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.File;
import java.io.FileNotFoundException;
import java.util.Scanner;

public class B {


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

        /*Scanner sc = null;
        try {
            sc = new Scanner(new File("input.txt"));
        } catch (FileNotFoundException e) {
            e.printStackTrace();
        }*/
        int n = sc.nextInt();
        int nums[] = new int[n + 1];

        for (int i = 1; i <= n; i++) {
            nums[i] = sc.nextInt();

        }
        int deadMen = 0;
        int count = nums[n];
        for (int i = n-1; i > 0; i--) {
            if (count > 0) deadMen++;
            count--;
            if (count < nums[i]) count = nums[i];
        }
        System.out.println(n-deadMen);
    }
}