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.math.BigDecimal;
import java.math.BigInteger;
import java.math.MathContext;
import java.util.*;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.lang.*;

public class Main {
    public static void main(String args[]) throws NumberFormatException, IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        int n = Integer.parseInt(br.readLine());
        int[] arr = new int[n];
        StringTokenizer stk = new StringTokenizer(br.readLine());
        for(int i=0;i<n;i++){
            arr[i] = Integer.parseInt(stk.nextToken());
        }
        Stack<Integer> stack = new Stack<>();
        for(int i=0;i<n;i++){
            if(stack.size()==0) stack.push(i);
            else{
                while(stack.size()!=0&&stack.peek()>=i-arr[i]){
                    stack.pop();
                }
                stack.push(i);
            }
        }
        System.out.println(stack.size());
    }
}
