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 A{
       public static void main(String args[]){
              Scanner sc = new Scanner(System.in);
              int n = sc.nextInt();
              if(n == 1){
                     System.out.println(n);
                     return;
              }
              int a[] = new int[n];
              for(int i = 0; i < n; i++)
                     a[i] = sc.nextInt();
              int i = a.length - 1;
              int j = i;
              int ans = 0;
              while(i >= 0){
                     if(i == j){
                            ans++;
                            i--;
                     }else{
                            while(i >= 0 && j - i > 0){
                                   if(a[j] >= (j-i)){
                                          int d = a[j] - (j-i) + 1;
                                          i -= d;
                                   }else{
                                          j--;
                                   }
                            }
                     }
              }
              System.out.println(ans);
       }
}