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.Scanner;

public class Partition {

    public static boolean[] b = new boolean[1000001];

    public static void main(String[] args) {
        Scanner input = new Scanner(System.in);
        int n = input.nextInt(), c = 0, c1 = 0;
        long[] a = new long[n];
        //long[] b = new long[n];
        for (int i = 0; i < n; i++) {
            a[i] = input.nextLong();
        }
        int j = n - 2, k = 0;
        for (int i = n - 1; i >= 0; i--) {

            for (k = j; k >= 0; k--) {
                if (k >= i - a[i] && k != i) {
                    b[k] = true;
                } else if (k == i) {

                } else {
                    break;
                }
            }
            j = k;
            //System.out.println(k);
            if (b[0] == true) {
                break;
            }

        }

        for (int i = 0; i < n; i++) {
            if (b[i] == false) {
                c++;
            }
        }
        System.out.println(c);
    }
}
