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.*;

public class Main {
    static InputReader in = new InputReader(System.in);
    static PrintWriter out = new PrintWriter(System.out);

    public static void main(String[] args) {
        new Solution().solve();
        out.close();
    }

    static class Solution {
        void solve() {
          int N = in.nextInt();
          int [] arr = new int [N];
          int q = N; 
          int p = N-1;
          int res = 0;
          for (int i = 0; i < N; i++){
            arr[i] = in.nextInt();
          }
          while (q > 0 || p > 0){
            //out.println("p " + p);
            //out.println("q " + q);
            if (p < q){
                res++;
            }
            if (p - arr[p] < q){
                q = p - arr[p];
                p--;
            }
            else{
              p--;
            }
            //out.println("p " + p);
            //out.println("q " + q);
          }
          out.println(res);
        }
    }

    static class InputReader {
        BufferedReader reader;
        StringTokenizer tokenizer;

        InputReader(InputStream inStream) {
            this.reader = new BufferedReader(new InputStreamReader(inStream));
            this.tokenizer = null;
        }

        /**
         * @return String the whole line (including all whitespaces)
         *         or null line is empty
         */
        String nextLine() {
            this.tokenizer = null;
            String line = null;
            try {
                line = this.reader.readLine();
            }
            catch (Exception e) {
                e.printStackTrace();
            }
            return line;
        }

        /**
         * @return String next token, or null if the current line is empty
         */
        String next() {
            while (this.tokenizer == null || !this.tokenizer.hasMoreTokens()) {
                String line = nextLine();
                if (line == null) return null;
                this.tokenizer = new StringTokenizer(line);
            }
            return this.tokenizer.nextToken();
        }

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

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        char nextChar() {
            return next().charAt(0);
        }
    }
}

