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.*;
import java.util.*;
public class Wrath{
    public static void main(String args[])
    {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int temp = n;
        long L[] = new long[n];
        for(int i =0;i<n;i++)
        {
            L[i] = sc.nextLong();
        }
        long j=L[n-1];
        for(int i=n-1;i>0;i--,j--)
        {
            if(j<0)
                    j=0;
            if(L[i]>=i)
            {
                temp=temp-i;
                if((int)j<i)
                {
                    temp = temp+(int)j;
                }
                break;
            }
            else
            {
                if(i==(n-1))
                    temp = temp - (int)j;
                if(L[i]>j)
                {
                    temp= temp+(int)(j-L[i]);
                    j = L[i];
                }
                //System.out.println(j+" "+temp);
            }
        }
        System.out.println(temp);
    }
}