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.math.*;
import java.security.*;
import java.text.*;
import java.util.*;
import java.util.concurrent.*;
import java.util.regex.*;

public class Solution {
    public static void main(String arg[]){
        int n;
        Scanner sc=new Scanner(System.in);
      n=sc.nextInt();
        int A[]=new int [n];
       for(int i=0;i<n;i++){
           A[i]=sc.nextInt();
       }
        int B[]=new int[n];
        for(int i=0;i<n;i++){
            B[i]=0;
        }
        int i,j=n-2;
        for( i=n-1;i>=1;i--){
            if(j<0) break;
            //System.out.println(Arrays.toString(B));
                if(j<i-A[i] || A[i]==0){
                    continue;
                }
            else{
                if(j>i-1){j=i-1;}
                for(;j>=i-A[i];j--){
                if(j>=0){
                         B[j]=1;
                }
                if(j<0) break;
            }
            }
            
        }
       // System.out.println(Arrays.toString(B));
        int count=0;
        for(i=0;i<n;i++){
            if(B[i]==0){
                count++;
            }
        }
        System.out.println(count);
        
    }
}
