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.
//package com.company;

import java.util.Arrays;
import java.util.Scanner;

public class Main {

    public static void main(String[] args) {
        Scanner sr=new Scanner(System.in);
        int n,a[]=new int[1000001];
        int dp[] = new int [1000001];
        n=sr.nextInt();
        for (int i=0;i<n;i++){
            a[i]=sr.nextInt();
        }
        int minx=n,ans=n;
        for (int i = n-1; i >=0 ; i--) {
            if(i>=minx)ans--;
            minx=Math.min(minx,i-a[i]);
        }
        System.out.println(ans);



    }

}