You are playing hopscotch on a one-indexed array ~a~ of ~N~ integers. You can choose to start at some index ~j~ (which is undecided). Your goal is to reach index ~N~. This game of hopscotch is strange. At index ~i~, it is already defined where you must hop to. At index ~i~, you must hop to index ~i + a_i~.

You want to find out, for how many starting indices ~j~ ~(1 \le j \le N)~ will you be able to reach index ~N~?

Input Specification

The first line will contain the integer ~N~ ~(1 \le N \le 10^5)~, the number of elements.

The second line will contain ~N~ integers, ~a_1, a_2, \ldots, a_N~ ~(1 \le a_i \le 10^3)~.

Output Specification

Output the number of starting indices ~j~ ~(1 \le j \le N)~ where you will be able to reach index ~N~.

Subtasks

For 3/15 of the points, ~N \le 10^3, a_i \le 10~.

For an additional 4/15 of the points, ~a_i \le 10~.

Sample Input

6
5 2 2 2 3 1

Sample Output

4

Explanation For Sample

You will be able to reach index ~N=6~ when starting at indices ~1, 2, 4,~ or ~6~.