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.*;
public class Codeforces{
	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);
		int n =sc.nextInt();
		int[] a = new int[n+1];
		long inti=Long.MAX_VALUE, ans=0;
		for( int i=1;i<=n;i++ )
			a[i]=sc.nextInt();
		boolean[]b12 = new boolean[n+1];Arrays.fill(b12, false);
		inti = n-a[n];
		for( int i=n-1;i>0;i-- ){
			inti = Math.min(inti,(i+1)-a[i+1]);
			if( inti<=i )b12[i]=true;
		}
		for( int i=1;i<=n;i++ )if( b12[i]==false ) ans++; 
		System.out.println(ans);		
	}
}