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.*;
import java.util.Map.Entry;
public class Wrath
{
	public static void main(String ar[])
	{
		Scanner s1 = new Scanner(System.in);
		int n;
		n = s1.nextInt();
		int a[] = new int[n+1];
		for(int i=1;i<=n;i++)
			a[i] = s1.nextInt();
		Map<Integer,Integer> hm = new TreeMap<>();
		for(int i=1;i<=n;i++)
			if(a[i] != 0)
				if(a[i] < i)
					hm.put(i-a[i],i-1);
				else
					hm.put(1, i-1);
		Iterator<Entry<Integer, Integer>> it = hm.entrySet().iterator();
		int end = -1,ct = 0;
		while(it.hasNext())
		{
			Map.Entry<Integer, Integer> pair = it.next();
			if(pair.getValue() <= end)
				continue;
			ct += (pair.getValue()-Math.max(pair.getKey(),end+1)+1);
			if(ct == n-1)
				break;
			end = Math.max(pair.getValue(),end);
		}
		System.out.println(n-ct);
		s1.close();
	}
}	