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.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.StringTokenizer;
public class Letters {
	public static void main(String[] args) throws java.lang.Exception {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		int n = Integer.parseInt(br.readLine());
		int[] length = new int[n];
		StringTokenizer st = new StringTokenizer(br.readLine());
		for (int i=0;i<n;i++)
			length[i] = Integer.parseInt(st.nextToken());
		int res = 0;
		for (int i=n-1, j=n; i>= 0; i--) {
			if (i < j)
				res++;
			j =Math.min(j, i-length[i]);
		}
		System.out.println(res);
	}
}