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.*;
import java.io.*;
public class _446_B_Wrath {

	public static void main(String[] args) throws IOException {
		// TODO Auto-generated method stub
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

		int N = Integer.parseInt(br.readLine());
		int arr[] = new int[N];
		boolean iskilled[] = new boolean[N];
		int point = N-1;
		StringTokenizer st = new StringTokenizer(br.readLine());
		for(int i = 0; i<N; i++) arr[i] = Integer.parseInt(st.nextToken());
		int count = 0;
		
		for(int i = N-1; i>=0; i--) {
			if(!iskilled[i]) count++;
			for(int j = point-1; j>=Math.max(i-arr[i], 0); j--) iskilled[j] = true;
			point = Math.min(point, Math.max(i-arr[i], 0));
//			System.out.println(i + " " + point);
		}
		System.out.println(count);

	}

}
