{"problem":{"name":"Min Cost Cycle","description":{"content":"We have a directed weighted graph with $N$ vertices. Each vertex has two integers written on it, and the integers written on Vertex $i$ are $A_i$ and $B_i$. In this graph, there is an edge from Vertex","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"agc028_c"},"statements":[{"statement_type":"Markdown","content":"We have a directed weighted graph with $N$ vertices. Each vertex has two integers written on it, and the integers written on Vertex $i$ are $A_i$ and $B_i$.\nIn this graph, there is an edge from Vertex $x$ to Vertex $y$ for all pairs $1 \\leq x,y \\leq N$, and its weight is ${\\rm min}(A_x,B_y)$.\nWe will consider a directed cycle in this graph that visits every vertex exactly once. Find the minimum total weight of the edges in such a cycle.\n\n## Constraints\n\n*   $2 \\leq N \\leq 10^5$\n*   $1 \\leq A_i \\leq 10^9$\n*   $1 \\leq B_i \\leq 10^9$\n*   All values in input are integers.\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$\n$A_1$ $B_1$\n$A_2$ $B_2$\n$:$\n$A_N$ $B_N$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"agc028_c","tags":[],"sample_group":[["3\n1 5\n4 2\n6 3","7\n\nConsider the cycle $1→3→2→1$. The weights of those edges are ${\\rm min}(A_1,B_3)=1$, ${\\rm min}(A_3,B_2)=2$ and ${\\rm min}(A_2,B_1)=4$, for a total of $7$. As there is no cycle with a total weight of less than $7$, the answer is $7$."],["4\n1 5\n2 6\n3 7\n4 8","10"],["6\n19 92\n64 64\n78 48\n57 33\n73 6\n95 73","227"]],"created_at":"2026-03-03 11:01:13"}}