31300번 - Two Rectangles 스페셜 저지다국어

문제

In this problem, you have to find two rectangles with the given total area which have the minimum possible total perimeter.

Recall that the area of a rectangle having sides of length $m$ and $n$ is $m \cdot n,ドル and its perimeter is 2ドル \cdot (m + n)$.

Given an integer $s \ge 2,ドル consider two rectangles with positive integer lengths of sides such that the sum of their areas is $s$. What is the minimum possible sum of their perimeters?

Formally, choose four positive side lengths $a,ドル $b,ドル $c$ and $d$ so that the total area $a \cdot b + c \cdot d$ equals $s$ and the total perimeter 2ドル \cdot (a + b) + 2 \cdot (c + d)$ is minimum possible.

입력

The first line of input contains one integer $s$ (2ドル \le s \le 10^{18}$).

출력

On the first line, print one number: the minimum possible total perimeter. On the second line, print $a$ and $b,ドル the side lengths of the first rectangle, separated by a space. On the third line, print $c$ and $d,ドル the side lengths of the second rectangle, also separated by a space. If there is more than one possible answer, print any one of them.

제한

힌트

In the first example, the only optimal answer is to choose squares of sizes 1ドル \times 1$ and 2ドル \times 2$. They can be printed in any order.

In the second example, there is another optimal answer: instead of rectangles 1ドル \times 2$ and 2ドル \times 3,ドル we can choose two squares of size 2ドル \times 2$ each.