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.*;

public class wrathCF {
    public static void main (String[]args) {
        Scanner scan = new Scanner (System.in);

        int length = scan.nextInt();
        int [] clawLengths = new int [length];

        for (int i = 0; i < length; i++) {
            clawLengths[i] = scan.nextInt();
        }

        int firstPointer = length - 2;
        int secondPointer = length - 1;

        boolean [] killedPeople = new boolean [length];

        while (firstPointer >= 0) {
            if (firstPointer >= secondPointer) {
                firstPointer = secondPointer - 1;
            }

            for (; firstPointer >= secondPointer - clawLengths[secondPointer]; firstPointer--) {
                if (firstPointer == -1) {
                    break;
                }

                killedPeople[firstPointer] = true;
            }

            secondPointer--;
        }

        int peopleAlive = 0;

        for (int i = 0; i < length; i++) {
            if (killedPeople[i] == false) {
                peopleAlive++;
            }
        }

        System.out.println(peopleAlive);
    }
}
