{"problem":{"name":"Close Group","description":{"content":"Given is a simple undirected graph with $N$ vertices and $M$ edges. The vertices are numbered $1, 2, \\dots, N$, and the $i$\\-th edge connects Vertices $A_i$ and $B_i$. Find the minimum possible number","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":3000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"abc187_f"},"statements":[{"statement_type":"Markdown","content":"Given is a simple undirected graph with $N$ vertices and $M$ edges. The vertices are numbered $1, 2, \\dots, N$, and the $i$\\-th edge connects Vertices $A_i$ and $B_i$.\nFind the minimum possible number of connected components in the graph after removing zero or more edges so that the following condition will be satisfied:\n**Condition:**  \nFor every pair of vertices $(a, b)$ such that $1 \\le a < b \\le N$, if Vertices $a$ and $b$ belong to the same connected component, there is an edge that directly connects Vertices $a$ and $b$.\n\n## Constraints\n\n*   All values in input are integers.\n*   $1 \\le N \\le 18$\n*   $0 \\le M \\le \\frac{N(N - 1)}{2}$\n*   $1 \\le A_i < B_i \\le N$\n*   $(A_i, B_i) \\neq (A_j, B_j)$ for $i \\neq j$.\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$ $M$\n$A_1$ $B_1$\n$\\vdots$\n$A_M$ $B_M$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"abc187_f","tags":[],"sample_group":[["3 2\n1 2\n1 3","2\n\nWithout removing edges, the pair $(2, 3)$ violates the condition. Removing one of the edges disconnects Vertices $2$ and $3$, satisfying the condition."],["4 6\n1 2\n1 3\n1 4\n2 3\n2 4\n3 4","1"],["10 11\n9 10\n2 10\n8 9\n3 4\n5 8\n1 8\n5 6\n2 5\n3 6\n6 9\n1 9","5"],["18 0","18"]],"created_at":"2026-03-03 11:01:14"}}