{"problem":{"name":"1D Matching","description":{"content":"#nck { width: 30px; height: auto; }There are $N$ computers and $N$ sockets in a one-dimensional world. The coordinate of the $i$\\-th computer is $a_i$, and the coordinate of the $i$\\-th socket is $b_i","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"cf16_exhibition_final_a"},"statements":[{"statement_type":"Markdown","content":"#nck { width: 30px; height: auto; }There are $N$ computers and $N$ sockets in a one-dimensional world. The coordinate of the $i$\\-th computer is $a_i$, and the coordinate of the $i$\\-th socket is $b_i$. It is guaranteed that these $2N$ coordinates are pairwise distinct.\nSnuke wants to connect each computer to a socket using a cable. Each socket can be connected to only one computer.\nIn how many ways can he minimize the total length of the cables? Compute the answer modulo $10^9+7$.\n\n## Constraints\n\n*   $1 ≤ N ≤ 10^5$\n*   $0 ≤ a_i, b_i ≤ 10^9$\n*   The coordinates are integers.\n*   The coordinates are pairwise distinct.\n\n## Input\n\nThe input is given from Standard Input in the following format:\n\n$N$\n$a_1$\n:\n$a_N$\n$b_1$\n:\n$b_N$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"cf16_exhibition_final_a","tags":[],"sample_group":[["2\n0\n10\n20\n30","2\n\nThere are two optimal connections: $0-20, 10-30$ and $0-30, 10-20$. In both connections the total length of the cables is $40$."],["3\n3\n10\n8\n7\n12\n5","1"]],"created_at":"2026-03-03 11:01:14"}}