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 wassim on 20/11/17.
 */
public class Main {
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        Long nb = in.nextLong();
        Long suspects[] = new Long[(int) Math.pow(10, 6) + 1];
        for (int i = 0; i < nb; i++) {
            suspects[i] = in.nextLong();
        }

        Long vivants = (long) 0, l = nb;
        for (long i = nb - 1; i >= 0; i--) {
            if (i < l) {
                vivants++;
                l = i;
            }
            if (l > (i - suspects[(int) i])) {
                l = (i - suspects[(int) i]);
            }
            if (l < 0)
                break;
        }
        System.out.println(vivants);
    }
}