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;

public class Wrath {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int[] l = new int[n];
        for (int i = 0; i < n; i++) {
            l[i] = sc.nextInt();
        }

        int alive = 1;
        int j = n - 1, i = n - 1;

        outer:
        while (i > 0) {
            if (l[i] != 0) {
                int k = l[i];
                while (j > i - k) {
                    j--;
                    if (j <= 0) {
                        break outer;
                    }

                    if (l[j] > k - (i - j)) {
                        k = l[j] + (i - j);
                    }
                }

            }

            i = j = j - 1;
            alive++;
        }
        
        System.out.println(alive);
    }
}

 	     	 		       		  		  	  		