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;

/**
 * Created by zviad on 12/7/17.
 *
 */
public class Wrath {

    public static void main(String argv[])  {

        Scanner scanner = new Scanner(System.in);
        int n=scanner.nextInt();
        int a[]=new int[n];
        for(int i=0;i<n;i++){
            a[i]=scanner.nextInt();
        }
        int b[]=new int[n];
        int lastlivndx=n-1;
        for(int i=n-1;i>=0;i--){
                if(a[i]>0){
                    int kk=0;
                   for(int j=lastlivndx-1;j>=(i-a[i]) && j>=0;j--) {
                       b[j]=1;
                       kk++;
                   }
                   lastlivndx-=kk;
                }
                if(i==lastlivndx){
                    lastlivndx=i-1;
                }
                if(lastlivndx<=0)break;
        }
        int result=0;
        for(int i=0;i<b.length;i++){
            if(b[i]==0)result++;
        }
        System.out.println(result);

    }
}