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 sbhowmik on 05/02/19
 */
public class Wrath {

   static public int findHowManyLeft(int arr[]) {

        int min = arr.length - 1 - arr[arr.length - 1];

        int count = 0;
        for(int i = arr.length - 2; i>=0; i--) {
            if(i >=min) {
                count++;
            }
            min = Math.min(i - arr[i], min);
        }
        return count;
    }
    public static void main(String []args) {

        Scanner scanner = new Scanner(System.in);
        int n = scanner.nextInt();
        int i = 0;
        int arr[] = new int[n];
        while ( i < n) {
            arr[i++] = scanner.nextInt();
        }

        System.out.println(arr.length - findHowManyLeft(arr));
    }
}
