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 BWrath {

  public static void main(String[] args) {

    Scanner scan = new Scanner(System.in);

    int n = scan.nextInt();
    int alive = n;
    int reach = 0;
    int[] ar = new int[n];

    for (int i = 0; i < n; ++i) {
      ar[i] = scan.nextInt();
    }
    for (int i = n-1; i >0; --i) {
      if (ar[i] == 0) {
        if (reach != 0)
        {reach--;}
        continue;
      }
      if (reach > ar[i]) {
        {reach--;}
        continue;
      }
      if (ar[i] > i) {
        alive -= (i - reach);
        break;
      }
      alive -= ar[i] - reach;
      reach = ar[i];
      if (i-reach == 0) {
        break;
      }
    //  System.out.println(alive);

      reach--;
    }

    System.out.println(alive);
  }
}
