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.*;
import java.io.*;
import java.math.*;
import java.util.StringTokenizer;
 
public class warth{
    public static void main(String[] args){
        FastReader scan = new FastReader();
        PrintStream p = System.out;
        int t =scan.nextInt();
        int arr[] = new int[t];
        for(int i=0;i<t;i++){
            arr[i] =scan.nextInt();
        }
        int min = arr.length;
        int count = 0;
        for(int i=arr.length-1;i>=0;i--){
            if(i<min){
                count++;
            }
            min = Math.min(min,i-arr[i]);
        }
        p.println(count);
    }
    static class FastReader{
        BufferedReader br;
        StringTokenizer st;
 
        public FastReader(){
            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;
        }
    }
}

