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.IOException;
import java.io.InputStreamReader;

public final class WrathCF {
    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new BufferedReader(new InputStreamReader(System.in)));
        int n = Integer.parseInt(br.readLine());
        String s[] = br.readLine().split(" ");
        int arr[] = new int[n];
        for (int i = 0; i < n; i++) {
            arr[i] = Integer.parseInt(s[i]);
        }
        boolean vis[] = new boolean[n];
        int j = n - 2;
        for (int i = n - 1; i >= 0; i--) {
            int index = i - arr[i];
           // System.out.println(i+" "+index);
            if (index == i)
                continue;
            if (j >= i) {
                j=i-1;
            }
            if (index <= j) {
                if (index < 0) index = 0;
                while (j >= index) {
                    vis[j] = true;
                    j--;
                }
            }
           // System.out.println(j);
            if (j < 0) break;
        }
       /* for(int i=0;i<n;i++){
            System.out.print(vis[i]+" ");
        }
        System.out.println();*/
        int count = 0;
        for (int i = 0; i < n; i++) {
            if (!vis[i])
                count++;
        }
        System.out.println(count);
    }
}
