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.FileInputStream;
import java.io.FileOutputStream;
import java.io.PrintStream;
import java.util.Scanner;

/**
 * Created by OLI30 on 17.11.17.
 */
public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        long[] mas = new long[n];
        for (int i = 0; i < n; i++) {
            mas[i] = sc.nextLong();
        }
        long c = 0, a = 0;
        for (int i = n - 1; i >= 0; i--) {
            if (c == 0) {
                a++;
                c = mas[i];
            } else {
                c--;
                if (mas[i] > c) {
                    c = mas[i];
                }
            }
        }
        System.out.println(a);
    }
}
