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.io.*;
public class solution
{
	public static void main(String args[])
	{
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int[] l = new int[n];
		for(int i=0;i<n;i++)
		{
			l[i] = sc.nextInt();
		}
		int dead = 0;
		int index = n;
		for(int i=n-1;i>=0;i--)
		{
			int j = i-l[i];
			if(j<0)
			{
				j = 0;
				if(i<=index)
				{
					dead = dead+i;
				}
				else
				{
					dead = dead+index;
				}
				break;
			}
			if(i==j)
			{
				continue;
			}
			if(i<=index)
			{
				dead = dead+l[i];
				index = j;
			}
			else
			{
				int x = l[i]+index-i;
				if(x>0)
				{
					dead = dead+x;
					index = j;
				}
			}
		}
		System.out.println(n-dead);
	}	
}