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;

/**
 *
 * @author arif_
 * date:
 * algo:
 * diff: 
 */
public class CF_892B {
    /* START OF I/O ROUTINE */
    // PrintWriter for faster output
    public static PrintWriter out;

    // MyInputReader class for faster input
    public static class MyInputReader {
        BufferedReader br;
        StringTokenizer st;

        public MyInputReader(InputStream stream) {
            br = new BufferedReader(new InputStreamReader(stream), 32768);
        }

        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;
        }
    } // end of class MyInputReader
    /* END OF I/O ROUTINE */


    public static void main(String[] args) {
        MyInputReader in = new MyInputReader(System.in);
        out = new PrintWriter(new BufferedOutputStream(System.out));

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

        int ans = 0;
        int lastDead = n;
        for (int i=n-1; i>= 0; i--) {
            if (i < lastDead) ans++;
            lastDead = Math.min(lastDead, i - a[i]);
            if (lastDead < 0) break;
        }

        out.println(ans);
        out.close();
    } // end of method main()
} // end of class Main