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.
//Codeforces Round #446 (Div. 2)
import java.io.*;
import java.util.*;

public class TaskB {

    public static void main (String[] args) throws IOException {
        FastScanner fs = new FastScanner(System.in);
        PrintWriter pw = new PrintWriter(new BufferedOutputStream(System.out));

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

        int i = n-1;
        int c = 0;
        while (i >= 0) {
            c++;
            int j = i - 1;
            int k = i - a[i];
            while (j >= 0 && j >= k) {
                if (j-a[j] < k) k = j-a[j];
                j--;                
            }
            i = j;
        }

        pw.println(c);

        pw.close();
    }

    static class FastScanner {
        BufferedReader reader;
        StringTokenizer tokenizer;
        FastScanner(InputStream i) {
            reader = new BufferedReader(new InputStreamReader(i));
            tokenizer = new StringTokenizer("");
        }
        String next() throws IOException {
            while(!tokenizer.hasMoreTokens()) tokenizer = new StringTokenizer(reader.readLine());
            return tokenizer.nextToken();
        }
        int nextInt() throws IOException {
            return Integer.parseInt(next());
        }
        long nextLong() throws IOException {
            return Long.parseLong(next());
        }
    }
}