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.Scanner;
import java.util.Arrays;

public class Main {

    
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int n;
        long x;
        n = in.nextInt();
        long bll[] = new long[n+1];
        for(int i = 1; i <= n; i++){
            x = in.nextLong();
            bll[i] = i-x;
        }
        long cnt = n;
        long mnn = bll[n];
        for(int i = n-1; i >= 1; i--){
            if(i >= mnn){
                cnt--;
            }
            if(bll[i] < mnn){
                mnn = bll[i];
            }
        }
        System.out.println(cnt);
    }
    
}
