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.IOException;
import java.io.InputStreamReader;

public class Wrath {
    public static void main(String[] args) throws IOException {
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        in.readLine();
        String[] inputs = in.readLine().split("\\s+");
        int[] claws = new int[inputs.length];
        for (int i = 0; i < inputs.length; i++) {
            claws[i] = Integer.parseInt(inputs[i]);
        }

        System.out.println(solve(claws));
    }

    public static int solve(int[] claws) {
        int aliveCount = 0;
        int nextAlive = claws.length - 1;
        for (int i = claws.length - 1; i >= 0; i--) {
            if (i == nextAlive) {
                aliveCount++;
            }
            if (nextAlive > i - claws[i] - 1) {
                nextAlive = i - claws[i] - 1;
                if (nextAlive < 0) {
                    break;
                }
            }
        }
        return aliveCount;
    }
}

