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.ArrayList;
import java.util.Scanner;

//892B
public class warth {
	public static long n;
	public static long []a=new long[10000006];
	public static ArrayList <Long> arrayList=new ArrayList<>(10000006);
	public static void solve(){
	//	long count=arrayList.get((int) (n-1));
		long count=a[(int)n-1];
		System.out.println();
		long answer =1;
		for(long i=n-2;i>=0;i--){
			if(count==0)answer++;
			count=Math.max(count-1, a[(int)i]);
		}
		System.out.println(answer);
		
	}
public static void main(String [] args){
Scanner in = new Scanner(System.in);
n=in.nextLong();
for(long i=0;i<n;i++)
	a[(int) i]=in.nextInt();
	//long ele=in.nextLong();
	//arrayList.add(ele);

solve();
}
}
