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.Scanner;


public class Wrath {

	/**
	 * @param args
	 */
	public static void main(String[] args) {
		// TODO Auto-generated method stub

		Scanner input = new Scanner(System.in);
		int n = input.nextInt();
		int[] arr = new int[n];
		int p = input.nextInt();
		for(int i=1; i<n;i++){
			int z = input.nextInt();
			int a = Math.max(0,i-z);
		if(z!=0){	
			arr[a]-= 1;
			arr[i]+= 1;
		}
		}
		int sum=0;
		int counter=0;
		for(int i=0; i<n;i++){
			sum+=arr[i];
			if(sum==0)counter++;
		//System.out.println(sum+" " +counter);
		}
		System.out.println(counter);
		
	}

}
