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.*;

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

        int j = n - 1;
        int lastKill = 0;
        int count = 0;
        for(int i = n - 1; i > -1; i--) {
            j = Math.min(i, j);
            lastKill = Math.max(0, i - victim.get(i));

            if(j > lastKill) {
                count += j - lastKill;
                j = lastKill;
            }
        }

        System.out.println(n - count);
    }
}
