Given N bricks, your program needs to find the number of different staircases that can be built using all of these bricks.

A staircase consists of steps of different sizes in a strictly increasing order. Two steps can not have the same height. Every staircase has a minimum of 2 steps and each step has at least 1 brick.

Example:

For N = 5, there are two different valid staircases that can be built 1 then 4 bricks 2 then 3 bricks

INPUT:

Line 1: An integer N representing the number of bricks.

OUTPUT:

Line 1: an integer representing the number of ways to build staircases using N bricks