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 static java.lang.Math.*;
public class TestClass {
    public static void main(String args[]) {
        Scanner in = new Scanner(System.in);
        int n = in.nextInt();
        int l[][] = new int[n+1][2];
        for(int i=1;i<=n;i++)
        {
            l[i][0] = in.nextInt();
        }
        for(int i=n;i>0;i--)
        {
            for(int j=max(i-l[i][0], 0);j<i && l[j][1]!=-1;j++)
            {
                l[j][1]=-1;
            }
        }
        int ans=0;
        for(int i=1;i<=n;i++)
        {
            if(l[i][1]!=-1)
            {
                ++ans;
            }
        }
        System.out.println(ans);

    }
        

}