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 Main {

	private static int[] input = new int[1000010];
	
	public static void main(String[] args) {
		
		Scanner scan = new Scanner(System.in);

		int i , n = scan.nextInt() , value = - 1 , ans = n;
		for (i = 0;i < n;i ++) {
			input[i] = scan.nextInt();
		}
		for (i = n - 1;i >= 0;i --) {
			if (i == n - 1) {
				value = i + 1 - input[i];
			} else {
				if (i + 1 >= value) {
					ans --;
				}
				if (i + 1 - input[i] < value) {
					value = i + 1 - input[i];
				}
			}
		}
		System.out.println(ans);
		
	}

}








