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;

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

/**
 * @author safat
 * @since 11/17/17.
 */

public class BWrath {
    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

        int n = Integer.parseInt(br.readLine());
        int[] claws = splitIntoInt(br.readLine());
        int aliveCount = 1;
        int rightToLeftCoverage = n - claws[n];

        for (int i = n - 1; i >= 1; i--) {
            if (i < rightToLeftCoverage) {
                aliveCount++;
            }

            rightToLeftCoverage = Math.min(rightToLeftCoverage, i - claws[i]);
        }


        System.out.println(aliveCount);
    }

    private static int[] splitIntoInt(String input) {
        String[] strNumbers = input.split(" ");
        int[] numbers = new int[strNumbers.length + 1];

        int i = 1;

        for (String number : strNumbers) {
            numbers[i++] = Integer.parseInt(number);
        }

        return numbers;
    }

    public static String join(int[] numbers) {
        if (numbers == null || numbers.length == 0) {
            return null;
        }

        StringBuilder result = new StringBuilder();

        for (int n : numbers) {
            result.append(n).append(", ");
        }

        return result.substring(0, result.length() - 1);
    }
}
