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 java.lang.*;
import java.io.*;
import java.io.BufferedReader; 
import java.io.IOException; 
import java.io.InputStreamReader; 
import java.util.Scanner; 
import java.util.StringTokenizer;

import javax.lang.model.util.ElementScanner6; 

/* Name of the class has to be "Main" only if the class is public. */
public class Main
{
    
    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; 
        } 
    
    }
    static long power(long x,long y) 
    { 
        long temp; 
        if( y == 0) 
            return 1; 
        temp = power(x, y/2);  
          
        if (y%2 == 0) 
            return temp*temp; 
        else
        { 
            if(y > 0) 
                return x * temp * temp; 
            else
                return (temp * temp) / x; 
        } 
    }  
     
public static void main(String args[])
{
    Scanner sc=new Scanner(System.in);
    int n=sc.nextInt();
    long a[]=new long[n];
    for( int i=0;i<n;i++)
    {
        a[i]=sc.nextLong();
    }
    long max=0;
    boolean ans[]=new boolean[n];
    for( int i=n-1;i>=0;i--)
    {
        if(max>0)
        {
            ans[i]=true;
            max--;
           
        }
        max=Math.max(max,a[i]);
    }
    int count=0;
    for( int i=0;i<n;i++)
    {
        if(ans[i]==false)
        {
            count++;
        }
    }
    System.out.println(count);
}
}

class myComparator implements Comparator<Long>
{
    public int compare(Long a,Long b)
    {
        if(b>a)
        return 1;
        else if(a>b)
        return -1;
        else
        return 0;

    }
}