Bun Lover (Codeforces 1822C)
Tags: Math, math

Tema loves cinnabon rolls — buns with cinnabon and chocolate in the shape of a "snail".Cinnabon rolls come in different sizes and are square when viewed from above. The most delicious part of a roll is the chocolate, which is poured in a thin layer over the cinnabon roll in the form of a spiral and around the bun, as in the following picture:  Cinnabon rolls of sizes 4, 5, 6 For a cinnabon roll of size $$$n$$$, the length of the outer side of the square is $$$n$$$, and the length of the shortest vertical chocolate segment in the central part is one.Formally, the bun consists of two dough spirals separated by chocolate. A cinnabon roll of size $$$n + 1$$$ is obtained from a cinnabon roll of size $$$n$$$ by wrapping each of the dough spirals around the cinnabon roll for another layer.It is important that a cinnabon roll of size $$$n$$$ is defined in a unique way.Tema is interested in how much chocolate is in his cinnabon roll of size $$$n$$$. Since Tema has long stopped buying small cinnabon rolls, it is guaranteed that $$$n \ge 4$$$.Answer this non-obvious question by calculating the total length of the chocolate layer.

Input: The first line of the input contains a single integer $$$t$$$ ($$$1 \le t \le 10^5$$$) — the number of test cases.The following $$$t$$$ lines describe the test cases.Each test case is described by a single integer $$$n$$$ ($$$4 \le n \le 10^9$$$) — the size of the cinnabon roll.

Output: Output $$$t$$$ integers. The $$$i$$$-th of them should be equal to the total length of the chocolate layer in the $$$i$$$-th test case.


Sample Inputs:
4
4
5
6
179179179

Sample Outputs:
26
37
50
32105178545472401

Solution (Python):
def i():
    n = int(input())
    return str(n * n + 2 * n + 2)
t = int(input())
a = []
for _ in range(t):
    a.append(i())
print('\n'.join(a))

Solution (Python):
for n in [*open(0)][1:]:
    print((int(n) + 1) ** 2 + 1)

Solution (Python):
for D in [*open(0)][1:]:
    print((int(D) + 1) ** 2 + 1)