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.InputStream;
import java.io.InputStreamReader;
import java.util.StringTokenizer;

public class Main4{
	
	public static void main(String[] args) throws Throwable 
	{
		Scanner sc = new Scanner((System.in));
		int n = sc.nextInt();
		int[][] arr = new int[n][2];
		int[] len = new int[n];
		for (int i = 0; i < len.length; i++) {
			len[i] = sc.nextInt();
			
			arr[Math.max(0, i-len[i])][0] ++;
			arr[i][1] --;
		}
		int cnt = 0 , ans = 0;
		for (int i = 0; i < arr.length; i++) {
			cnt += arr[i][0];
			cnt += arr[i][1];
			if(cnt==0)ans++;
		}
		System.out.println(ans);
	}
	
	static class Scanner 
	{
		StringTokenizer st;
		BufferedReader br;
		public Scanner(InputStream s){	br = new BufferedReader(new InputStreamReader(s));}
		public Scanner(String s) throws FileNotFoundException {
			br = new BufferedReader(new FileReader(s));
		}
		public String next() throws IOException 
		{
			while (st == null || !st.hasMoreTokens()) 
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}
		public int nextInt() throws IOException {return Integer.parseInt(next());}
		public String nextLine() throws IOException {return br.readLine();}		
		public long nextLong() throws IOException {return Long.parseLong(next());}		
		public double nextDouble() throws IOException {return Double.parseDouble(next());}	
		public boolean ready() throws IOException {return br.ready();}
	}
}