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 Solution{ 
	
 public static void main(String[] args) { 
     
     Scanner in = new Scanner(System.in);
     
     int n,i,max,discard=0;
     int[] l;
     
     n=in.nextInt();
     l=new int[n+1];
     
     for(i=1;i<=n;i++){
    	 l[i]=Integer.parseInt(in.next());
     }
     
     max=l[n];
     
     for(i=n-1;i>=1;i--){
    	 max=Math.max(max-1, l[i+1]);
    	 if(max>0)discard++;
     }
     
     System.out.println((n-discard));
     
 }
     
}
 