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.FileNotFoundException;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Collections;
import java.util.Scanner;
import java.util.StringTokenizer;

public class B {

	public static void main(String[] args) {
		new B();
	}

	int N,a[];
	
	B() {
		
		FastScanner in = new FastScanner();
		
		N = in.nextInt();
		a = new int[N];
		ArrayList<Event> events = new ArrayList<>();
		
		for(int i=0;i<N;i++){
			a[i] = in.nextInt();
			events.add(new Event(Math.max(i-a[i],0),0));
			events.add(new Event(i,1));
		}
		
		Collections.shuffle(events); //if this is it.......
		Collections.sort(events);
		int clawCount = 0, deadCount = 0;
		int prev = 0;
		for(Event e : events){
			if(clawCount>0)
				deadCount += e.time-prev;
			if(e.type==0){
				clawCount++;
			}else{
				clawCount--;
			}
			prev = e.time;
		}
		
		System.out.println(N-deadCount);

	}
	
	static class Event implements Comparable<Event>{
		int time,type;
		public Event(int time, int type){
			this.time = time;
			this.type = type;
		}
		@Override
		public int compareTo(Event e) {
			if(this.time==e.time)
				return this.type - e.type;
			else
				return this.time - e.time;
		}
	}
	
	public static class FastScanner
	{
		BufferedReader br;
		StringTokenizer st;

		public FastScanner(String s)
		{
			try {
				br = new BufferedReader(new FileReader(s));
			} catch (FileNotFoundException e) {
				// TODO Auto-generated catch block
				e.printStackTrace();
			}
		}

		public FastScanner()
		{
			br = new BufferedReader(new InputStreamReader(System.in));
		}

		String nextToken()
		{
			while (st == null || !st.hasMoreElements())
			{
				try {
					st = new StringTokenizer(br.readLine());
				} catch (IOException e) {
					// TODO Auto-generated catch block
					e.printStackTrace();
				}
			}
			return st.nextToken();
		}

		int nextInt()
		{
			return Integer.parseInt(nextToken());
		}

		long nextLong()
		{
			return Long.parseLong(nextToken());
		}

		double nextDouble()
		{
			return Double.parseDouble(nextToken());
		}
		
		String next()
		{
			return nextToken();
		}
		
		public boolean hasNext()
		{
			if(st != null && st.hasMoreElements())
				return true;
			
			try {
				st = new StringTokenizer(br.readLine());
			} catch (Exception e) {
				// TODO Auto-generated catch block
				return false;
			}
			
			if(st == null) return false;
			return st.hasMoreElements();
		}
	}
	
}
