# Task
 A lock has `n` buttons in it, numbered from `1 to n`. To open the lock, you have to press all buttons in some order, i.e. a key to the lock is a permutation of the first `n` integers. If you push the right button in the right order, it will be pressed into the lock. Otherwise all pressed buttons will pop out. When all buttons are pressed into the lock, it opens.
 
 Your task is to calculate the number of times you've got to push buttons in order to open the lock in the `worst-case scenario`.

# Example

 For `n = 3`, the result should be `7`.
 ```
 Let's assume the right order is 3-2-1.
 In the worst-case scenario, we press the buttons:
 Press 1, wrong, button 1 pop out
 Press 2, wrong, button 2 pop out
 Press 3, right, button 3 pressed in
 Press 1, wrong, button 1,3 pop out
 Press 3, right, button 3 pressed in
 Press 2, right, button 2 pressed in
 Press 1, right, button 1 pressed in
 We pressed button total 7 times.``` 
 
 For `n = 4`, the result should be `14`.
 ```
 Let's assume the right order is 4-3-2-1.
 In the worst-case scenario, we press the buttons:
 Press 1, wrong, button 1 pop out
 Press 2, wrong, button 2 pop out
 Press 3, wrong, button 3 pop out
 Press 4, right, button 4 pressed in
 Press 1, wrong, button 1,4 pop out
 Press 4, right, button 4 pressed in
 Press 2, wrong, button 2,4 pop out
 Press 4, right, button 4 pressed in
 Press 3, right, button 3 pressed in
 Press 1, wrong, button 1,3,4 pop out
 Press 4, right, button 4 pressed in
 Press 3, right, button 3 pressed in
 Press 2, right, button 2 pressed in
 Press 1, right, button 1 pressed in
 We pressed button total 14 times.``` 

# Input/Output


 - `[input]` integer `n`

  The number of buttons in the lock.
  
  `0 < n ≤ 2000`


 - `[output]` an integer

 The number of times you've got to push buttons in the `worst-case scenario`.

Difficulty: introductory

Starter code:

def press_button(n):
	

Solutions:
def press_button(n):
  return (n*n+5)*n/6

def press_button(n):
  return sum((n-i)*(i+1)-i for i in range(n))

press_button=lambda n:sum(i*(n-i) for i in range(1,n))+n

def press_button(n):
    return n + sum(i * (n-i) for i in range(1, n))

def press_button(n):
    return n*(n**2 + 5)/6

def press_button(n):
  return sum(i * (n - i) + 1 for i in range(1, n + 1))


def press_button(n):
    return n*(n*n+5)/6

press_button=lambda n:n*(n*n+5)/6

def press_button(n):
    return n+sum([i*(n-i) for i in range(1,n+1)])