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 sol {
	private static int N;
	private static int[] array;
	private static boolean[] killed;

	public static void main(String[] args) throws IOException {
		BufferedReader f = new BufferedReader(new InputStreamReader(System.in));
		N = Integer.parseInt(f.readLine());
		array = new int[N];
		killed = new boolean[N];
		StringTokenizer st = new StringTokenizer(f.readLine());
		for (int i = 0; i < N; i++) {
			array[i] = Integer.parseInt(st.nextToken());
		}
		int index = N - 1;
		int left = N;
		while (index >= 0) {
			if (index >= left)
				killed[index] = true;
			left = Math.min(left, index - array[index]);
			index--;
		}
		int result = 0;
		for (int i = 0; i < N; i++) {
			if (!killed[i])
				result++;
		}
		System.out.println(result);
	}
}
