{"raw_statement":[{"iden":"problem statement","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 $|a - b|$."},{"iden":"notes","content":"For 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 $X_k < Y_k$."},{"iden":"constraints","content":"*   $2 \\leq N \\leq 8$\n*   $P$ and $Q$ are permutations of size $N$."},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$\n$P_1$ $P_2$ $...$ $P_N$\n$Q_1$ $Q_2$ $...$ $Q_N$"},{"iden":"sample input 1","content":"3\n1 3 2\n3 1 2"},{"iden":"sample output 1","content":"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 $|2 - 5| = 3$."},{"iden":"sample input 2","content":"8\n7 3 5 4 2 1 6 8\n3 8 2 5 4 6 7 1"},{"iden":"sample output 2","content":"17517"},{"iden":"sample input 3","content":"3\n1 2 3\n1 2 3"},{"iden":"sample output 3","content":"0"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}