{"raw_statement":[{"iden":"problem statement","content":"We have a grid with $2$ rows and $N$ columns. Let $(i,j)$ denote the square at the $i$\\-th row from the top and $j$\\-th column from the left. $(i,j)$ has a postive integer $x_{i,j}$ written on it.\nTwo squares are said to be **adjacent** when they share a side.\nA **path** from square $X$ to $Y$ is a sequence $(P_1, \\ldots, P_n)$ of distinct squares such that $P_1 = X$, $P_n = Y$, and $P_i$ and $P_{i+1}$ are adjacent for every $1\\leq i \\leq n-1$. Additionally, the **weight** of that path is the sum of integers written on $P_1, \\ldots, P_n$.\nFor two squares $X$ and $Y$, let $f(X, Y)$ denote the minimum weight of a path from $X$ to $Y$. Find the sum of $f(X, Y)$ over all pairs of squares $(X,Y)$, modulo $998244353$."},{"iden":"constraints","content":"*   $1\\leq N\\leq 2\\times 10^5$\n*   $1\\leq x_{i,j} \\leq 10^9$"},{"iden":"input","content":"The input is given from Standard Input in the following format:\n\n$N$\n$x_{1,1}$ $\\ldots$ $x_{1,N}$\n$x_{2,1}$ $\\ldots$ $x_{2,N}$"},{"iden":"sample input 1","content":"1\n3\n5"},{"iden":"sample output 1","content":"24\n\nYou should find the sum of the following four values.\n\n*   For $X = (1,1), Y = (1,1)$: $f(X, Y) = 3$.\n*   For $X = (1,1), Y = (2,1)$: $f(X, Y) = 8$.\n*   For $X = (2,1), Y = (1,1)$: $f(X, Y) = 8$.\n*   For $X = (2,1), Y = (2,1)$: $f(X, Y) = 5$."},{"iden":"sample input 2","content":"2\n1 2\n3 4"},{"iden":"sample output 2","content":"76"},{"iden":"sample input 3","content":"5\n1 1000000000 1 1 1\n1 1 1 1000000000 1"},{"iden":"sample output 3","content":"66714886"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}