{"raw_statement":[{"iden":"problem statement","content":"There are $N$ cards numbered $1,\\ldots,N$. Card $i$ has $P_i$ written on the front and $Q_i$ written on the back.  \nHere, $P=(P_1,\\ldots,P_N)$ and $Q=(Q_1,\\ldots,Q_N)$ are permutations of $(1, 2, \\dots, N)$.\nHow many ways are there to choose some of the $N$ cards such that the following condition is satisfied? Find the count modulo $998244353$.\nCondition: every number $1,2,\\ldots,N$ is written on at least one of the chosen cards."},{"iden":"constraints","content":"*   $1 \\leq N \\leq 2\\times 10^5$\n*   $1 \\leq P_i,Q_i \\leq N$\n*   $P$ and $Q$ are permutations of $(1, 2, \\dots, N)$.\n*   All values in input are integers."},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$\n$P_1$ $P_2$ $\\ldots$ $P_N$\n$Q_1$ $Q_2$ $\\ldots$ $Q_N$"},{"iden":"sample input 1","content":"3\n1 2 3\n2 1 3"},{"iden":"sample output 1","content":"3\n\nFor example, if you choose Cards $1$ and $3$, then $1$ is written on the front of Card $1$, $2$ on the back of Card $1$, and $3$ on the front of Card $3$, so this combination satisfies the condition.\nThere are $3$ ways to choose cards satisfying the condition: ${1,3},{2,3},{1,2,3}$."},{"iden":"sample input 2","content":"5\n2 3 5 4 1\n4 2 1 3 5"},{"iden":"sample output 2","content":"12"},{"iden":"sample input 3","content":"8\n1 2 3 4 5 6 7 8\n1 2 3 4 5 6 7 8"},{"iden":"sample output 3","content":"1"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}