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 Main {

    public static void main(String[] args) {
        // read input 
        Scanner sc = new Scanner(System.in);

        int n;
        n = sc.nextInt();
        int killedPeople = 0, lastPos = n, startPos = n;
        int claws[] = new int[n];
        for (int i = 0; i < n; ++i)
        {
            int t;
            t = sc.nextInt();
            claws[i] = t;
        }
        for (int i = n - 1; i >= 0; --i)
        {
            if (claws[i] >= i)
            {
                if (i >= lastPos && i <= startPos)
                {
                    killedPeople += lastPos;
                }
                else
                    killedPeople += i;
                break;
            }
            if (i >= lastPos && i <= startPos && (i - claws[i]) < lastPos)
            {
                killedPeople += lastPos - (i - claws[i]);
                lastPos = i - claws[i];
                startPos = i;
            }
            else if (i < lastPos)
            {
                if (claws[i] != 0)
                {
                    killedPeople += claws[i];
                    startPos = i - 1;
                    lastPos = i - claws[i];
                }
            }
        }
        System.out.print(n - killedPeople);
    } 

}
