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 Wrath {

	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		int n = in.nextInt();
		int l[] = new int[n];
		//System.out.println("\nn="+n);
		int total = 0;
		int killedTill=0;
		int x = 0;
		for(int i = 0 ;i<n;i++) {
			l[i]=in.nextInt();
		}
		int kill = 0;
		for(int i=0;i<n;i++) {
			x = l[n-i-1];
			if(x+i>=n) {
				x=n-i-1;
			}
			if(i+x > killedTill) {
				kill = x;
				if(killedTill>i) {
					kill=(i+x)-killedTill;
				}
				total+=kill;
				killedTill=i+x;
			}
			//System.out.println("i= "+i+ " x =  " + x + " total =" + total +" killedTill = " + killedTill);
		}
		System.out.println(n-total);
		in.close();
	}

}
