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.Scanner;

/**
 * Created by rene on 24/11/17.
 */
//http://codeforces.com/problemset/problem/892/B
//https://www.codepit.io/#/problems/5a111f9342101c6312b25076/view?index=5
public class Main {

    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);

        int totalPeople = scanner.nextInt();
        int[] people = new int[totalPeople];
        int alive = 0;

        for(int i = 0; i < totalPeople; i++) {
            people[i] = scanner.nextInt();
        }

        int killedRange = totalPeople;

        for(int i = people.length - 1; i >= 0; i--) {
            if(i < 0) {
                break;
            }

            if(i < killedRange) {
                alive++;
            }

            int killed = people[i];

            if(i - killed < killedRange) {
                killedRange = i - killed;
            }
        }

        System.out.println(alive);
    }

}
