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.*;

public class solution {
	public static void main(String[] args)  {
		Scanner sc = new Scanner(System.in);
		int n=sc.nextInt();
		int[] a=new int[n];
		for(int i=0;i<n;i++) {
			a[i]=sc.nextInt();
		}
		boolean f=true;
		int c=0,k=0;
		for(int i=n-1;i>=0;i--) {
			if(f) {
				if(a[i]>0) {
					f=false;
					k=i-a[i];
					c++;
				}
				else {
					c++;
				}
			}
			else {
				if(k<=i) {
					if(i-a[i]<k) {
						k=i-a[i];
					}
				}
				else {
					f=true;
					i++;
				}				
			}
		}
		System.out.println(c);
	}
}