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 Wrath {
        public static void main(String[] args) {
            Scanner sc = new Scanner(System.in);
            int n = sc.nextInt();
            int[] l = new int[n];
            for (int i = 0; i < n; i++) {
                l[i] = sc.nextInt();
            }
            int alive = 1;
            int j=n-1,i=n-1;
            outer:
            while (i>0){
                if(l[i]!=0){
                    int k = l[i];
                    while (j>i-k){
                        j--;
                        if(j<0){
                            break outer;
                        }
                        if(l[j] > k - (i-j)){
                            k = l[j] + (i-j);
                        }
                    }

                }
                i=j=j-1;
                if(i > -1) {
                    alive++;
                }
            }
            System.out.println(alive);
        }
    }
