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 Test {
	public static void main(String[] args) {
		Scanner scanner = new Scanner(System.in);
		int n = scanner.nextInt();
		int arr[]= new int [n];
		for(int i =0;i<n;i++)
			arr[i] =scanner.nextInt();
		int res[] = new int [n];
		int k  =arr[n-1];
		for(int i =n-1;i>0;i--) {
			int tmp = arr[i];
			while(i>0&&tmp>0) {
				res[--i] =1;
				tmp--;
				if (arr[i]>tmp) {
					tmp =arr[i];
				}
				
			}
		}
		int save =0;
		for(int i =0 ;i<n;i++) {
			if (res[i]==0) {
				save++;
			}
		}
		System.out.println(save);
	}
}

	 	  	  	 				 		 	   	 	    		