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.
/**
 * @author Finn Lidbetter
 */
import java.util.*;
import java.io.*;
import java.awt.geom.*;

public class TaskB {
  public static void main(String[] args) throws IOException {
    BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    StringBuilder sb = new StringBuilder();
    
    int n = Integer.parseInt(br.readLine());
    Person head = new Person(0);
    Person prev = head;
    for (int i=1; i<n; i++) {
      Person curr = new Person(i);
      curr.prev = prev;
      prev.next = curr;
      prev = curr;
    }
    String[] s = br.readLine().split(" ");
    int[] lens = new int[n];
    for (int i=0; i<n; i++) {
      lens[i] = Integer.parseInt(s[i]);
    }
    Person curr = head;
    for (int i=0; i<n; i++) {
      int len = lens[i];
      int minId = i-len;
      while (curr.prev!=null && curr.prev.id>=minId) {
        if (curr.prev.prev!=null) {
          curr.prev.prev.next = curr;
        }
        curr.prev = curr.prev.prev;
      }
      if (curr.prev==null) {
        head = curr;
      }
      curr = curr.next;
    }
    int count = 1;
    curr = head;
    while (curr.next!=null) {
      curr = curr.next;
      count++;
    }
    System.out.println(count);
  }
}
class Person {
  Person prev;
  Person next;
  int id;
  public Person (int idd) {
    id = idd;
  }
}
