Consider integer coordinates x, y in the Cartesian plan and three functions f, g, h
defined by:
```
f: 1 <= x <= n, 1 <= y <= n --> f(x, y) = min(x, y)
g: 1 <= x <= n, 1 <= y <= n --> g(x, y) = max(x, y)
h: 1 <= x <= n, 1 <= y <= n --> h(x, y) = x + y
``` 
where n is a given integer (n >= 1, guaranteed) and x, y are integers.
In the table below you can see the value of the function f with n = 6.
  ---|*0* |*1*|*2*|*3*|*4*|*5*|*6*|
  -- |--|--|--|--|--|--|--|
  *6*|- |1 |2 |3 |4 |5 |6 |
  *5*|- |1 |2 |3 |4 |5 |5 |
  *4*|- |1 |2 |3 |4 |4 |4 |
  *3*|- |1 |2 |3 |3 |3 |3 |
  *2*|- |1 |2 |2 |2 |2 |2 |
  *1*|- |1 |1 |1 |1 |1 |1 |
  *0*|- |- |- |- |- |- |- |
The task is to calculate the sum of f(x, y), g(x, y) and h(x, y) for all integers x and y such that (1 <= x <= n, 1 <= y <= n).
The function sumin (sum of f) will take n as a parameter and return the sum of min(x, y) in the domain 1 <= x <= n, 1 <= y <= n.
The function sumax (sum of g) will take n as a parameter and return the sum of max(x, y) in the same domain.
The function sumsum (sum of h) will take n as a parameter and return the sum of x + y in the same domain.
#Examples:
```
sumin(6) --> 91
sumin(45) --> 31395
sumin(999) --> 332833500
sumin(5000) --> 41679167500
sumax(6) --> 161
sumax(45) --> 61755
sumax(999) --> 665167500
sumax(5000) --> 83345832500
sumsum(6) --> 252
sumsum(45) --> 93150
sumsum(999) --> 998001000
sumsum(5000) --> 125025000000
```
#Hint:
1. Try to avoid nested loops
2. Note that h = f + g
# https://en.wikipedia.org/wiki/Square_pyramidal_number
def sumin(n):
    return n * (n + 1) * (2 * n + 1) / 6
def sumax(n):
    return n * (n + 1) * (4 * n - 1) / 6
def sumsum(n):
    return sumin(n) + sumax(n)
# https://en.wikipedia.org/wiki/Square_pyramidal_number
def sumin(n):
    return n * (n + 1) * (2 * n + 1) / 6
def sumax(n):
    return n * (n + 1) * (4 * n - 1) / 6
def sumsum(n):
    return sumin(n) + sumax(n)