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.BufferedOutputStream;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.HashMap;
import java.util.StringTokenizer;

public class abc {
public static PrintWriter out = new PrintWriter (new BufferedOutputStream(System.out));
	
	public static class FastReader {
		BufferedReader br;
		StringTokenizer st;
		//it reads the data about the specified point and divide the data about it ,it is quite fast
		//than using direct 

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

		String next() {
			while (st == null || !st.hasMoreTokens()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (Exception e) {
					e.printStackTrace();
				}
			}
			return st.nextToken();
		}

		int nextInt() {
			return Integer.parseInt(next());//converts string to integer
		}

		double nextDouble() {
			return Double.parseDouble(next());
		}

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

		String nextLine() {
			String ch = "";
			try {
				ch = br.readLine();
			} catch (Exception e) {
				e.printStackTrace();
			}
			return ch;
		}
	}
	

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		FastReader sc = new FastReader();
		
		 
		
		int n = sc.nextInt();
		long[] a = new long[n+1];
		for(int i=1;i<=n;++i) a[i] = sc.nextLong();
		long ptr = n,run = 0,kill = 0;
		for(int i=n;i>=1;) {
			run = i-a[i];
			--i;
		     	for(int j=i;j>=Math.max(1,run);--j) {
		     		++kill; --i;
		     		run = Math.min(run,j-a[j]);
		     	}
		 
		
		}
		out.println(n-kill);
		out.close();
		
	}

}
