P8154 "PMOI-5" Chessboard

Given an infinite chessboard (which can be viewed as a 2D Cartesian coordinate system) and $n$ white pieces and $n$ black pieces, you need to place them on integer lattice points of the board without overlap, such that there exist **exactly** $n$ straight lines satisfying: - Each line passes through and **only** passes through a total of 4 pieces (black and white together). - Along the line in order, it passes through black, white, white, black pieces. Output any valid construction.

The input contains only one line: $n$ as described in the statement.

If it is impossible to construct a solution, output `NO`. Otherwise output $2n+1$ lines: the first line outputs `YES`. Lines $2\sim n+1$ each contain two integers, the coordinates $x_i,y_i$ of a white piece. Lines $n+2\sim 2n+1$ each contain two integers, the coordinates $x_j,y_j$ of a black piece. You must ensure that $-5\times 10^5\le x_i,y_i,x_j,y_j\le 5\times 10^5$.

[Sample Explanation] Explanation for Sample 2: (The output lists points $A\sim N$ in order (points $A\sim G$ are white pieces, points $H\sim N$ are black pieces), and the lines are shown in the figure).  [Constraints] **This problem uses bundled testdata.** - Subtask 1 (10 pts): $n\equiv 0 \pmod{7}$. - Subtask 2 (20 pts): $40\le n\le 400$. - Subtask 3 (30 pts): $1\le n\le 9$. - Subtask 4 (40 pts): no special restrictions. For $100\%$ of the testdata, $1\le n\le 10^3$. [SPJ link](https://www.luogu.com.cn/paste/eamtmrw5) Usage: after compiling to `checker.exe`, in the same directory run on the command line: ```checker.exe chessboard.in chessboard.out chessboard.ans``` You also need to use it together with `testlib.h`. [testlib download link](https://github.com/MikeMirzayanov/testlib). If you find the SPJ is broken, please contact the problem setter. Translated by ChatGPT 5