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.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;

public class Main {

	public static void main(String[] args) throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st = new StringTokenizer(br.readLine());
		int n = Integer.valueOf(st.nextToken());
		int claw[] = new int[n + 1];
		st = new StringTokenizer(br.readLine());
		for (int i = n; i >= 1; i--)
			claw[i] = Integer.valueOf(st.nextToken());
		
		br.close();
		
		int cnt = 0;
		int now = 1;
		int endPoint = 0;
		boolean alive = true;
		while (now <= n) {
			if (now <= endPoint)
				alive = false;
			else
				alive = true;

			if (alive)
				cnt++;
			endPoint = Math.max(endPoint, now + claw[now]);
			now++;
		}
		System.out.println(cnt);
	}

}