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.util.Scanner;

public class Array_1056 {
    public static void main(String[] args) {
        Scanner sn = new Scanner(System.in);
        int n = sn.nextInt();
        int[] L = new int[n];
        for (int i = 0; i < n; i++) {
            L[i] = sn.nextInt();
        }
        int result = solution(L);
        System.out.println(result);
    }
    private static int solution(int[] L) {
        if (L.length == 1) {
            return 1;
        }
        if (L[L.length - 1] >= L.length - 1) {
            return 1;
        }
        int mark = L.length - 1;
        int kill = 0;
        for (int j = L.length - 1; j >= 0 ; j--) {
            if (L[j] != 0) {
                if (mark >= j - L[j]) {
                    int a = Math.max(0, j - L[j]);
                    if (a < mark) {
                        kill += mark - a;
                        mark -= mark - a;
                    }
                }
            } else {
                if (mark == j) {
                    mark--;
                }
            }
        }
        return L.length - kill;
    }
}
