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.*;
import java.lang.reflect.Array;
import java.util.*;
import java.text.*;
import java.math.*;

public class Solution {
	private static Scanner input = new Scanner(System.in);
	
    public static void main(String[] args) {
    	int n = input.nextInt();
    	int a[] = new int[n];
    	
    	for (int i = 0; i < n; i++)
    		a[i] = input.nextInt();
    	
    	int res = 0, killed = 0;
    	for (int i = n - 1; i >= 0; i--) {
    		//System.out.println(a[i] + " " + killed);
    		//System.out.println(killed);
    		if (killed ==  0) {
    			res++;
    		}
    		
    		killed = Math.max(a[i], killed - 1);    		
    	}
    	
    	System.out.println(res);
    }
}