P6741 [BalticOI 2014] Demarcation (Day2)

Given a polygon, find a line segment that divides this polygon into two congruent polygons. You must ensure that this line segment is parallel to the coordinate axes.

The first line contains an integer $N$, meaning that the polygon consists of $N$ points. The next $N$ lines each contain two integers $X_i, Y_i$, representing a vertex of the polygon $(X_i, Y_i)$.

If it is impossible to divide it into two congruent polygons, output the string `NO`. If it is possible, output four integers $x_1, y_1, x_2, y_2$, representing the segment $(x_1, y_1)\to (x_2, y_2)$.

#### Sample Explanation For sample $1$, as shown in the figure below, it can be divided into two congruent polygons:  Similarly, outputting `3 2 1 2` is also acceptable. For sample $2$, as shown in the figure below, it cannot be divided into two congruent polygons:  #### Constraints and Notes **This problem uses bundled testdata.** - Subtask 1 (12 pts): A solution is guaranteed to exist. - Subtask 2 (15 pts): $N \le 200$. - Subtask 3 (23 pts): $N \le 2000$. - Subtask 4 (50 pts): No special restrictions. For $100\%$ of the testdata, $4 \le N \le 10^5$. **This problem uses Special Judge.** #### Note Translated from [BalticOI 2014 Day2 A Demarcation](https://boi.cses.fi/files/boi2014_day2.pdf)。 Translated by ChatGPT 5