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.BufferedReader;
import java.io.FileNotFoundException;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;

public class main {
    
    public static void main(String[] args) throws IOException {
        Reader.init(System.in);
        StringBuilder out = new StringBuilder();
        int n = Reader.nextInt();
        long[] l = new long[n];
        for(int i = 0; i < n; i++)
            l[i] = Reader.nextLong();
        int cnt = 0;
        long max = 0;
        for(int i = n - 1; i > -1; i--) {
            max--;
            if(max < 0)
                cnt++;
            if(l[i] > max)
                max = l[i];
        }
        out.append(cnt).append('\n');
        PrintWriter pw = new PrintWriter(System.out);
        pw.print(out);
        pw.close();
    }
    
}

class Reader {
    
    public static BufferedReader reader;
    public static StringTokenizer tokenizer;
    
    public static void init(InputStream input) {
        reader = new BufferedReader(new InputStreamReader(input));
        tokenizer = new StringTokenizer("");
    }
    
    public static void init(String url) throws FileNotFoundException {
        reader = new BufferedReader(new FileReader(url));
        tokenizer = new StringTokenizer("");
    }
    
    public static String next() throws IOException {
        while(!tokenizer.hasMoreTokens())
            tokenizer = new StringTokenizer(reader.readLine());
        return tokenizer.nextToken();
    }
    
    public static String nextLine() throws IOException {
        return reader.readLine();
    }
    
    public static int nextInt() throws IOException {
        return Integer.parseInt(next());
    }
    
    public static long nextLong() throws IOException {
        return Long.parseLong(next());
    }
    
    public static double nextDouble() throws IOException {
        return Double.parseDouble(next());
    }
    
}
