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.
// package codeforces.B;

import java.io.*;

public class cf892B {
    public static void main(String[] args) throws IOException {
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter out = new PrintWriter(new OutputStreamWriter(System.out));

        int n = Integer.parseInt(in.readLine().trim().split("\\s+")[0]);
        String[] strings = in.readLine().trim().split("\\s+");
        int[] peoples = new int[n];
        for (int i = 0; i < n; i++) {
            peoples[i] = Integer.parseInt(strings[i]);
        }

        int s = n;
        int killed = 0;
        for (int i = n - 1; i >= 0;) {
            killed--;

            if (killed < 0) {
                killed = 0;
            }

            if (peoples[i] >= i) {
                s -= i - killed;
                break;
            }
            else if (peoples[i] > killed) {
                s -= peoples[i] - killed;
                killed = peoples[i];
                i --;
            }
            else if (peoples[i] <= killed) {
                i--;
            }
        }
        out.print(s);

        in.close();
        out.close();
    }
}
