Hands that shed innocent blood!

There are n guilty people in a line, the i-th of them holds a claw with length L_i. 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 - L_i.

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, ..., L_n (0 ≤ L_i ≤ 10⁹), where L_i is the length of the i-th person's claw.

Output

Print one integer — the total number of alive people after the bell rings.

Note

In first sample the last person kills everyone in front of him.

Wrath

Examples