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.*;
import java.math.BigInteger;
import java.util.*;
import java.util.concurrent.SynchronousQueue;

public class Mainn {

	public static class FastReader {
		BufferedReader br;
		StringTokenizer st;

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

		String next() {
			while (st == null || !st.hasMoreElements()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			}
			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 = br.readLine();
			} catch (IOException e) {
				e.printStackTrace();
			}
			return str;
		}
	}

	public static void main(String[] args) {
		FastReader scn = new FastReader();


		int n = scn.nextInt();
		int[] arr = new int[n], kill = new int[n];
		for(int i = 0; i < n ; i++) {
			arr[i] = scn.nextInt();
		}
		int c = 0;
		for(int i = n - 1; i >= 0; i--) {
			int ind = i - arr[i];
			if(ind < 0) {
				ind = 0;
			}
			kill[ind] += -1;
			kill[i] += 1;
		}
		if(kill[0] == 0) {
			c++;
		}
		for(int i = 1; i < n; i++) {
			kill[i] += kill[i - 1];
			if(kill[i] == 0) {
				c++;
			}
		}
		System.out.println(c);
	}
}