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.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.stream.Stream;

/**
 * Success is not final, failure is not fatal. The courage to continue is what counts.
 * @author bodmas
 */
public class ProblemB {

    private int solve(int[] a) {
        int[] x = new int[a.length];
        for (int i = 0; i < a.length; i++) {
            int back = Math.max(0, i - a[i]);
            x[back] += 1;
            x[i] -= 1;
        }
        int sum = 0;
        int count = 0;
        for (int i = 0; i < x.length; i++) {
            sum += x[i];
            if (sum == 0)
                count++;
        }
        return count;
    }

    public static void main(String[] args) throws IOException {
        try (BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
                PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out))) {
            in.readLine();
            int[] a = Stream.of(in.readLine().split(" ")).mapToInt(Integer::parseInt).toArray();
            out.println(new ProblemB().solve(a));
        }
    }
}
