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 Main
{
     public static void main(String args[])
     {
          Scanner sc = new Scanner(System.in);
          int n = sc.nextInt();
          int arr[] = new int[n];
          for(int i=0;i<n;i++)
          {
              arr[i] = sc.nextInt();
          }
          int i = n-1;
          int ans = 0;
          while(i>=0)
          {
              int j = i;
              int min = i-arr[i];
              while(j>=0 && j>=min)
              {
                  min = Math.min(min,j-arr[j]);
                  j--;
              }
              ans++;
              i=j;
          }
          System.out.println(ans);
     }
}