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.util.StringTokenizer;

import static java.lang.Math.max;

public class B {
	public static void main(String[] args) throws FileNotFoundException {
		int toFile = 0;
		InputStream inputStream;
		OutputStream outputStream;
		if (toFile == 0) {
			inputStream = System.in;
			outputStream = System.out;
		} else {
			inputStream = new FileInputStream(new File("B.in"));
			outputStream = new FileOutputStream(new File("B.out"));
		}
		InputReader in = new InputReader(inputStream);
		PrintWriter out = new PrintWriter(outputStream);
		TaskB solver = new TaskB();
		solver.solve(in, out);
		out.close();
	}

	static class TaskB {

		public void solve(InputReader in, PrintWriter out) {
			int n = in.nextInt();
			int l[] = new int[n];

			for (int i=0; i<n; i++)
				l[i] = in.nextInt();

			int res = 0;
			int k = 0;
			for (int i=n-1; i>=0; i--) {
				if (k == 0)
					res++;

				if (l[i] >= k)
					k = l[i];
				else
					k = Math.max(k - 1, 0);

			}
			out.print(res);
		}

	}

	static class InputReader {
		public BufferedReader reader;
		public StringTokenizer tokenizer;

		public InputReader(InputStream stream) {
			reader = new BufferedReader(new InputStreamReader(stream), 32768);
			tokenizer = null;
		}

		public String next() {
			while (tokenizer == null || !tokenizer.hasMoreTokens()) {
				try {
					tokenizer = new StringTokenizer(reader.readLine());
				} catch (IOException e) {
					throw new RuntimeException(e);
				}
			}
			return tokenizer.nextToken();
		}

		public int nextInt() {
			return Integer.parseInt(next());
		}

	}
}
