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.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.*;

public class Main {

    public static void main(String[] args) throws Exception {

        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));

        int n = Integer.parseInt(in.readLine());
        String[] temp = in.readLine().split(" ");

        int[] len = new int[n];
        for (int i = 0; i < n; i++) {
            len[i] = Integer.parseInt(temp[i]);
        }

        int survive = 1;
        int extend = n - 1;
        for (int i = n - 1; i >= 0; i--) {
            if (extend > i) survive++;
            extend = Math.min(i - len[i], extend);
        }
        System.out.println(survive);

    }

}