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 TestClass {
 public static void main(String[] args) {
        // TODO code application logic here
        Scanner sc=new Scanner(System.in);
        int n=sc.nextInt();
        int a[]=new int[n+1];
        for(int i=1;i<n+1;i++){
            a[i]=sc.nextInt();
        }
        int dp[]=new int[n+1];
     dp[0]=1;
     for(int i=1;i<n+1;i++){
         dp[i]+=-1;
         if(i-a[i]<1)dp[1]+=1;
         else dp[i-a[i]]+=1;
     }
     
     int sum=0;
     int j=dp[1];
     if(j==0) sum++;
     else sum=0;
     for(int i=2;i<n+1;i++){
         j+=dp[i];
         if(j==0)sum++;
         
     }
       System.out.println(sum); 
    }
    
}