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.*;
import java.io.*;
import java.math.*;

public class practice {
    public static int M = 1000003;

    public static int gcd(int a, int b) {
        if (b == 0) return a;
        else {
            return (gcd(b, a % b));
        }
    }

    public static int fact(int n) {
        if (n == 0) return 1;
        else return (n * (fact(n - 1)) % M);
    }

    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        int n = Integer.parseInt(br.readLine());
        int a[] = new int[n + 1];
        StringTokenizer st = new StringTokenizer(br.readLine());
        for (int i = 1; i <= n; ++i) {
            a[i] = Integer.parseInt(st.nextToken());
            a[i] = Math.min(a[i] + 1, i);
        }
        int ans = 0, cur_alive = n;
        for (int i = n; i >= 1; --i) {
            if (cur_alive >= i) ++ans;
            cur_alive = Math.min(cur_alive, i - a[i]);
        }
        System.out.println(ans);
    }
}
