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 Wrath {
    public static void main(String args[]) {
        Scanner in = new Scanner(System.in);
        int n = in.nextInt();
        int arr[]=new int[n];
        int ar[]=new int [n];
        ar[n-1]=1;
        for (int i=0;i<n;i++)
            arr[i]=in.nextInt();
        int count=0;
        int ch=n-1;
        for (int i=n-1;i>=0;i--) {
            if (i<ch) {
                ar[i] = 1;
                ch = i;
            }
            if (i - arr[i] <= ch)
                ch = i - arr[i];
        }
        for (int i=0;i<n;i++)
        {
            if (ar[i]==1)
                count++;
        }
        System.out.println(count);
    }
}
