P6711 [BalticOI 2005] Polygon (Day2)

Given the length of each edge of a convex hull, construct this convex hull.

The first line contains an integer $N$, representing the number of points. The next $N$ lines each contain an integer $a_i$, representing the length of one edge. Here, $a_i\ (i

Output $N$ lines. Each line contains two real numbers $x_i, y_i$, representing the coordinates of a point. (They must satisfy $|x_i|, |y_i| \le 10^7$.) If there are multiple solutions, output any one of them. If there is no solution, output `NO SOLUTION`. #### Requirements for judging on Luogu **Note: please output the points on the convex hull in counterclockwise order.** Although the original statement allows either clockwise or counterclockwise order, in this problem you **must output strictly in counterclockwise order**. You do not have to output in the original numbering order. For example, if $P_1 \to P_2 \to P_3$ is counterclockwise, then $P_2 \to P_3 \to P_1$ is also acceptable.

#### Sample Explanation For sample $1$:  #### Constraints For $100\%$ of the testdata, $3 \le N \le 1000$, $1 \le a_i \le 10^4$. **This problem uses Special Judge.** Thanks to the spj author @[tiger2005](https://www.luogu.com.cn/user/60864). #### Notes Translated from [BalticOI 2005 Day2 C Polygon](https://boi.cses.fi/files/boi2005_day2.pdf). Translated by ChatGPT 5