{"problem":{"name":"Skolem XOR Tree","description":{"content":"You are given an integer $N$. Determine if there exists a tree with $2N$ vertices numbered $1$ to $2N$ satisfying the following condition, and show one such tree if the answer is yes. *   Assume that","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"agc035_c"},"statements":[{"statement_type":"Markdown","content":"You are given an integer $N$. Determine if there exists a tree with $2N$ vertices numbered $1$ to $2N$ satisfying the following condition, and show one such tree if the answer is yes.\n\n*   Assume that, for each integer $i$ between $1$ and $N$ (inclusive), Vertex $i$ and $N+i$ have the weight $i$. Then, for each integer $i$ between $1$ and $N$, the bitwise XOR of the weights of the vertices on the path between Vertex $i$ and $N+i$ (including themselves) is $i$.\n\n## Constraints\n\n*   $N$ is an integer.\n*   $1 \\leq N \\leq 10^{5}$\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":"agc035_c","tags":[],"sample_group":[["3","Yes\n1 2\n2 3\n3 4\n4 5\n5 6\n\n*   The sample output represents the following graph:\n    \n    ![image](https://img.atcoder.jp/agc035/d004b05438497d50637b534e89f7a511.png)"],["1","No\n\n*   There is no tree satisfying the condition."]],"created_at":"2026-03-03 11:01:14"}}