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.Arrays;
import java.util.Scanner;

public class n2 {

    public static void main(String[]args) {
        Scanner in = new Scanner(System.in);
        int N = in.nextInt();
        long [] mas = new long[N+1];
        for (int i = 1; i < N+1; i++) {
            mas[i] = in.nextLong();
            mas[i] = Math.min(mas[i]+1, i);
        }
        int ans = 0; long cur_alive = N;
        for (int i = N; i >= 1; --i) {
            if (cur_alive >= i)
                ans++;
            cur_alive = Math.min(cur_alive, i - mas[i]);
        }
        System.out.println(ans);
    }

}
/*        for (int i = N; i > 0; i--) {
            long L = in.nextLong();
            if (L>0){
                long j = L-N;
                if (j<0){
                    count-=i+j;
                }else{
                    count-=i-1;
                    break;
                }
            }
        }*/
