{"problem":{"name":"Count Order","description":{"content":"We have two permutations $P$ and $Q$ of size $N$ (that is, $P$ and $Q$ are both rearrangements of $(1,~2,~...,~N)$). There are $N!$ possible permutations of size $N$. Among them, let $P$ and $Q$ be th","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"abc150_c"},"statements":[{"statement_type":"Markdown","content":"We have two permutations $P$ and $Q$ of size $N$ (that is, $P$ and $Q$ are both rearrangements of $(1,~2,~...,~N)$).\nThere are $N!$ possible permutations of size $N$. Among them, let $P$ and $Q$ be the $a$\\-th and $b$\\-th lexicographically smallest permutations, respectively. Find $|a - b|$.\n\n## Constraints\n\n*   $2 \\leq N \\leq 8$\n*   $P$ and $Q$ are permutations of size $N$.\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$\n$P_1$ $P_2$ $...$ $P_N$\n$Q_1$ $Q_2$ $...$ $Q_N$\n\n[samples]\n\n## Notes\n\nFor two sequences $X$ and $Y$, $X$ is said to be lexicographically smaller than $Y$ if and only if there exists an integer $k$ such that $X_i = Y_i~(1 \\leq i < k)$ and $X_k < Y_k$.","is_translate":false,"language":"English"}],"meta":{"iden":"abc150_c","tags":[],"sample_group":[["3\n1 3 2\n3 1 2","3\n\nThere are $6$ permutations of size $3$: $(1,~2,~3)$, $(1,~3,~2)$, $(2,~1,~3)$, $(2,~3,~1)$, $(3,~1,~2)$, and $(3,~2,~1)$. Among them, $(1,~3,~2)$ and $(3,~1,~2)$ come $2$\\-nd and $5$\\-th in lexicographical order, so the answer is $|2 - 5| = 3$."],["8\n7 3 5 4 2 1 6 8\n3 8 2 5 4 6 7 1","17517"],["3\n1 2 3\n1 2 3","0"]],"created_at":"2026-03-03 11:01:14"}}