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.*;
import java.lang.*;
import java.math.*;

public class Main {

    static class TaskG {

        private void solve(int test, Main.FastScanner in, PrintWriter out) {
            int n = in.nextInt();
            ArrayList<Integer> arr = new ArrayList<>();
            for (int i = 0; i < n; i++) {
                arr.add(in.nextInt());
            }
            Collections.reverse(arr);
            int ans = 0;
            int count = 0;
            for (int i = 0; i < n; i++) {
                if(count != 0){
                    count--;
                    if(count == 0){
                        if (arr.get(i) != 0) {
                            count = arr.get(i);
                        }
                    }
                    if(count < arr.get(i)){
                        count = arr.get(i);
                    }
                }else if(arr.get(i) == 0){
                    ans++;
                }else{
                    count = arr.get(i);
                    ans++;
                }
            }
            out.println(ans);
        }
    }

    public static void main(String[] args) throws IOException {
        FastScanner in = new FastScanner(System.in);
        PrintWriter out = new PrintWriter(System.out);
//        FastScanner in = new FastScanner("file");
//        PrintWriter out = new PrintWriter(new FileWriter("file"));
        new TaskG().solve(1, in, out);
        out.close();
    }

    static class FastScanner {
        BufferedReader br;
        StringTokenizer token;

        public FastScanner(InputStream is) {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        public FastScanner(String s) {
            try {
                br = new BufferedReader(new FileReader(s));
            } catch (FileNotFoundException e) {
                e.printStackTrace();
            }
        }

        public String nextToken() {
            while (token == null || !token.hasMoreTokens()) {
                try {
                    token = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return token.nextToken();
        }

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

        public long nextLong() {
            return Long.parseLong(nextToken());
        }

        public double nextDouble() {
            return Double.parseDouble(nextToken());
        }
    }
}