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.
/*package whatever //do not write package name here */

import java.util.*;
import java.lang.*;
import java.io.*;

public class Codeforce {
	public static void main (String[] args) {
	    FastReader fr = new FastReader();
	    int n = fr.nextInt();
	    int[] l = new int[n+1];
	    for(int i = 1;i < n+1;i++) {
	        l[i] = fr.nextInt();
	    }
	    boolean[] dead = new boolean[n+1];
	    int lenClaw = l[n];
	    for(int i = n-1;i > 0;i--) {
	        if(lenClaw !=0) {
	            dead[i] = true;
	            lenClaw--;
	        }
	        lenClaw = Math.max(lenClaw, l[i]);
	    }
	    int cnt = 0;
	    for(int i = 1;i < n+1;i++) {
	        if(!dead[i]) cnt++;
	    }
	    System.out.println(cnt);
	}
}

            
class FastReader {
 
    BufferedReader bf;
    StringTokenizer st;
 
    public FastReader() {
        bf = new BufferedReader(new InputStreamReader(System.in));
    }
 
    String next() {
        while (st == null || !st.hasMoreElements()) {
            try {
                st = new StringTokenizer(bf.readLine());
            } catch (Exception e) {
                System.out.println(e);
            }
        }
        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 = bf.readLine();
        } catch (Exception e) {
            System.out.println(e);
        }
        return str;
    }
}