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.util.Scanner;

public class Main {
   public static void main(String[] args) {
       Scanner scan=new Scanner(System.in); 
       int n=scan.nextInt();
       boolean b[]=new boolean[n];
       long count=0;
       long a[]=new long[n];
       for(int i=0;i<n;i++)        
           a[i]=scan.nextLong();
              long l=0,m=n;
       for(int i=n-1;i>=0;i--){
               long t=i-a[i];
               if(i<m)
                   count++;
               if(t<m)
                   m=t;
        }

       System.out.println(count);
   }}

    
    

