));
            out = new PrintWriter(System.out);
            //br = new BufferedReader(new FileReader("birthday.in"));
            //out = new PrintWriter(new FileWriter("birthday.out"));
            solve();
            br.close();
            out.close();
        } catch (IOException e) {
            e.printStackTrace();
        }
    }

    private int nextInt() {
        return Integer.parseInt(next());
    }

    private String next() {
        while (st == null || !st.hasMoreTokens()) {
            try {
                st = new StringTokenizer(br.readLine());
            } catch (IOException e) {
                e.printStackTrace();
                return "END_OF_FILE";
            }
        }
        return st.nextToken();
    }
}