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 liex.util.zzz;

public class p4342 {
    
    public static void main(String[] args) {
        java.util.Scanner sc = new java.util.Scanner(System.in);
        int n = sc.nextInt();
        int[] L = new int[n];
        boolean[] dead = new boolean[n];
        for (int i = 0; i < n; i++) L[i] = sc.nextInt();
        
        int minDead = n-1;
        // 0 1 0 10
        for (int m = n-1; m >= 0; m--) {
            int to = Math.max(0, m-L[m]);
            minDead = Math.min(minDead, m);
            for (int i = minDead-1; i >= to; i--) dead[i] = true;
            minDead = Math.min(minDead, m-L[m]);
        }
        
        int x = 0;
        for (int i = 0; i < n; i++) {
            if (!dead[i]) x ++;
        }
        System.out.println(x);
    }
}
