{"problem":{"name":"Christmas Wreath","description":{"content":"Takahashi has Christmas decoration consisting of $N$ balls and $\\frac{N(N-1)}{2}$ ropes. The balls are numbered $1$ to $N$, and for any two different balls, there is exactly one rope that connects the","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":3000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"arc131_e"},"statements":[{"statement_type":"Markdown","content":"Takahashi has Christmas decoration consisting of $N$ balls and $\\frac{N(N-1)}{2}$ ropes. The balls are numbered $1$ to $N$, and for any two different balls, there is exactly one rope that connects them.\n![image](https://img.atcoder.jp/arc131/f18d2d54777d013bec4a137f048d4609.png)\nHe decides to light up each rope in red, blue, or white.\nFor better appearance, he wants to satisfy all of the following conditions.\n\n> **Condition 1** the numbers of ropes lighted in red, blue, and white are all equal.\n> **Condition 2** there is no triple of integers $a, b, c$ $(1 \\leq a < b < c \\leq N)$ such that all of the following three ropes have different colors:\n> \n> *   the rope connecting $a$ and $b$,\n> *   the rope connecting $b$ and $c$,\n> *   the rope connecting $a$ and $c$.\n\nCreate a way to light up the ropes to satisfy the conditions. If there is no such way, report so.\n\n## Constraints\n\n*   $3 \\leq N \\leq 50$\n*   $N$ is an integer.\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"arc131_e","tags":[],"sample_group":[["4","No\n\nFor $N=4$, there is no way to light up the ropes to satisfy the conditions, so the output `No` is correct.\nBelow is an example of an output in the `Yes` case, **which is incorrect in this case.** This is because, for $(a, b, c) = (1, 2, 3)$ in **Condition 2**, the rope connecting $a, b$ is red, the rope connecting $b, c$ is white, and the rope connecting $a, c$ is blue, all of which have different colors.\n\nYes\nRBW\nWB\nR"]],"created_at":"2026-03-03 11:01:13"}}