{"problem":{"name":"Squared Graph","description":{"content":"Takahashi has received an undirected graph with $N$ vertices, numbered $1$, $2$, ..., $N$. The edges in this graph are represented by $(u_i, v_i)$. There are no self-loops and multiple edges in this g","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"agc011_c"},"statements":[{"statement_type":"Markdown","content":"Takahashi has received an undirected graph with $N$ vertices, numbered $1$, $2$, ..., $N$. The edges in this graph are represented by $(u_i, v_i)$. There are no self-loops and multiple edges in this graph.\nBased on this graph, Takahashi is now constructing a new graph with $N^2$ vertices, where each vertex is labeled with a pair of integers $(a, b)$ ($1 \\leq a \\leq N$, $1 \\leq b \\leq N$). The edges in this new graph are generated by the following rule:\n\n*   Span an edge between vertices $(a, b)$ and $(a', b')$ if and only if both of the following two edges exist in the original graph: an edge between vertices $a$ and $a'$, and an edge between vertices $b$ and $b'$.\n\nHow many connected components are there in this new graph?\n\n## Constraints\n\n*   $2 \\leq N \\leq 100,000$\n*   $0 \\leq M \\leq 200,000$\n*   $1 \\leq u_i < v_i \\leq N$\n*   There exists no pair of distinct integers $i$ and $j$ such that $u_i = u_j$ and $v_i = v_j$.\n\n## Input\n\nThe input is given from Standard Input in the following format:\n\n$N$ $M$\n$u_1$ $v_1$\n$u_2$ $v_2$\n:\n$u_M$ $v_M$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"agc011_c","tags":[],"sample_group":[["3 1\n1 2","7\n\nThe graph constructed by Takahashi is as follows.\n![image](https://atcoder.jp/img/agc011/6d34a4ddeba67b2286c00acda56abbcc.png)"],["7 5\n1 2\n3 4\n3 5\n4 5\n2 6","18"]],"created_at":"2026-03-03 11:01:13"}}