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 ProblemB446 {
    private static Scanner in = new Scanner(System.in);
    public static void main(String[] args){
        int n = in.nextInt();
        long[] guilt = new long[n];
        for(int i = 0; i < n; i++){
            guilt[i] = in.nextLong();
        }
        int alive = 0;
        long length = 0;

        ArrayList<Long> lengths = new ArrayList<>();
        for(int i = guilt.length - 1; i >= 0; i --){
            if(i < guilt.length - 1) if(length < guilt[i+1]) length = guilt[i+1];
            lengths.add(length);
            if(length != 0) length--;
        }


        for(int i = 0; i < lengths.size(); i++) {
            if(lengths.get(i) == 0) alive++;
        }
        System.out.println(alive);
    }
}
