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.BufferedReader;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.LinkedList;
import java.util.Queue;
import java.util.Stack;
import java.util.StringTokenizer;
import java.util.Vector;

public class vaja1{
	static BufferedReader in=new BufferedReader(new InputStreamReader(System.in));
	static PrintWriter out=new PrintWriter(System.out);
	public static void main(String[] args) throws Exception{
		int n=Integer.parseInt(in.readLine());
		int[]q=new int[n];
		StringTokenizer st=new StringTokenizer(in.readLine());
		for(int i=0;i<n;i++){
			q[i]=Integer.parseInt(st.nextToken());
		}
		boolean[]killed=new boolean[n];
		int len=-1;
		for(int i=n-1;i>=0;i--){
			if(len>=0){
				killed[i]=true;
			}
			if(len<q[i]){
				len=q[i];
			}
			len--;
		}
		int count=0;
		for(int i=0;i<n;i++){
			if(!killed[i])count++;
		}
		System.out.println(count);
	}
}



























