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.
/* package whatever; // don't place package name! */

import java.util.*;
import java.lang.*;
import java.io.*;


/* Name of the class has to be "Main" only if the class is public. */
public class Ideone
{	
	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[] claw = new int[n];
		boolean[] dead = new boolean[n];
		StringTokenizer st = new StringTokenizer(br.readLine());
		for (int i=0; i<n; i++){
			claw[i] = Integer.parseInt(st.nextToken());
		}
		int alive = 0;
		int kill_left = 0;
		for (int i=n-1; i>=0; i--){
			if (kill_left == 0) alive++;
			kill_left = Math.max(claw[i], kill_left-1);
		}
		System.out.println(alive);
	}
}