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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Arrays;
import java.util.StringTokenizer;
 
public class main {
public static void main(String[] args) {
        input in = new input();
        int n = in.nextInt();
        long arr[] = new long[n];
        for(int i=0; i<n; i++) arr[i] = in.nextLong();
        //boolean alive[] = new boolean[n];
        long j=n-1;
        int k=2147483647;
        long ans=0;
        for(int i=n-1; i>=0; i--) {
        	/*for(j=i; j>0&&temp-->0; j--) {
        		alive[(int) j] = true;
        	}*/
        	if(i<k) {
        		ans++;
        	}
        	if(i-arr[i]<k) {
        		if(i-arr[i]<0) k=0;
        		else k = (int) (i-arr[i]);
        	} 
        }
        /*for(int i=0; i<n; i++) {
        	if(!alive[i]) ans++; 
        }*/
        System.out.println(ans);
    }

 	static class input 
 	{
	        BufferedReader br;
	        StringTokenizer st;
	 
	        public input()
	        {
	            br = new BufferedReader(new
	                     InputStreamReader(System.in));
	        }
	 
	        String next()
	        {
	            while (st == null || !st.hasMoreElements())
	            {
	                try
	                {
	                    st = new StringTokenizer(br.readLine());
	                }
	                catch (IOException  e)
	                {
	                    e.printStackTrace();
	                }
	            }
	            return st.nextToken();
	        }
	 
	        int nextInt()
	        {
	            return Integer.parseInt(next());
	        }
	 
	        long nextLong()
	        {
	            return Long.parseLong(next());
	        }
	 
	        double nextDouble()
	        {
	            return Double.parseDouble(next());
	        }
	 
	        String nextLine()
	        {
	            String str = "";
	    try
	    {
	        str = br.readLine();
	    }
	    catch (IOException e)
	    {
	        e.printStackTrace();
	    }
	    return str;
	}
  }
 
}
